id sid tid token lemma pos american_scientific_journal-3571 1 1 17 17 NUM american_scientific_journal-3571 1 2 american american ADJ american_scientific_journal-3571 1 3 scientific scientific ADJ american_scientific_journal-3571 1 4 research research NOUN american_scientific_journal-3571 1 5 journal journal NOUN american_scientific_journal-3571 1 6 for for ADP american_scientific_journal-3571 1 7 engineering engineering NOUN american_scientific_journal-3571 1 8 , , PUNCT american_scientific_journal-3571 1 9 technology technology NOUN american_scientific_journal-3571 1 10 , , PUNCT american_scientific_journal-3571 1 11 and and CCONJ american_scientific_journal-3571 1 12 sciences science NOUN american_scientific_journal-3571 1 13 ( ( PUNCT american_scientific_journal-3571 1 14 asrjets asrjet NOUN american_scientific_journal-3571 1 15 ) ) PUNCT american_scientific_journal-3571 1 16 issn issn PROPN american_scientific_journal-3571 1 17 ( ( PUNCT american_scientific_journal-3571 1 18 print print NOUN american_scientific_journal-3571 1 19 ) ) PUNCT american_scientific_journal-3571 1 20 2313 2313 NUM american_scientific_journal-3571 1 21 - - SYM american_scientific_journal-3571 1 22 4410 4410 NUM american_scientific_journal-3571 1 23 , , PUNCT american_scientific_journal-3571 1 24 issn issn PROPN american_scientific_journal-3571 1 25 ( ( PUNCT american_scientific_journal-3571 1 26 online online ADJ american_scientific_journal-3571 1 27 ) ) PUNCT american_scientific_journal-3571 1 28 2313 2313 NUM american_scientific_journal-3571 1 29 - - SYM american_scientific_journal-3571 1 30 4402 4402 NUM american_scientific_journal-3571 1 31 Β© Β© PROPN american_scientific_journal-3571 1 32 global global ADJ american_scientific_journal-3571 1 33 society society NOUN american_scientific_journal-3571 1 34 of of ADP american_scientific_journal-3571 1 35 scientific scientific ADJ american_scientific_journal-3571 1 36 research research NOUN american_scientific_journal-3571 1 37 and and CCONJ american_scientific_journal-3571 1 38 researchers researcher NOUN american_scientific_journal-3571 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ ADJ american_scientific_journal-3571 1 40 comparative comparative ADJ american_scientific_journal-3571 1 41 study study NOUN american_scientific_journal-3571 1 42 between between ADP american_scientific_journal-3571 1 43 classical classical ADJ american_scientific_journal-3571 1 44 and and CCONJ american_scientific_journal-3571 1 45 optimized optimize VERB american_scientific_journal-3571 1 46 stability stability NOUN american_scientific_journal-3571 1 47 margins margin NOUN american_scientific_journal-3571 1 48 of of ADP american_scientific_journal-3571 1 49 quadruped quadruped NOUN american_scientific_journal-3571 1 50 robot robot NOUN american_scientific_journal-3571 1 51 creeping creep VERB american_scientific_journal-3571 1 52 gait gait PROPN american_scientific_journal-3571 1 53 firas firas PROPN american_scientific_journal-3571 1 54 a. a. PROPN american_scientific_journal-3571 1 55 raheema raheema PROPN american_scientific_journal-3571 1 56 * * NOUN american_scientific_journal-3571 1 57 , , PUNCT american_scientific_journal-3571 1 58 murtadha murtadha PROPN american_scientific_journal-3571 1 59 khudhair khudhair PROPN american_scientific_journal-3571 1 60 flayyihb flayyihb NOUN american_scientific_journal-3571 1 61 a a PRON american_scientific_journal-3571 1 62 , , PUNCT american_scientific_journal-3571 1 63 buniversity buniversity NOUN american_scientific_journal-3571 1 64 of of ADP american_scientific_journal-3571 1 65 technology technology NOUN american_scientific_journal-3571 1 66 , , PUNCT american_scientific_journal-3571 1 67 control control NOUN american_scientific_journal-3571 1 68 and and CCONJ american_scientific_journal-3571 1 69 systems system NOUN american_scientific_journal-3571 1 70 engineering engineering NOUN american_scientific_journal-3571 1 71 department department NOUN american_scientific_journal-3571 1 72 aemail aemail NOUN american_scientific_journal-3571 1 73 : : PUNCT american_scientific_journal-3571 1 74 60124@uotechnology.edu.iq 60124@uotechnology.edu.iq NUM american_scientific_journal-3571 1 75 bemail bemail NOUN american_scientific_journal-3571 1 76 : : PUNCT american_scientific_journal-3571 1 77 cse.60354@uotechnology.edu.iq cse.60354@uotechnology.edu.iq PUNCT american_scientific_journal-3571 1 78 abstract abstract VERB american_scientific_journal-3571 1 79 the the DET american_scientific_journal-3571 1 80 ability ability NOUN american_scientific_journal-3571 1 81 of of ADP american_scientific_journal-3571 1 82 the the DET american_scientific_journal-3571 1 83 quadruped quadruped NOUN american_scientific_journal-3571 1 84 ( ( PUNCT american_scientific_journal-3571 1 85 four four NUM american_scientific_journal-3571 1 86 - - PUNCT american_scientific_journal-3571 1 87 legged legged ADJ american_scientific_journal-3571 1 88 ) ) PUNCT american_scientific_journal-3571 1 89 robot robot NOUN american_scientific_journal-3571 1 90 locomotion locomotion NOUN american_scientific_journal-3571 1 91 was be AUX american_scientific_journal-3571 1 92 used use VERB american_scientific_journal-3571 1 93 in in ADP american_scientific_journal-3571 1 94 a a DET american_scientific_journal-3571 1 95 lot lot NOUN american_scientific_journal-3571 1 96 of of ADP american_scientific_journal-3571 1 97 different different ADJ american_scientific_journal-3571 1 98 applications application NOUN american_scientific_journal-3571 1 99 like like ADP american_scientific_journal-3571 1 100 walking walk VERB american_scientific_journal-3571 1 101 over over ADP american_scientific_journal-3571 1 102 soft soft ADJ american_scientific_journal-3571 1 103 and and CCONJ american_scientific_journal-3571 1 104 rough rough ADJ american_scientific_journal-3571 1 105 terrains terrain NOUN american_scientific_journal-3571 1 106 . . PUNCT american_scientific_journal-3571 2 1 these these DET american_scientific_journal-3571 2 2 applications application NOUN american_scientific_journal-3571 2 3 needed need VERB american_scientific_journal-3571 2 4 to to PART american_scientific_journal-3571 2 5 guarantee guarantee VERB american_scientific_journal-3571 2 6 the the DET american_scientific_journal-3571 2 7 flexibility flexibility NOUN american_scientific_journal-3571 2 8 and and CCONJ american_scientific_journal-3571 2 9 mobility mobility NOUN american_scientific_journal-3571 2 10 . . PUNCT american_scientific_journal-3571 3 1 generally generally ADV american_scientific_journal-3571 3 2 , , PUNCT american_scientific_journal-3571 3 3 quadruped quadrupe VERB american_scientific_journal-3571 3 4 robots robot NOUN american_scientific_journal-3571 3 5 have have VERB american_scientific_journal-3571 3 6 three three NUM american_scientific_journal-3571 3 7 basic basic ADJ american_scientific_journal-3571 3 8 periodic periodic ADJ american_scientific_journal-3571 3 9 gaits gait NOUN american_scientific_journal-3571 3 10 : : PUNCT american_scientific_journal-3571 3 11 creeping creep VERB american_scientific_journal-3571 3 12 gait gait NOUN american_scientific_journal-3571 3 13 , , PUNCT american_scientific_journal-3571 3 14 running run VERB american_scientific_journal-3571 3 15 gait gait NOUN american_scientific_journal-3571 3 16 and and CCONJ american_scientific_journal-3571 3 17 galloping gallop VERB american_scientific_journal-3571 3 18 gait gait NOUN american_scientific_journal-3571 3 19 . . PUNCT american_scientific_journal-3571 4 1 the the DET american_scientific_journal-3571 4 2 stability stability NOUN american_scientific_journal-3571 4 3 criteria criterion NOUN american_scientific_journal-3571 4 4 are be AUX american_scientific_journal-3571 4 5 the the DET american_scientific_journal-3571 4 6 main main ADJ american_scientific_journal-3571 4 7 issue issue NOUN american_scientific_journal-3571 4 8 of of ADP american_scientific_journal-3571 4 9 the the DET american_scientific_journal-3571 4 10 quadruped quadruped NOUN american_scientific_journal-3571 4 11 robot robot NOUN american_scientific_journal-3571 4 12 throughout throughout ADP american_scientific_journal-3571 4 13 walking walk VERB american_scientific_journal-3571 4 14 with with ADP american_scientific_journal-3571 4 15 the the DET american_scientific_journal-3571 4 16 slow slow ADJ american_scientific_journal-3571 4 17 motion motion NOUN american_scientific_journal-3571 4 18 gait gait ADJ american_scientific_journal-3571 4 19 like like ADP american_scientific_journal-3571 4 20 creeping creep VERB american_scientific_journal-3571 4 21 gait gait NOUN american_scientific_journal-3571 4 22 . . PUNCT american_scientific_journal-3571 5 1 the the DET american_scientific_journal-3571 5 2 gait gait NOUN american_scientific_journal-3571 5 3 of of ADP american_scientific_journal-3571 5 4 static static ADJ american_scientific_journal-3571 5 5 stability stability NOUN american_scientific_journal-3571 5 6 is be AUX american_scientific_journal-3571 5 7 completely completely ADV american_scientific_journal-3571 5 8 bases basis NOUN american_scientific_journal-3571 5 9 on on ADP american_scientific_journal-3571 5 10 the the DET american_scientific_journal-3571 5 11 stability stability NOUN american_scientific_journal-3571 5 12 margins margin NOUN american_scientific_journal-3571 5 13 in in ADP american_scientific_journal-3571 5 14 the the DET american_scientific_journal-3571 5 15 walking walking NOUN american_scientific_journal-3571 5 16 that that PRON american_scientific_journal-3571 5 17 was be AUX american_scientific_journal-3571 5 18 calculated calculate VERB american_scientific_journal-3571 5 19 in in ADP american_scientific_journal-3571 5 20 this this DET american_scientific_journal-3571 5 21 paper paper NOUN american_scientific_journal-3571 5 22 . . PUNCT american_scientific_journal-3571 6 1 the the DET american_scientific_journal-3571 6 2 quadruped quadruped NOUN american_scientific_journal-3571 6 3 robot robot NOUN american_scientific_journal-3571 6 4 legs leg NOUN american_scientific_journal-3571 6 5 walking walk VERB american_scientific_journal-3571 6 6 sequence sequence NOUN american_scientific_journal-3571 6 7 and and CCONJ american_scientific_journal-3571 6 8 creeping creep VERB american_scientific_journal-3571 6 9 gait gait NOUN american_scientific_journal-3571 6 10 within within ADP american_scientific_journal-3571 6 11 the the DET american_scientific_journal-3571 6 12 leg leg NOUN american_scientific_journal-3571 6 13 fixing fix VERB american_scientific_journal-3571 6 14 and and CCONJ american_scientific_journal-3571 6 15 swinging swinge VERB american_scientific_journal-3571 6 16 phases phase NOUN american_scientific_journal-3571 6 17 carried carry VERB american_scientific_journal-3571 6 18 out out ADP american_scientific_journal-3571 6 19 . . PUNCT american_scientific_journal-3571 7 1 the the DET american_scientific_journal-3571 7 2 kinematics kinematics NOUN american_scientific_journal-3571 7 3 model model NOUN american_scientific_journal-3571 7 4 of of ADP american_scientific_journal-3571 7 5 quadruped quadruped NOUN american_scientific_journal-3571 7 6 robot robot NOUN american_scientific_journal-3571 7 7 of of ADP american_scientific_journal-3571 7 8 the the DET american_scientific_journal-3571 7 9 forward forward ADJ american_scientific_journal-3571 7 10 and and CCONJ american_scientific_journal-3571 7 11 inverse inverse ADJ american_scientific_journal-3571 7 12 kinematics kinematic NOUN american_scientific_journal-3571 7 13 for for ADP american_scientific_journal-3571 7 14 each each DET american_scientific_journal-3571 7 15 leg leg NOUN american_scientific_journal-3571 7 16 3 3 NOUN american_scientific_journal-3571 7 17 - - PUNCT american_scientific_journal-3571 7 18 dof dof NOUN american_scientific_journal-3571 7 19 was be AUX american_scientific_journal-3571 7 20 calculated calculate VERB american_scientific_journal-3571 7 21 that that SCONJ american_scientific_journal-3571 7 22 lead lead NOUN american_scientific_journal-3571 7 23 to to PART american_scientific_journal-3571 7 24 discover discover VERB american_scientific_journal-3571 7 25 the the DET american_scientific_journal-3571 7 26 minimum minimum ADJ american_scientific_journal-3571 7 27 stability stability NOUN american_scientific_journal-3571 7 28 margins margin NOUN american_scientific_journal-3571 7 29 with with ADP american_scientific_journal-3571 7 30 walking walk VERB american_scientific_journal-3571 7 31 on on ADP american_scientific_journal-3571 7 32 the the DET american_scientific_journal-3571 7 33 vertical vertical ADJ american_scientific_journal-3571 7 34 projection projection NOUN american_scientific_journal-3571 7 35 of of ADP american_scientific_journal-3571 7 36 the the DET american_scientific_journal-3571 7 37 robot robot NOUN american_scientific_journal-3571 7 38 geometrical geometrical ADJ american_scientific_journal-3571 7 39 body body NOUN american_scientific_journal-3571 7 40 . . PUNCT american_scientific_journal-3571 8 1 these these DET american_scientific_journal-3571 8 2 stability stability NOUN american_scientific_journal-3571 8 3 margins margin NOUN american_scientific_journal-3571 8 4 needed need VERB american_scientific_journal-3571 8 5 to to PART american_scientific_journal-3571 8 6 be be AUX american_scientific_journal-3571 8 7 optimized optimize VERB american_scientific_journal-3571 8 8 in in ADP american_scientific_journal-3571 8 9 order order NOUN american_scientific_journal-3571 8 10 to to PART american_scientific_journal-3571 8 11 obtain obtain VERB american_scientific_journal-3571 8 12 the the DET american_scientific_journal-3571 8 13 best good ADJ american_scientific_journal-3571 8 14 stability stability NOUN american_scientific_journal-3571 8 15 margin margin NOUN american_scientific_journal-3571 8 16 throughout throughout ADP american_scientific_journal-3571 8 17 this this DET american_scientific_journal-3571 8 18 robot robot NOUN american_scientific_journal-3571 8 19 walking walk VERB american_scientific_journal-3571 8 20 . . PUNCT american_scientific_journal-3571 9 1 in in ADP american_scientific_journal-3571 9 2 this this DET american_scientific_journal-3571 9 3 paper paper NOUN american_scientific_journal-3571 9 4 we we PRON american_scientific_journal-3571 9 5 use use VERB american_scientific_journal-3571 9 6 the the DET american_scientific_journal-3571 9 7 pso pso NOUN american_scientific_journal-3571 9 8 optimization optimization NOUN american_scientific_journal-3571 9 9 algorithm algorithm NOUN american_scientific_journal-3571 9 10 to to PART american_scientific_journal-3571 9 11 get get VERB american_scientific_journal-3571 9 12 the the DET american_scientific_journal-3571 9 13 best good ADJ american_scientific_journal-3571 9 14 stability stability NOUN american_scientific_journal-3571 9 15 margins margin NOUN american_scientific_journal-3571 9 16 value value NOUN american_scientific_journal-3571 9 17 . . PUNCT american_scientific_journal-3571 10 1 simulation simulation NOUN american_scientific_journal-3571 10 2 and and CCONJ american_scientific_journal-3571 10 3 results result NOUN american_scientific_journal-3571 10 4 are be AUX american_scientific_journal-3571 10 5 verified verify VERB american_scientific_journal-3571 10 6 the the DET american_scientific_journal-3571 10 7 range range NOUN american_scientific_journal-3571 10 8 of of ADP american_scientific_journal-3571 10 9 the the DET american_scientific_journal-3571 10 10 stability stability NOUN american_scientific_journal-3571 10 11 margin margin NOUN american_scientific_journal-3571 10 12 values value NOUN american_scientific_journal-3571 10 13 and and CCONJ american_scientific_journal-3571 10 14 the the DET american_scientific_journal-3571 10 15 optimized optimize VERB american_scientific_journal-3571 10 16 results result NOUN american_scientific_journal-3571 10 17 . . PUNCT american_scientific_journal-3571 11 1 keywords keyword NOUN american_scientific_journal-3571 11 2 : : PUNCT american_scientific_journal-3571 11 3 quadruped quadruped NOUN american_scientific_journal-3571 11 4 robot robot NOUN american_scientific_journal-3571 11 5 simulation simulation NOUN american_scientific_journal-3571 11 6 ; ; PUNCT american_scientific_journal-3571 11 7 stability stability NOUN american_scientific_journal-3571 11 8 margins margin NOUN american_scientific_journal-3571 11 9 ; ; PUNCT american_scientific_journal-3571 11 10 quadruped quadruped NOUN american_scientific_journal-3571 11 11 robot robot NOUN american_scientific_journal-3571 11 12 gait gait PROPN american_scientific_journal-3571 11 13 pso pso PROPN american_scientific_journal-3571 11 14 optimization optimization NOUN american_scientific_journal-3571 11 15 . . PUNCT american_scientific_journal-3571 12 1 1 1 X american_scientific_journal-3571 12 2 . . X american_scientific_journal-3571 12 3 introduction introduction NOUN american_scientific_journal-3571 12 4 in in ADP american_scientific_journal-3571 12 5 recent recent ADJ american_scientific_journal-3571 12 6 years year NOUN american_scientific_journal-3571 12 7 , , PUNCT american_scientific_journal-3571 12 8 utilization utilization NOUN american_scientific_journal-3571 12 9 of of ADP american_scientific_journal-3571 12 10 the the DET american_scientific_journal-3571 12 11 leg leg NOUN american_scientific_journal-3571 12 12 - - PUNCT american_scientific_journal-3571 12 13 based base VERB american_scientific_journal-3571 12 14 walking walking NOUN american_scientific_journal-3571 12 15 systems system NOUN american_scientific_journal-3571 12 16 has have AUX american_scientific_journal-3571 12 17 been be AUX american_scientific_journal-3571 12 18 transformed transform VERB american_scientific_journal-3571 12 19 into into ADP american_scientific_journal-3571 12 20 a a DET american_scientific_journal-3571 12 21 very very ADV american_scientific_journal-3571 12 22 familiar familiar ADJ american_scientific_journal-3571 12 23 field field NOUN american_scientific_journal-3571 12 24 in in ADP american_scientific_journal-3571 12 25 robotics robotic NOUN american_scientific_journal-3571 12 26 . . PUNCT american_scientific_journal-3571 13 1 these these DET american_scientific_journal-3571 13 2 systems system NOUN american_scientific_journal-3571 13 3 adapted adapt VERB american_scientific_journal-3571 13 4 their their PRON american_scientific_journal-3571 13 5 ability ability NOUN american_scientific_journal-3571 13 6 in in ADP american_scientific_journal-3571 13 7 order order NOUN american_scientific_journal-3571 13 8 to to PART american_scientific_journal-3571 13 9 deal deal VERB american_scientific_journal-3571 13 10 with with ADP american_scientific_journal-3571 13 11 irregular irregular ADJ american_scientific_journal-3571 13 12 territories territory NOUN american_scientific_journal-3571 13 13 especially especially ADV american_scientific_journal-3571 13 14 when when SCONJ american_scientific_journal-3571 13 15 compared compare VERB american_scientific_journal-3571 13 16 with with ADP american_scientific_journal-3571 13 17 wheel wheel NOUN american_scientific_journal-3571 13 18 systems system NOUN american_scientific_journal-3571 13 19 [ [ X american_scientific_journal-3571 13 20 1 1 NUM american_scientific_journal-3571 13 21 ] ] PUNCT american_scientific_journal-3571 13 22 . . PUNCT american_scientific_journal-3571 14 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-3571 15 1 * * PUNCT american_scientific_journal-3571 15 2 corresponding correspond VERB american_scientific_journal-3571 15 3 author author NOUN american_scientific_journal-3571 15 4 . . PUNCT american_scientific_journal-3571 16 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-3571 16 2 american american PROPN american_scientific_journal-3571 16 3 scientific scientific PROPN american_scientific_journal-3571 16 4 research research NOUN american_scientific_journal-3571 16 5 journal journal NOUN american_scientific_journal-3571 16 6 for for ADP american_scientific_journal-3571 16 7 engineering engineering NOUN american_scientific_journal-3571 16 8 , , PUNCT american_scientific_journal-3571 16 9 technology technology NOUN american_scientific_journal-3571 16 10 , , PUNCT american_scientific_journal-3571 16 11 and and CCONJ american_scientific_journal-3571 16 12 sciences science NOUN american_scientific_journal-3571 16 13 ( ( PUNCT american_scientific_journal-3571 16 14 asrjets asrjet NOUN american_scientific_journal-3571 16 15 ) ) PUNCT american_scientific_journal-3571 16 16 ( ( PUNCT american_scientific_journal-3571 16 17 2017 2017 NUM american_scientific_journal-3571 16 18 ) ) PUNCT american_scientific_journal-3571 16 19 volume volume NOUN american_scientific_journal-3571 16 20 38 38 NUM american_scientific_journal-3571 16 21 , , PUNCT american_scientific_journal-3571 16 22 no no DET american_scientific_journal-3571 16 23 1 1 NUM american_scientific_journal-3571 16 24 , , PUNCT american_scientific_journal-3571 16 25 pp pp ADV american_scientific_journal-3571 16 26 17 17 NUM american_scientific_journal-3571 16 27 - - SYM american_scientific_journal-3571 16 28 32 32 NUM american_scientific_journal-3571 16 29 18 18 NUM american_scientific_journal-3571 16 30 this this DET american_scientific_journal-3571 16 31 legged legged ADJ american_scientific_journal-3571 16 32 systems system NOUN american_scientific_journal-3571 16 33 ability ability NOUN american_scientific_journal-3571 16 34 for for ADP american_scientific_journal-3571 16 35 transact transact NOUN american_scientific_journal-3571 16 36 with with ADP american_scientific_journal-3571 16 37 uneven uneven ADJ american_scientific_journal-3571 16 38 territories territory NOUN american_scientific_journal-3571 16 39 also also ADV american_scientific_journal-3571 16 40 avoiding avoid VERB american_scientific_journal-3571 16 41 the the DET american_scientific_journal-3571 16 42 obstacles obstacle NOUN american_scientific_journal-3571 16 43 that that PRON american_scientific_journal-3571 16 44 with with ADP american_scientific_journal-3571 16 45 the the DET american_scientific_journal-3571 16 46 quadruped quadruped NOUN american_scientific_journal-3571 16 47 robots robot NOUN american_scientific_journal-3571 16 48 in in ADP american_scientific_journal-3571 16 49 the the DET american_scientific_journal-3571 16 50 planning planning NOUN american_scientific_journal-3571 16 51 of of ADP american_scientific_journal-3571 16 52 standard standard ADJ american_scientific_journal-3571 16 53 walking walking NOUN american_scientific_journal-3571 16 54 gaits gait NOUN american_scientific_journal-3571 17 1 [ [ X american_scientific_journal-3571 17 2 2 2 NUM american_scientific_journal-3571 17 3 , , PUNCT american_scientific_journal-3571 17 4 3 3 NUM american_scientific_journal-3571 17 5 ] ] PUNCT american_scientific_journal-3571 17 6 . . PUNCT american_scientific_journal-3571 18 1 the the DET american_scientific_journal-3571 18 2 quadruped quadruped NOUN american_scientific_journal-3571 18 3 robots robot NOUN american_scientific_journal-3571 18 4 distinguish distinguish VERB american_scientific_journal-3571 18 5 among among ADP american_scientific_journal-3571 18 6 the the DET american_scientific_journal-3571 18 7 other other ADJ american_scientific_journal-3571 18 8 legged legged ADJ american_scientific_journal-3571 18 9 robots robot NOUN american_scientific_journal-3571 18 10 by by SCONJ american_scientific_journal-3571 18 11 have have VERB american_scientific_journal-3571 18 12 the the DET american_scientific_journal-3571 18 13 less less ADV american_scientific_journal-3571 18 14 complex complex ADJ american_scientific_journal-3571 18 15 structure structure NOUN american_scientific_journal-3571 18 16 , , PUNCT american_scientific_journal-3571 18 17 this this DET american_scientific_journal-3571 18 18 structure structure NOUN american_scientific_journal-3571 18 19 give give VERB american_scientific_journal-3571 18 20 it it PRON american_scientific_journal-3571 18 21 to to PART american_scientific_journal-3571 18 22 accomplish accomplish VERB american_scientific_journal-3571 18 23 the the DET american_scientific_journal-3571 18 24 requirements requirement NOUN american_scientific_journal-3571 18 25 of of ADP american_scientific_journal-3571 18 26 the the DET american_scientific_journal-3571 18 27 static static ADJ american_scientific_journal-3571 18 28 stability stability NOUN american_scientific_journal-3571 18 29 gait gait VERB american_scientific_journal-3571 18 30 throughout throughout ADP american_scientific_journal-3571 18 31 walking walk VERB american_scientific_journal-3571 18 32 . . PUNCT american_scientific_journal-3571 19 1 the the DET american_scientific_journal-3571 19 2 quadruped quadruped NOUN american_scientific_journal-3571 19 3 robots robot NOUN american_scientific_journal-3571 19 4 locomotion locomotion NOUN american_scientific_journal-3571 19 5 frequently frequently ADV american_scientific_journal-3571 19 6 utilized utilize VERB american_scientific_journal-3571 19 7 in in ADP american_scientific_journal-3571 19 8 many many ADJ american_scientific_journal-3571 19 9 research research NOUN american_scientific_journal-3571 19 10 that that PRON american_scientific_journal-3571 19 11 talked talk VERB american_scientific_journal-3571 19 12 about about ADP american_scientific_journal-3571 19 13 the the DET american_scientific_journal-3571 19 14 quadruped quadruped NOUN american_scientific_journal-3571 19 15 robot robot NOUN american_scientific_journal-3571 19 16 , , PUNCT american_scientific_journal-3571 19 17 its its PRON american_scientific_journal-3571 19 18 similarity similarity NOUN american_scientific_journal-3571 19 19 in in ADP american_scientific_journal-3571 19 20 the the DET american_scientific_journal-3571 19 21 investigation investigation NOUN american_scientific_journal-3571 19 22 of of ADP american_scientific_journal-3571 19 23 insects insect NOUN american_scientific_journal-3571 19 24 and and CCONJ american_scientific_journal-3571 19 25 biological biological ADJ american_scientific_journal-3571 19 26 animals animal NOUN american_scientific_journal-3571 19 27 walking walk VERB american_scientific_journal-3571 19 28 gaits gait NOUN american_scientific_journal-3571 19 29 . . PUNCT american_scientific_journal-3571 20 1 these these DET american_scientific_journal-3571 20 2 studies study NOUN american_scientific_journal-3571 20 3 have have AUX american_scientific_journal-3571 20 4 led lead VERB american_scientific_journal-3571 20 5 to to PART american_scientific_journal-3571 20 6 improve improve VERB american_scientific_journal-3571 20 7 both both PRON american_scientific_journal-3571 20 8 dynamic dynamic ADJ american_scientific_journal-3571 20 9 running running NOUN american_scientific_journal-3571 20 10 gaits gait NOUN american_scientific_journal-3571 20 11 and and CCONJ american_scientific_journal-3571 20 12 statically statically ADV american_scientific_journal-3571 20 13 stable stable ADJ american_scientific_journal-3571 20 14 walking walking NOUN american_scientific_journal-3571 20 15 gait gait NOUN american_scientific_journal-3571 20 16 for for ADP american_scientific_journal-3571 20 17 legged legged ADJ american_scientific_journal-3571 20 18 robots robot NOUN american_scientific_journal-3571 20 19 [ [ X american_scientific_journal-3571 20 20 4 4 NUM american_scientific_journal-3571 20 21 ] ] PUNCT american_scientific_journal-3571 20 22 . . PUNCT american_scientific_journal-3571 21 1 the the DET american_scientific_journal-3571 21 2 objective objective NOUN american_scientific_journal-3571 21 3 of of ADP american_scientific_journal-3571 21 4 this this DET american_scientific_journal-3571 21 5 paper paper NOUN american_scientific_journal-3571 21 6 is be AUX american_scientific_journal-3571 21 7 to to PART american_scientific_journal-3571 21 8 design design VERB american_scientific_journal-3571 21 9 and and CCONJ american_scientific_journal-3571 21 10 implement implement VERB american_scientific_journal-3571 21 11 with with ADP american_scientific_journal-3571 21 12 robustness robustness NOUN american_scientific_journal-3571 21 13 quadruped quadrupe VERB american_scientific_journal-3571 21 14 robot robot NOUN american_scientific_journal-3571 21 15 that that PRON american_scientific_journal-3571 21 16 has have VERB american_scientific_journal-3571 21 17 the the DET american_scientific_journal-3571 21 18 static static ADJ american_scientific_journal-3571 21 19 stable stable ADJ american_scientific_journal-3571 21 20 ability ability NOUN american_scientific_journal-3571 21 21 during during ADP american_scientific_journal-3571 21 22 its its PRON american_scientific_journal-3571 21 23 walking walking NOUN american_scientific_journal-3571 21 24 . . PUNCT american_scientific_journal-3571 22 1 these these DET american_scientific_journal-3571 22 2 walking walk VERB american_scientific_journal-3571 22 3 gaits gait NOUN american_scientific_journal-3571 22 4 are be AUX american_scientific_journal-3571 22 5 repeated repeat VERB american_scientific_journal-3571 22 6 to to PART american_scientific_journal-3571 22 7 obtain obtain VERB american_scientific_journal-3571 22 8 the the DET american_scientific_journal-3571 22 9 main main ADJ american_scientific_journal-3571 22 10 sequence sequence NOUN american_scientific_journal-3571 22 11 step step NOUN american_scientific_journal-3571 22 12 which which PRON american_scientific_journal-3571 22 13 needed need VERB american_scientific_journal-3571 22 14 to to PART american_scientific_journal-3571 22 15 make make VERB american_scientific_journal-3571 22 16 the the DET american_scientific_journal-3571 22 17 quadruped quadruped NOUN american_scientific_journal-3571 22 18 robot robot NOUN american_scientific_journal-3571 22 19 stable stable ADJ american_scientific_journal-3571 22 20 on on ADP american_scientific_journal-3571 22 21 irregular irregular ADJ american_scientific_journal-3571 22 22 places place NOUN american_scientific_journal-3571 22 23 [ [ X american_scientific_journal-3571 22 24 5 5 NUM american_scientific_journal-3571 22 25 ] ] PUNCT american_scientific_journal-3571 22 26 . . PUNCT american_scientific_journal-3571 23 1 the the DET american_scientific_journal-3571 23 2 quadruped quadruped NOUN american_scientific_journal-3571 23 3 robots robot NOUN american_scientific_journal-3571 23 4 also also ADV american_scientific_journal-3571 23 5 has have VERB american_scientific_journal-3571 23 6 the the DET american_scientific_journal-3571 23 7 ability ability NOUN american_scientific_journal-3571 23 8 of of ADP american_scientific_journal-3571 23 9 arranging arrange VERB american_scientific_journal-3571 23 10 the the DET american_scientific_journal-3571 23 11 step step NOUN american_scientific_journal-3571 23 12 sequences sequence NOUN american_scientific_journal-3571 23 13 and and CCONJ american_scientific_journal-3571 23 14 verification verification NOUN american_scientific_journal-3571 23 15 criteria criterion NOUN american_scientific_journal-3571 23 16 of of ADP american_scientific_journal-3571 23 17 stability stability NOUN american_scientific_journal-3571 23 18 on on ADP american_scientific_journal-3571 23 19 incline incline ADJ american_scientific_journal-3571 23 20 surfaces surface NOUN american_scientific_journal-3571 23 21 that that PRON american_scientific_journal-3571 23 22 needed need VERB american_scientific_journal-3571 23 23 for for ADP american_scientific_journal-3571 23 24 verifying verify VERB american_scientific_journal-3571 23 25 the the DET american_scientific_journal-3571 23 26 omni omni ADJ american_scientific_journal-3571 23 27 - - PUNCT american_scientific_journal-3571 23 28 directional directional ADJ american_scientific_journal-3571 23 29 statically statically ADV american_scientific_journal-3571 23 30 stable stable ADJ american_scientific_journal-3571 23 31 throughout throughout ADP american_scientific_journal-3571 23 32 this this DET american_scientific_journal-3571 23 33 walking walking NOUN american_scientific_journal-3571 24 1 [ [ X american_scientific_journal-3571 24 2 6 6 NUM american_scientific_journal-3571 24 3 ] ] PUNCT american_scientific_journal-3571 24 4 . . PUNCT american_scientific_journal-3571 25 1 the the DET american_scientific_journal-3571 25 2 criteria criterion NOUN american_scientific_journal-3571 25 3 of of ADP american_scientific_journal-3571 25 4 stability stability NOUN american_scientific_journal-3571 25 5 depended depend VERB american_scientific_journal-3571 25 6 on on ADP american_scientific_journal-3571 25 7 some some DET american_scientific_journal-3571 25 8 elements element NOUN american_scientific_journal-3571 25 9 such such ADJ american_scientific_journal-3571 25 10 as as ADP american_scientific_journal-3571 25 11 center center NOUN american_scientific_journal-3571 25 12 of of ADP american_scientific_journal-3571 25 13 gravity gravity NOUN american_scientific_journal-3571 25 14 ( ( PUNCT american_scientific_journal-3571 25 15 cog cog PROPN american_scientific_journal-3571 25 16 ) ) PUNCT american_scientific_journal-3571 25 17 , , PUNCT american_scientific_journal-3571 25 18 stability stability NOUN american_scientific_journal-3571 25 19 margin margin NOUN american_scientific_journal-3571 25 20 ( ( PUNCT american_scientific_journal-3571 25 21 sm sm NOUN american_scientific_journal-3571 25 22 ) ) PUNCT american_scientific_journal-3571 25 23 and and CCONJ american_scientific_journal-3571 25 24 the the DET american_scientific_journal-3571 25 25 support support NOUN american_scientific_journal-3571 25 26 polygon polygon NOUN american_scientific_journal-3571 25 27 which which PRON american_scientific_journal-3571 25 28 framed frame VERB american_scientific_journal-3571 25 29 by by ADP american_scientific_journal-3571 25 30 the the DET american_scientific_journal-3571 25 31 legs leg NOUN american_scientific_journal-3571 25 32 tip tip NOUN american_scientific_journal-3571 25 33 of of ADP american_scientific_journal-3571 25 34 the the DET american_scientific_journal-3571 25 35 quadruped quadruped NOUN american_scientific_journal-3571 25 36 robot robot NOUN american_scientific_journal-3571 25 37 . . PUNCT american_scientific_journal-3571 26 1 these these DET american_scientific_journal-3571 26 2 elements element NOUN american_scientific_journal-3571 26 3 are be AUX american_scientific_journal-3571 26 4 very very ADV american_scientific_journal-3571 26 5 important important ADJ american_scientific_journal-3571 26 6 particularly particularly ADV american_scientific_journal-3571 26 7 when when SCONJ american_scientific_journal-3571 26 8 the the DET american_scientific_journal-3571 26 9 quadruped quadruped NOUN american_scientific_journal-3571 26 10 robot robot NOUN american_scientific_journal-3571 26 11 walking walk VERB american_scientific_journal-3571 26 12 utilizing utilize VERB american_scientific_journal-3571 26 13 creeping creep VERB american_scientific_journal-3571 26 14 gaits gait NOUN american_scientific_journal-3571 26 15 for for ADP american_scientific_journal-3571 26 16 walking walk VERB american_scientific_journal-3571 26 17 [ [ X american_scientific_journal-3571 26 18 7 7 NUM american_scientific_journal-3571 26 19 , , PUNCT american_scientific_journal-3571 26 20 8 8 NUM american_scientific_journal-3571 26 21 ] ] PUNCT american_scientific_journal-3571 26 22 . . PUNCT american_scientific_journal-3571 27 1 generate generate NOUN american_scientific_journal-3571 27 2 of of ADP american_scientific_journal-3571 27 3 the the DET american_scientific_journal-3571 27 4 leg leg NOUN american_scientific_journal-3571 27 5 sequence sequence NOUN american_scientific_journal-3571 27 6 of of ADP american_scientific_journal-3571 27 7 placing place VERB american_scientific_journal-3571 27 8 and and CCONJ american_scientific_journal-3571 27 9 lifting lift VERB american_scientific_journal-3571 27 10 throughout throughout ADP american_scientific_journal-3571 27 11 the the DET american_scientific_journal-3571 27 12 quadruped quadruped NOUN american_scientific_journal-3571 27 13 robot robot NOUN american_scientific_journal-3571 27 14 walking walking NOUN american_scientific_journal-3571 27 15 is be AUX american_scientific_journal-3571 27 16 called call VERB american_scientific_journal-3571 27 17 gait gait NOUN american_scientific_journal-3571 28 1 [ [ X american_scientific_journal-3571 28 2 9 9 NUM american_scientific_journal-3571 28 3 ] ] PUNCT american_scientific_journal-3571 28 4 . . PUNCT american_scientific_journal-3571 29 1 generally generally ADV american_scientific_journal-3571 29 2 , , PUNCT american_scientific_journal-3571 29 3 the the DET american_scientific_journal-3571 29 4 quadruped quadruped NOUN american_scientific_journal-3571 29 5 robot robot NOUN american_scientific_journal-3571 29 6 gaits gait NOUN american_scientific_journal-3571 29 7 are be AUX american_scientific_journal-3571 29 8 dividing divide VERB american_scientific_journal-3571 29 9 in in ADP american_scientific_journal-3571 29 10 two two NUM american_scientific_journal-3571 29 11 types type NOUN american_scientific_journal-3571 29 12 , , PUNCT american_scientific_journal-3571 29 13 the the DET american_scientific_journal-3571 29 14 first first ADJ american_scientific_journal-3571 29 15 type type NOUN american_scientific_journal-3571 29 16 is be AUX american_scientific_journal-3571 29 17 the the DET american_scientific_journal-3571 29 18 static static ADJ american_scientific_journal-3571 29 19 stability stability NOUN american_scientific_journal-3571 29 20 gait gait NOUN american_scientific_journal-3571 29 21 , , PUNCT american_scientific_journal-3571 29 22 and and CCONJ american_scientific_journal-3571 29 23 the the DET american_scientific_journal-3571 29 24 second second ADJ american_scientific_journal-3571 29 25 type type NOUN american_scientific_journal-3571 29 26 is be AUX american_scientific_journal-3571 29 27 dynamic dynamic ADJ american_scientific_journal-3571 29 28 stability stability NOUN american_scientific_journal-3571 29 29 gait gait NOUN american_scientific_journal-3571 30 1 [ [ X american_scientific_journal-3571 30 2 10 10 NUM american_scientific_journal-3571 30 3 ] ] PUNCT american_scientific_journal-3571 30 4 . . PUNCT american_scientific_journal-3571 31 1 during during ADP american_scientific_journal-3571 31 2 the the DET american_scientific_journal-3571 31 3 movement movement NOUN american_scientific_journal-3571 31 4 of of ADP american_scientific_journal-3571 31 5 the the DET american_scientific_journal-3571 31 6 walking walk VERB american_scientific_journal-3571 31 7 the the DET american_scientific_journal-3571 31 8 body body NOUN american_scientific_journal-3571 31 9 of of ADP american_scientific_journal-3571 31 10 quadruped quadruped NOUN american_scientific_journal-3571 31 11 robot robot NOUN american_scientific_journal-3571 31 12 should should AUX american_scientific_journal-3571 31 13 be be AUX american_scientific_journal-3571 31 14 remain remain VERB american_scientific_journal-3571 31 15 stable stable ADJ american_scientific_journal-3571 31 16 and and CCONJ american_scientific_journal-3571 31 17 has have VERB american_scientific_journal-3571 31 18 the the DET american_scientific_journal-3571 31 19 ability ability NOUN american_scientific_journal-3571 31 20 to to PART american_scientific_journal-3571 31 21 travel travel VERB american_scientific_journal-3571 31 22 from from ADP american_scientific_journal-3571 31 23 one one NUM american_scientific_journal-3571 31 24 place place NOUN american_scientific_journal-3571 31 25 to to ADP american_scientific_journal-3571 31 26 another another PRON american_scientific_journal-3571 31 27 . . PUNCT american_scientific_journal-3571 32 1 the the DET american_scientific_journal-3571 32 2 static static ADJ american_scientific_journal-3571 32 3 stability stability NOUN american_scientific_journal-3571 32 4 gait gait NOUN american_scientific_journal-3571 32 5 is be AUX american_scientific_journal-3571 32 6 the the DET american_scientific_journal-3571 32 7 easier easy ADJ american_scientific_journal-3571 32 8 gait gait NOUN american_scientific_journal-3571 32 9 which which PRON american_scientific_journal-3571 32 10 used use VERB american_scientific_journal-3571 32 11 by by ADP american_scientific_journal-3571 32 12 the the DET american_scientific_journal-3571 32 13 quadruped quadruped NOUN american_scientific_journal-3571 32 14 robot robot NOUN american_scientific_journal-3571 32 15 when when SCONJ american_scientific_journal-3571 32 16 it it PRON american_scientific_journal-3571 32 17 needs need VERB american_scientific_journal-3571 32 18 a a DET american_scientific_journal-3571 32 19 slow slow ADJ american_scientific_journal-3571 32 20 motion motion NOUN american_scientific_journal-3571 32 21 movement movement NOUN american_scientific_journal-3571 32 22 to to PART american_scientific_journal-3571 32 23 walk walk VERB american_scientific_journal-3571 32 24 . . PUNCT american_scientific_journal-3571 33 1 but but CCONJ american_scientific_journal-3571 33 2 when when SCONJ american_scientific_journal-3571 33 3 the the DET american_scientific_journal-3571 33 4 quadruped quadruped NOUN american_scientific_journal-3571 33 5 robot robot NOUN american_scientific_journal-3571 33 6 walking walk VERB american_scientific_journal-3571 33 7 at at ADP american_scientific_journal-3571 33 8 fast fast ADJ american_scientific_journal-3571 33 9 speed speed NOUN american_scientific_journal-3571 33 10 like like ADP american_scientific_journal-3571 33 11 trotting trotting NOUN american_scientific_journal-3571 33 12 gait gait NOUN american_scientific_journal-3571 33 13 , , PUNCT american_scientific_journal-3571 33 14 the the DET american_scientific_journal-3571 33 15 one one NOUN american_scientific_journal-3571 33 16 must must AUX american_scientific_journal-3571 33 17 be be AUX american_scientific_journal-3571 33 18 used use VERB american_scientific_journal-3571 33 19 is be AUX american_scientific_journal-3571 33 20 the the DET american_scientific_journal-3571 33 21 dynamic dynamic ADJ american_scientific_journal-3571 33 22 gait gait NOUN american_scientific_journal-3571 33 23 , , PUNCT american_scientific_journal-3571 33 24 which which PRON american_scientific_journal-3571 33 25 aims aim VERB american_scientific_journal-3571 33 26 to to ADP american_scientific_journal-3571 33 27 reality reality NOUN american_scientific_journal-3571 33 28 of of ADP american_scientific_journal-3571 33 29 that that PRON american_scientific_journal-3571 33 30 the the DET american_scientific_journal-3571 33 31 vertical vertical ADJ american_scientific_journal-3571 33 32 projection projection NOUN american_scientific_journal-3571 33 33 of of ADP american_scientific_journal-3571 33 34 cog cog PROPN american_scientific_journal-3571 33 35 is be AUX american_scientific_journal-3571 33 36 derivative derivative ADJ american_scientific_journal-3571 33 37 of of ADP american_scientific_journal-3571 33 38 the the DET american_scientific_journal-3571 33 39 supporting support VERB american_scientific_journal-3571 33 40 polygon polygon NOUN american_scientific_journal-3571 33 41 and and CCONJ american_scientific_journal-3571 33 42 not not PART american_scientific_journal-3571 33 43 inside inside ADP american_scientific_journal-3571 33 44 it it PRON american_scientific_journal-3571 33 45 . . PUNCT american_scientific_journal-3571 34 1 for for ADP american_scientific_journal-3571 34 2 this this DET american_scientific_journal-3571 34 3 case case NOUN american_scientific_journal-3571 34 4 the the DET american_scientific_journal-3571 34 5 quadruped quadruped NOUN american_scientific_journal-3571 34 6 robot robot NOUN american_scientific_journal-3571 34 7 will will AUX american_scientific_journal-3571 34 8 be be AUX american_scientific_journal-3571 34 9 unstable unstable ADJ american_scientific_journal-3571 34 10 and and CCONJ american_scientific_journal-3571 34 11 it it PRON american_scientific_journal-3571 34 12 is be AUX american_scientific_journal-3571 34 13 imminence imminence NOUN american_scientific_journal-3571 34 14 to to PART american_scientific_journal-3571 34 15 drop drop VERB american_scientific_journal-3571 34 16 down down ADP american_scientific_journal-3571 34 17 . . PUNCT american_scientific_journal-3571 35 1 thus thus ADV american_scientific_journal-3571 35 2 at at ADP american_scientific_journal-3571 35 3 the the DET american_scientific_journal-3571 35 4 quadruped quadruped NOUN american_scientific_journal-3571 35 5 robot robot NOUN american_scientific_journal-3571 35 6 running running NOUN american_scientific_journal-3571 35 7 gaits gait NOUN american_scientific_journal-3571 35 8 , , PUNCT american_scientific_journal-3571 35 9 its its PRON american_scientific_journal-3571 35 10 need need NOUN american_scientific_journal-3571 35 11 to to PART american_scientific_journal-3571 35 12 be be AUX american_scientific_journal-3571 35 13 content content ADJ american_scientific_journal-3571 35 14 with with ADP american_scientific_journal-3571 35 15 the the DET american_scientific_journal-3571 35 16 conditions condition NOUN american_scientific_journal-3571 35 17 of of ADP american_scientific_journal-3571 35 18 dynamic dynamic ADJ american_scientific_journal-3571 35 19 stability stability NOUN american_scientific_journal-3571 35 20 instead instead ADV american_scientific_journal-3571 35 21 of of ADP american_scientific_journal-3571 35 22 the the DET american_scientific_journal-3571 35 23 requirements requirement NOUN american_scientific_journal-3571 35 24 of of ADP american_scientific_journal-3571 35 25 static static ADJ american_scientific_journal-3571 35 26 stability stability NOUN american_scientific_journal-3571 35 27 [ [ X american_scientific_journal-3571 35 28 11 11 NUM american_scientific_journal-3571 35 29 ] ] PUNCT american_scientific_journal-3571 35 30 . . PUNCT american_scientific_journal-3571 36 1 generally generally ADV american_scientific_journal-3571 36 2 , , PUNCT american_scientific_journal-3571 36 3 the the DET american_scientific_journal-3571 36 4 quadruped quadruped NOUN american_scientific_journal-3571 36 5 robot robot NOUN american_scientific_journal-3571 36 6 is be AUX american_scientific_journal-3571 36 7 attempt attempt NOUN american_scientific_journal-3571 36 8 to to PART american_scientific_journal-3571 36 9 be be AUX american_scientific_journal-3571 36 10 statically statically ADV american_scientific_journal-3571 36 11 stable stable ADJ american_scientific_journal-3571 36 12 with with ADP american_scientific_journal-3571 36 13 its its PRON american_scientific_journal-3571 36 14 three three NUM american_scientific_journal-3571 36 15 legs leg NOUN american_scientific_journal-3571 36 16 fixed fix VERB american_scientific_journal-3571 36 17 on on ADP american_scientific_journal-3571 36 18 the the DET american_scientific_journal-3571 36 19 ground ground NOUN american_scientific_journal-3571 36 20 while while SCONJ american_scientific_journal-3571 36 21 the the DET american_scientific_journal-3571 36 22 fourth fourth ADJ american_scientific_journal-3571 36 23 leg leg NOUN american_scientific_journal-3571 36 24 is be AUX american_scientific_journal-3571 36 25 swing swe VERB american_scientific_journal-3571 36 26 . . PUNCT american_scientific_journal-3571 37 1 in in ADP american_scientific_journal-3571 37 2 this this DET american_scientific_journal-3571 37 3 paper paper NOUN american_scientific_journal-3571 37 4 , , PUNCT american_scientific_journal-3571 37 5 the the DET american_scientific_journal-3571 37 6 pso pso NOUN american_scientific_journal-3571 37 7 optimization optimization NOUN american_scientific_journal-3571 37 8 algorithm algorithm NOUN american_scientific_journal-3571 37 9 utilized utilize VERB american_scientific_journal-3571 37 10 to to PART american_scientific_journal-3571 37 11 obtain obtain VERB american_scientific_journal-3571 37 12 the the DET american_scientific_journal-3571 37 13 best good ADJ american_scientific_journal-3571 37 14 stability stability NOUN american_scientific_journal-3571 37 15 margins margin NOUN american_scientific_journal-3571 37 16 throughout throughout ADP american_scientific_journal-3571 37 17 the the DET american_scientific_journal-3571 37 18 robot robot NOUN american_scientific_journal-3571 37 19 walking walk VERB american_scientific_journal-3571 37 20 gait gait PROPN american_scientific_journal-3571 37 21 . . PUNCT american_scientific_journal-3571 38 1 the the DET american_scientific_journal-3571 38 2 creeping creep VERB american_scientific_journal-3571 38 3 gait gait NOUN american_scientific_journal-3571 38 4 matches match VERB american_scientific_journal-3571 38 5 the the DET american_scientific_journal-3571 38 6 nature nature NOUN american_scientific_journal-3571 38 7 of of ADP american_scientific_journal-3571 38 8 the the DET american_scientific_journal-3571 38 9 biological biological ADJ american_scientific_journal-3571 38 10 stable stable ADJ american_scientific_journal-3571 38 11 gait gait NOUN american_scientific_journal-3571 38 12 of of ADP american_scientific_journal-3571 38 13 animals animal NOUN american_scientific_journal-3571 38 14 and and CCONJ american_scientific_journal-3571 38 15 insects insect NOUN american_scientific_journal-3571 38 16 . . PUNCT american_scientific_journal-3571 39 1 in in ADP american_scientific_journal-3571 39 2 this this DET american_scientific_journal-3571 39 3 case case NOUN american_scientific_journal-3571 39 4 the the DET american_scientific_journal-3571 39 5 statically statically ADV american_scientific_journal-3571 39 6 stable stable ADJ american_scientific_journal-3571 39 7 gait gait NOUN american_scientific_journal-3571 39 8 is be AUX american_scientific_journal-3571 39 9 necessary necessary ADJ american_scientific_journal-3571 39 10 in in ADP american_scientific_journal-3571 39 11 order order NOUN american_scientific_journal-3571 39 12 to to PART american_scientific_journal-3571 39 13 guarantee guarantee VERB american_scientific_journal-3571 39 14 a a DET american_scientific_journal-3571 39 15 stable stable ADJ american_scientific_journal-3571 39 16 walking walking NOUN american_scientific_journal-3571 39 17 . . PUNCT american_scientific_journal-3571 40 1 also also ADV american_scientific_journal-3571 40 2 during during ADP american_scientific_journal-3571 40 3 the the DET american_scientific_journal-3571 40 4 quadruped quadruped NOUN american_scientific_journal-3571 40 5 walking walk VERB american_scientific_journal-3571 40 6 in in ADP american_scientific_journal-3571 40 7 the the DET american_scientific_journal-3571 40 8 creeping creep VERB american_scientific_journal-3571 40 9 gait gait NOUN american_scientific_journal-3571 40 10 , , PUNCT american_scientific_journal-3571 40 11 its its PRON american_scientific_journal-3571 40 12 stability stability NOUN american_scientific_journal-3571 40 13 will will AUX american_scientific_journal-3571 40 14 be be AUX american_scientific_journal-3571 40 15 achieved achieve VERB american_scientific_journal-3571 40 16 if if SCONJ american_scientific_journal-3571 40 17 and and CCONJ american_scientific_journal-3571 40 18 only only ADV american_scientific_journal-3571 40 19 if if SCONJ american_scientific_journal-3571 40 20 the the DET american_scientific_journal-3571 40 21 cog cog PROPN american_scientific_journal-3571 40 22 vertical vertical PROPN american_scientific_journal-3571 40 23 projection projection PROPN american_scientific_journal-3571 40 24 inside inside ADP american_scientific_journal-3571 40 25 the the DET american_scientific_journal-3571 40 26 supporting support VERB american_scientific_journal-3571 40 27 polygon polygon NOUN american_scientific_journal-3571 40 28 which which PRON american_scientific_journal-3571 40 29 is be AUX american_scientific_journal-3571 40 30 framed frame VERB american_scientific_journal-3571 40 31 by by ADP american_scientific_journal-3571 40 32 the the DET american_scientific_journal-3571 40 33 legs leg NOUN american_scientific_journal-3571 40 34 tips tip NOUN american_scientific_journal-3571 40 35 . . PUNCT american_scientific_journal-3571 41 1 the the DET american_scientific_journal-3571 41 2 basic basic ADJ american_scientific_journal-3571 41 3 problem problem NOUN american_scientific_journal-3571 41 4 is be AUX american_scientific_journal-3571 41 5 how how SCONJ american_scientific_journal-3571 41 6 to to PART american_scientific_journal-3571 41 7 achieve achieve VERB american_scientific_journal-3571 41 8 and and CCONJ american_scientific_journal-3571 41 9 control control NOUN american_scientific_journal-3571 41 10 of of ADP american_scientific_journal-3571 41 11 the the DET american_scientific_journal-3571 41 12 legs leg NOUN american_scientific_journal-3571 41 13 sequences sequence NOUN american_scientific_journal-3571 41 14 of of ADP american_scientific_journal-3571 41 15 lifting lift VERB american_scientific_journal-3571 41 16 and and CCONJ american_scientific_journal-3571 41 17 putting put VERB american_scientific_journal-3571 41 18 all all DET american_scientific_journal-3571 41 19 legs leg NOUN american_scientific_journal-3571 41 20 within within ADP american_scientific_journal-3571 41 21 the the DET american_scientific_journal-3571 41 22 period period NOUN american_scientific_journal-3571 41 23 of of ADP american_scientific_journal-3571 41 24 time time NOUN american_scientific_journal-3571 41 25 when when SCONJ american_scientific_journal-3571 41 26 the the DET american_scientific_journal-3571 41 27 quadruped quadruped NOUN american_scientific_journal-3571 41 28 robot robot NOUN american_scientific_journal-3571 41 29 walking walking NOUN american_scientific_journal-3571 41 30 . . PUNCT american_scientific_journal-3571 42 1 2 2 X american_scientific_journal-3571 42 2 . . X american_scientific_journal-3571 42 3 description description NOUN american_scientific_journal-3571 42 4 of of ADP american_scientific_journal-3571 42 5 quadruped quadruped NOUN american_scientific_journal-3571 42 6 robot robot NOUN american_scientific_journal-3571 42 7 there there PRON american_scientific_journal-3571 42 8 are be VERB american_scientific_journal-3571 42 9 a a DET american_scientific_journal-3571 42 10 different different ADJ american_scientific_journal-3571 42 11 models model NOUN american_scientific_journal-3571 42 12 of of ADP american_scientific_journal-3571 42 13 the the DET american_scientific_journal-3571 42 14 quadruped quadruped NOUN american_scientific_journal-3571 42 15 robot robot NOUN american_scientific_journal-3571 42 16 , , PUNCT american_scientific_journal-3571 42 17 these these DET american_scientific_journal-3571 42 18 models model NOUN american_scientific_journal-3571 42 19 is be AUX american_scientific_journal-3571 42 20 based base VERB american_scientific_journal-3571 42 21 on on ADP american_scientific_journal-3571 42 22 some some DET american_scientific_journal-3571 42 23 attributes attribute NOUN american_scientific_journal-3571 42 24 and and CCONJ american_scientific_journal-3571 42 25 guide guide VERB american_scientific_journal-3571 42 26 lines line NOUN american_scientific_journal-3571 42 27 to to PART american_scientific_journal-3571 42 28 design design VERB american_scientific_journal-3571 42 29 the the DET american_scientific_journal-3571 42 30 robot robot NOUN american_scientific_journal-3571 42 31 structure structure NOUN american_scientific_journal-3571 42 32 and and CCONJ american_scientific_journal-3571 42 33 the the DET american_scientific_journal-3571 42 34 gait gait PROPN american_scientific_journal-3571 42 35 movement movement NOUN american_scientific_journal-3571 42 36 . . PUNCT american_scientific_journal-3571 43 1 the the DET american_scientific_journal-3571 43 2 main main ADJ american_scientific_journal-3571 43 3 criteria criterion NOUN american_scientific_journal-3571 43 4 to to PART american_scientific_journal-3571 43 5 achieve achieve VERB american_scientific_journal-3571 43 6 these these DET american_scientific_journal-3571 43 7 attributes attribute NOUN american_scientific_journal-3571 43 8 are be AUX american_scientific_journal-3571 43 9 [ [ X american_scientific_journal-3571 43 10 13 13 NUM american_scientific_journal-3571 43 11 ] ] SYM american_scientific_journal-3571 43 12 : : PUNCT american_scientific_journal-3571 44 1 1 1 X american_scientific_journal-3571 44 2 . . X american_scientific_journal-3571 44 3 the the DET american_scientific_journal-3571 44 4 standard standard PROPN american_scientific_journal-3571 44 5 walking walking NOUN american_scientific_journal-3571 44 6 of of ADP american_scientific_journal-3571 44 7 quadruped quadruped NOUN american_scientific_journal-3571 44 8 robot robot NOUN american_scientific_journal-3571 44 9 is be AUX american_scientific_journal-3571 44 10 repeated repeat VERB american_scientific_journal-3571 44 11 periodically periodically ADV american_scientific_journal-3571 44 12 during during ADP american_scientific_journal-3571 44 13 the the DET american_scientific_journal-3571 44 14 planning planning NOUN american_scientific_journal-3571 44 15 path path NOUN american_scientific_journal-3571 44 16 with with ADP american_scientific_journal-3571 44 17 a a DET american_scientific_journal-3571 44 18 constant constant ADJ american_scientific_journal-3571 44 19 speed speed NOUN american_scientific_journal-3571 44 20 , , PUNCT american_scientific_journal-3571 44 21 steady steady ADJ american_scientific_journal-3571 44 22 state state NOUN american_scientific_journal-3571 44 23 movement movement NOUN american_scientific_journal-3571 44 24 of of ADP american_scientific_journal-3571 44 25 the the DET american_scientific_journal-3571 44 26 legs leg NOUN american_scientific_journal-3571 44 27 over over ADP american_scientific_journal-3571 44 28 even even ADV american_scientific_journal-3571 44 29 territories territory NOUN american_scientific_journal-3571 44 30 . . PUNCT american_scientific_journal-3571 45 1 2 2 X american_scientific_journal-3571 45 2 . . X american_scientific_journal-3571 45 3 the the DET american_scientific_journal-3571 45 4 standard standard ADJ american_scientific_journal-3571 45 5 design design NOUN american_scientific_journal-3571 45 6 of of ADP american_scientific_journal-3571 45 7 the the DET american_scientific_journal-3571 45 8 quadruped quadruped NOUN american_scientific_journal-3571 45 9 robot robot NOUN american_scientific_journal-3571 45 10 must must AUX american_scientific_journal-3571 45 11 be be AUX american_scientific_journal-3571 45 12 symmetrical symmetrical ADJ american_scientific_journal-3571 45 13 in in ADP american_scientific_journal-3571 45 14 both both CCONJ american_scientific_journal-3571 45 15 longitudinal longitudinal ADJ american_scientific_journal-3571 45 16 body body NOUN american_scientific_journal-3571 45 17 direction direction NOUN american_scientific_journal-3571 45 18 and and CCONJ american_scientific_journal-3571 45 19 american american ADJ american_scientific_journal-3571 45 20 scientific scientific ADJ american_scientific_journal-3571 45 21 research research NOUN american_scientific_journal-3571 45 22 journal journal NOUN american_scientific_journal-3571 45 23 for for ADP american_scientific_journal-3571 45 24 engineering engineering NOUN american_scientific_journal-3571 45 25 , , PUNCT american_scientific_journal-3571 45 26 technology technology NOUN american_scientific_journal-3571 45 27 , , PUNCT american_scientific_journal-3571 45 28 and and CCONJ american_scientific_journal-3571 45 29 sciences science NOUN american_scientific_journal-3571 45 30 ( ( PUNCT american_scientific_journal-3571 45 31 asrjets asrjet NOUN american_scientific_journal-3571 45 32 ) ) PUNCT american_scientific_journal-3571 45 33 ( ( PUNCT american_scientific_journal-3571 45 34 2017 2017 NUM american_scientific_journal-3571 45 35 ) ) PUNCT american_scientific_journal-3571 45 36 volume volume NOUN american_scientific_journal-3571 45 37 38 38 NUM american_scientific_journal-3571 45 38 , , PUNCT american_scientific_journal-3571 45 39 no no DET american_scientific_journal-3571 45 40 1 1 NUM american_scientific_journal-3571 45 41 , , PUNCT american_scientific_journal-3571 45 42 pp pp ADV american_scientific_journal-3571 45 43 17 17 NUM american_scientific_journal-3571 45 44 - - SYM american_scientific_journal-3571 45 45 32 32 NUM american_scientific_journal-3571 45 46 19 19 NUM american_scientific_journal-3571 45 47 lateral lateral ADJ american_scientific_journal-3571 45 48 body body NOUN american_scientific_journal-3571 45 49 direction direction NOUN american_scientific_journal-3571 45 50 . . PUNCT american_scientific_journal-3571 46 1 this this DET american_scientific_journal-3571 46 2 point point NOUN american_scientific_journal-3571 46 3 is be AUX american_scientific_journal-3571 46 4 also also ADV american_scientific_journal-3571 46 5 applied apply VERB american_scientific_journal-3571 46 6 to to ADP american_scientific_journal-3571 46 7 the the DET american_scientific_journal-3571 46 8 legs leg NOUN american_scientific_journal-3571 46 9 structure structure NOUN american_scientific_journal-3571 46 10 leads lead VERB american_scientific_journal-3571 46 11 to to ADP american_scientific_journal-3571 46 12 a a DET american_scientific_journal-3571 46 13 less less ADV american_scientific_journal-3571 46 14 mechanical mechanical ADJ american_scientific_journal-3571 46 15 complexity complexity NOUN american_scientific_journal-3571 46 16 . . PUNCT american_scientific_journal-3571 47 1 3 3 X american_scientific_journal-3571 47 2 . . X american_scientific_journal-3571 47 3 when when SCONJ american_scientific_journal-3571 47 4 the the DET american_scientific_journal-3571 47 5 quadruped quadruped NOUN american_scientific_journal-3571 47 6 robot robot NOUN american_scientific_journal-3571 47 7 has have VERB american_scientific_journal-3571 47 8 a a DET american_scientific_journal-3571 47 9 regular regular ADJ american_scientific_journal-3571 47 10 shape shape NOUN american_scientific_journal-3571 47 11 and and CCONJ american_scientific_journal-3571 47 12 symmetric symmetric NOUN american_scientific_journal-3571 47 13 , , PUNCT american_scientific_journal-3571 47 14 the the DET american_scientific_journal-3571 47 15 vertical vertical ADJ american_scientific_journal-3571 47 16 projection projection NOUN american_scientific_journal-3571 47 17 of of ADP american_scientific_journal-3571 47 18 cog cog PROPN american_scientific_journal-3571 47 19 of of ADP american_scientific_journal-3571 47 20 the the DET american_scientific_journal-3571 47 21 robot robot NOUN american_scientific_journal-3571 47 22 body body NOUN american_scientific_journal-3571 47 23 is be AUX american_scientific_journal-3571 47 24 located locate VERB american_scientific_journal-3571 47 25 at at ADP american_scientific_journal-3571 47 26 the the DET american_scientific_journal-3571 47 27 center center NOUN american_scientific_journal-3571 47 28 of of ADP american_scientific_journal-3571 47 29 the the DET american_scientific_journal-3571 47 30 supporting support VERB american_scientific_journal-3571 47 31 polygon polygon NOUN american_scientific_journal-3571 47 32 that that PRON american_scientific_journal-3571 47 33 is be AUX american_scientific_journal-3571 47 34 resulted result VERB american_scientific_journal-3571 47 35 from from ADP american_scientific_journal-3571 47 36 the the DET american_scientific_journal-3571 47 37 legs leg NOUN american_scientific_journal-3571 47 38 tips tip NOUN american_scientific_journal-3571 47 39 on on ADP american_scientific_journal-3571 47 40 the the DET american_scientific_journal-3571 47 41 ground ground NOUN american_scientific_journal-3571 47 42 . . PUNCT american_scientific_journal-3571 48 1 the the DET american_scientific_journal-3571 48 2 quadruped quadruped NOUN american_scientific_journal-3571 48 3 robot robot NOUN american_scientific_journal-3571 48 4 is be AUX american_scientific_journal-3571 48 5 design design NOUN american_scientific_journal-3571 48 6 in in ADP american_scientific_journal-3571 48 7 fig.(1 fig.(1 PROPN american_scientific_journal-3571 48 8 ) ) PUNCT american_scientific_journal-3571 48 9 , , PUNCT american_scientific_journal-3571 48 10 based base VERB american_scientific_journal-3571 48 11 on on ADP american_scientific_journal-3571 48 12 the the DET american_scientific_journal-3571 48 13 above above ADJ american_scientific_journal-3571 48 14 three three NUM american_scientific_journal-3571 48 15 criteria criterion NOUN american_scientific_journal-3571 48 16 . . PUNCT american_scientific_journal-3571 49 1 in in ADP american_scientific_journal-3571 49 2 this this DET american_scientific_journal-3571 49 3 research research NOUN american_scientific_journal-3571 49 4 the the DET american_scientific_journal-3571 49 5 walking walk VERB american_scientific_journal-3571 49 6 direction direction NOUN american_scientific_journal-3571 49 7 assumed assume VERB american_scientific_journal-3571 49 8 that that SCONJ american_scientific_journal-3571 49 9 the the DET american_scientific_journal-3571 49 10 quadruped quadruped NOUN american_scientific_journal-3571 49 11 robot robot NOUN american_scientific_journal-3571 49 12 is be AUX american_scientific_journal-3571 49 13 walking walk VERB american_scientific_journal-3571 49 14 foreword foreword NOUN american_scientific_journal-3571 49 15 along along ADP american_scientific_journal-3571 49 16 the the DET american_scientific_journal-3571 49 17 x x NOUN american_scientific_journal-3571 49 18 - - NOUN american_scientific_journal-3571 49 19 axis axis NOUN american_scientific_journal-3571 49 20 only only ADV american_scientific_journal-3571 49 21 . . PUNCT american_scientific_journal-3571 50 1 this this PRON american_scientific_journal-3571 50 2 means mean VERB american_scientific_journal-3571 50 3 that that SCONJ american_scientific_journal-3571 50 4 there there PRON american_scientific_journal-3571 50 5 is be VERB american_scientific_journal-3571 50 6 no no DET american_scientific_journal-3571 50 7 motion motion NOUN american_scientific_journal-3571 50 8 in in ADP american_scientific_journal-3571 50 9 the the DET american_scientific_journal-3571 50 10 y y ADJ american_scientific_journal-3571 50 11 - - PUNCT american_scientific_journal-3571 50 12 axis axis NOUN american_scientific_journal-3571 50 13 stride stride NOUN american_scientific_journal-3571 50 14 .so .so PUNCT american_scientific_journal-3571 50 15 the the DET american_scientific_journal-3571 50 16 stride stride NOUN american_scientific_journal-3571 50 17 of of ADP american_scientific_journal-3571 50 18 every every DET american_scientific_journal-3571 50 19 leg leg NOUN american_scientific_journal-3571 50 20 is be AUX american_scientific_journal-3571 50 21 a a DET american_scientific_journal-3571 50 22 line line NOUN american_scientific_journal-3571 50 23 . . PUNCT american_scientific_journal-3571 51 1 these these DET american_scientific_journal-3571 51 2 stride stride ADJ american_scientific_journal-3571 51 3 lines line NOUN american_scientific_journal-3571 51 4 are be AUX american_scientific_journal-3571 51 5 situated situate VERB american_scientific_journal-3571 51 6 in in ADP american_scientific_journal-3571 51 7 the the DET american_scientific_journal-3571 51 8 longitudinal longitudinal ADJ american_scientific_journal-3571 51 9 body body NOUN american_scientific_journal-3571 51 10 direction direction NOUN american_scientific_journal-3571 51 11 to to PART american_scientific_journal-3571 51 12 meet meet VERB american_scientific_journal-3571 51 13 the the DET american_scientific_journal-3571 51 14 condition condition NOUN american_scientific_journal-3571 51 15 of of ADP american_scientific_journal-3571 51 16 forward forward ADV american_scientific_journal-3571 51 17 walking walk VERB american_scientific_journal-3571 51 18 . . PUNCT american_scientific_journal-3571 52 1 figure figure VERB american_scientific_journal-3571 52 2 1 1 NUM american_scientific_journal-3571 52 3 : : PUNCT american_scientific_journal-3571 52 4 quadruped quadruped NOUN american_scientific_journal-3571 52 5 robot robot NOUN american_scientific_journal-3571 52 6 ( ( PUNCT american_scientific_journal-3571 52 7 top top ADJ american_scientific_journal-3571 52 8 view view NOUN american_scientific_journal-3571 52 9 ) ) PUNCT american_scientific_journal-3571 52 10 illustrate illustrate VERB american_scientific_journal-3571 52 11 the the DET american_scientific_journal-3571 52 12 length length NOUN american_scientific_journal-3571 52 13 ( ( PUNCT american_scientific_journal-3571 52 14 2b 2b NUM american_scientific_journal-3571 52 15 ) ) PUNCT american_scientific_journal-3571 52 16 and and CCONJ american_scientific_journal-3571 52 17 the the DET american_scientific_journal-3571 52 18 width width ADJ american_scientific_journal-3571 52 19 ( ( PUNCT american_scientific_journal-3571 52 20 2c 2c NOUN american_scientific_journal-3571 52 21 ) ) PUNCT american_scientific_journal-3571 52 22 and and CCONJ american_scientific_journal-3571 52 23 the the DET american_scientific_journal-3571 52 24 cog cog PROPN american_scientific_journal-3571 52 25 point point NOUN american_scientific_journal-3571 52 26 as as SCONJ american_scientific_journal-3571 52 27 seen see VERB american_scientific_journal-3571 52 28 in in ADP american_scientific_journal-3571 52 29 fig.(1 fig.(1 PROPN american_scientific_journal-3571 52 30 ) ) PUNCT american_scientific_journal-3571 52 31 , , PUNCT american_scientific_journal-3571 52 32 ( ( PUNCT american_scientific_journal-3571 52 33 2a 2a NUM american_scientific_journal-3571 52 34 ) ) PUNCT american_scientific_journal-3571 52 35 is be AUX american_scientific_journal-3571 52 36 the the DET american_scientific_journal-3571 52 37 distance distance NOUN american_scientific_journal-3571 52 38 between between ADP american_scientific_journal-3571 52 39 the the DET american_scientific_journal-3571 52 40 minimum minimum ADJ american_scientific_journal-3571 52 41 point point NOUN american_scientific_journal-3571 52 42 limit limit NOUN american_scientific_journal-3571 52 43 of of ADP american_scientific_journal-3571 52 44 the the DET american_scientific_journal-3571 52 45 front front ADJ american_scientific_journal-3571 52 46 leg leg NOUN american_scientific_journal-3571 52 47 stride stride NOUN american_scientific_journal-3571 52 48 line line NOUN american_scientific_journal-3571 52 49 to to ADP american_scientific_journal-3571 52 50 the the DET american_scientific_journal-3571 52 51 maximum maximum ADJ american_scientific_journal-3571 52 52 point point NOUN american_scientific_journal-3571 52 53 limit limit NOUN american_scientific_journal-3571 52 54 of of ADP american_scientific_journal-3571 52 55 the the DET american_scientific_journal-3571 52 56 back back ADJ american_scientific_journal-3571 52 57 leg leg NOUN american_scientific_journal-3571 52 58 . . PUNCT american_scientific_journal-3571 53 1 ( ( PUNCT american_scientific_journal-3571 53 2 2b 2b NUM american_scientific_journal-3571 53 3 ) ) PUNCT american_scientific_journal-3571 53 4 is be AUX american_scientific_journal-3571 53 5 the the DET american_scientific_journal-3571 53 6 distance distance NOUN american_scientific_journal-3571 53 7 between between ADP american_scientific_journal-3571 53 8 the the DET american_scientific_journal-3571 53 9 maximum maximum ADJ american_scientific_journal-3571 53 10 point point NOUN american_scientific_journal-3571 53 11 limit limit NOUN american_scientific_journal-3571 53 12 of of ADP american_scientific_journal-3571 53 13 the the DET american_scientific_journal-3571 53 14 front front ADJ american_scientific_journal-3571 53 15 leg leg NOUN american_scientific_journal-3571 53 16 stride stride NOUN american_scientific_journal-3571 53 17 line line NOUN american_scientific_journal-3571 53 18 to to ADP american_scientific_journal-3571 53 19 the the DET american_scientific_journal-3571 53 20 maximum maximum ADJ american_scientific_journal-3571 53 21 point point NOUN american_scientific_journal-3571 53 22 limit limit NOUN american_scientific_journal-3571 53 23 of of ADP american_scientific_journal-3571 53 24 the the DET american_scientific_journal-3571 53 25 back back ADJ american_scientific_journal-3571 53 26 leg leg NOUN american_scientific_journal-3571 53 27 . . PUNCT american_scientific_journal-3571 54 1 ( ( PUNCT american_scientific_journal-3571 54 2 2c 2c NOUN american_scientific_journal-3571 54 3 ) ) PUNCT american_scientific_journal-3571 54 4 is be AUX american_scientific_journal-3571 54 5 the the DET american_scientific_journal-3571 54 6 distance distance NOUN american_scientific_journal-3571 54 7 from from ADP american_scientific_journal-3571 54 8 front front ADJ american_scientific_journal-3571 54 9 / / SYM american_scientific_journal-3571 54 10 back back ADV american_scientific_journal-3571 54 11 left leave VERB american_scientific_journal-3571 54 12 leg leg NOUN american_scientific_journal-3571 54 13 stride stride NOUN american_scientific_journal-3571 54 14 line line NOUN american_scientific_journal-3571 54 15 to to ADP american_scientific_journal-3571 54 16 the the DET american_scientific_journal-3571 54 17 right right ADJ american_scientific_journal-3571 54 18 leg leg NOUN american_scientific_journal-3571 54 19 stride stride NOUN american_scientific_journal-3571 54 20 line line NOUN american_scientific_journal-3571 54 21 . . PUNCT american_scientific_journal-3571 55 1 so so ADV american_scientific_journal-3571 55 2 the the DET american_scientific_journal-3571 55 3 definition definition NOUN american_scientific_journal-3571 55 4 of of ADP american_scientific_journal-3571 55 5 the the DET american_scientific_journal-3571 55 6 leg leg NOUN american_scientific_journal-3571 55 7 stride stride NOUN american_scientific_journal-3571 55 8 line line NOUN american_scientific_journal-3571 55 9 is be AUX american_scientific_journal-3571 55 10 [ [ X american_scientific_journal-3571 55 11 13 13 NUM american_scientific_journal-3571 55 12 ] ] SYM american_scientific_journal-3571 55 13 : : PUNCT american_scientific_journal-3571 55 14 stride stride ADJ american_scientific_journal-3571 55 15 line line NOUN american_scientific_journal-3571 55 16 = = SYM american_scientific_journal-3571 55 17 b b PROPN american_scientific_journal-3571 55 18 – – PUNCT american_scientific_journal-3571 55 19 a a DET american_scientific_journal-3571 55 20 ( ( PUNCT american_scientific_journal-3571 55 21 1 1 NUM american_scientific_journal-3571 55 22 ) ) PUNCT american_scientific_journal-3571 55 23 along along ADP american_scientific_journal-3571 55 24 these these DET american_scientific_journal-3571 55 25 considerations consideration NOUN american_scientific_journal-3571 55 26 , , PUNCT american_scientific_journal-3571 55 27 the the DET american_scientific_journal-3571 55 28 largest large ADJ american_scientific_journal-3571 55 29 stride stride NOUN american_scientific_journal-3571 55 30 of of ADP american_scientific_journal-3571 55 31 the the DET american_scientific_journal-3571 55 32 reachable reachable ADJ american_scientific_journal-3571 55 33 area area NOUN american_scientific_journal-3571 55 34 for for ADP american_scientific_journal-3571 55 35 a a DET american_scientific_journal-3571 55 36 quadruped quadruped NOUN american_scientific_journal-3571 55 37 robot robot NOUN american_scientific_journal-3571 55 38 can can AUX american_scientific_journal-3571 55 39 be be AUX american_scientific_journal-3571 55 40 calculated calculate VERB american_scientific_journal-3571 55 41 from from ADP american_scientific_journal-3571 55 42 equ equ PROPN american_scientific_journal-3571 55 43 . . PROPN american_scientific_journal-3571 56 1 1 1 NUM american_scientific_journal-3571 56 2 . . PUNCT american_scientific_journal-3571 56 3 most most ADJ american_scientific_journal-3571 56 4 of of ADP american_scientific_journal-3571 56 5 quadruped quadruped NOUN american_scientific_journal-3571 56 6 robots robot NOUN american_scientific_journal-3571 56 7 have have VERB american_scientific_journal-3571 56 8 the the DET american_scientific_journal-3571 56 9 value value NOUN american_scientific_journal-3571 56 10 of of ADP american_scientific_journal-3571 56 11 length length NOUN american_scientific_journal-3571 56 12 equals equal VERB american_scientific_journal-3571 56 13 to to ADP american_scientific_journal-3571 56 14 2b 2b NUM american_scientific_journal-3571 56 15 and and CCONJ american_scientific_journal-3571 56 16 the the DET american_scientific_journal-3571 56 17 value value NOUN american_scientific_journal-3571 56 18 of of ADP american_scientific_journal-3571 56 19 width width NOUN american_scientific_journal-3571 56 20 equals equal VERB american_scientific_journal-3571 56 21 to to ADP american_scientific_journal-3571 56 22 2c 2c NUM american_scientific_journal-3571 56 23 . . PUNCT american_scientific_journal-3571 57 1 henceforth henceforth ADV american_scientific_journal-3571 57 2 , , PUNCT american_scientific_journal-3571 57 3 the the DET american_scientific_journal-3571 57 4 ratio ratio NOUN american_scientific_journal-3571 57 5 between between ADP american_scientific_journal-3571 57 6 the the DET american_scientific_journal-3571 57 7 length length NOUN american_scientific_journal-3571 57 8 and and CCONJ american_scientific_journal-3571 57 9 width width NOUN american_scientific_journal-3571 57 10 is be AUX american_scientific_journal-3571 57 11 equal equal ADJ american_scientific_journal-3571 57 12 to to ADP american_scientific_journal-3571 57 13 c c PROPN american_scientific_journal-3571 57 14 / / SYM american_scientific_journal-3571 57 15 b. b. PROPN american_scientific_journal-3571 57 16 in in ADP american_scientific_journal-3571 57 17 this this DET american_scientific_journal-3571 57 18 paper paper NOUN american_scientific_journal-3571 57 19 , , PUNCT american_scientific_journal-3571 57 20 the the DET american_scientific_journal-3571 57 21 simulation simulation NOUN american_scientific_journal-3571 57 22 design design VERB american_scientific_journal-3571 57 23 the the DET american_scientific_journal-3571 57 24 quadruped quadruped NOUN american_scientific_journal-3571 57 25 robot robot NOUN american_scientific_journal-3571 57 26 leg leg NOUN american_scientific_journal-3571 57 27 shown show VERB american_scientific_journal-3571 57 28 that that SCONJ american_scientific_journal-3571 57 29 it it PRON american_scientific_journal-3571 57 30 has have VERB american_scientific_journal-3571 57 31 three three NUM american_scientific_journal-3571 57 32 joints joint NOUN american_scientific_journal-3571 57 33 named name VERB american_scientific_journal-3571 57 34 as as ADP american_scientific_journal-3571 57 35 the the DET american_scientific_journal-3571 57 36 biological biological NOUN american_scientific_journal-3571 57 37 of of ADP american_scientific_journal-3571 57 38 the the DET american_scientific_journal-3571 57 39 nature nature NOUN american_scientific_journal-3571 57 40 insects insect NOUN american_scientific_journal-3571 57 41 as as ADP american_scientific_journal-3571 57 42 ( ( PUNCT american_scientific_journal-3571 57 43 coxa coxa ADJ american_scientific_journal-3571 57 44 joint joint NOUN american_scientific_journal-3571 57 45 , , PUNCT american_scientific_journal-3571 57 46 femur femur ADJ american_scientific_journal-3571 57 47 joint joint NOUN american_scientific_journal-3571 57 48 , , PUNCT american_scientific_journal-3571 57 49 tibia tibia NOUN american_scientific_journal-3571 57 50 joint joint NOUN american_scientific_journal-3571 57 51 ) ) PUNCT american_scientific_journal-3571 57 52 this this PRON american_scientific_journal-3571 57 53 make make VERB american_scientific_journal-3571 57 54 each each DET american_scientific_journal-3571 57 55 leg leg NOUN american_scientific_journal-3571 57 56 has have VERB american_scientific_journal-3571 57 57 three three NUM american_scientific_journal-3571 57 58 dof dof NOUN american_scientific_journal-3571 57 59 ( ( PUNCT american_scientific_journal-3571 57 60 degree degree NOUN american_scientific_journal-3571 57 61 of of ADP american_scientific_journal-3571 57 62 freedom freedom NOUN american_scientific_journal-3571 57 63 ) ) PUNCT american_scientific_journal-3571 57 64 . . PUNCT american_scientific_journal-3571 58 1 for for ADP american_scientific_journal-3571 58 2 all all DET american_scientific_journal-3571 58 3 legs leg NOUN american_scientific_journal-3571 58 4 , , PUNCT american_scientific_journal-3571 58 5 hence hence ADV american_scientific_journal-3571 58 6 , , PUNCT american_scientific_journal-3571 58 7 the the DET american_scientific_journal-3571 58 8 total total ADJ american_scientific_journal-3571 58 9 numbers number NOUN american_scientific_journal-3571 58 10 dofs dof NOUN american_scientific_journal-3571 58 11 equal equal ADJ american_scientific_journal-3571 58 12 to to ADP american_scientific_journal-3571 58 13 12 12 NUM american_scientific_journal-3571 58 14 . . PUNCT american_scientific_journal-3571 59 1 the the DET american_scientific_journal-3571 59 2 quadruped quadruped NOUN american_scientific_journal-3571 59 3 robot robot NOUN american_scientific_journal-3571 59 4 structure structure NOUN american_scientific_journal-3571 59 5 is be AUX american_scientific_journal-3571 59 6 showing show VERB american_scientific_journal-3571 59 7 in in ADP american_scientific_journal-3571 59 8 fig.(2 fig.(2 NOUN american_scientific_journal-3571 59 9 ) ) PUNCT american_scientific_journal-3571 59 10 . . PUNCT american_scientific_journal-3571 60 1 in in ADP american_scientific_journal-3571 60 2 fig.(2 fig.(2 PROPN american_scientific_journal-3571 60 3 - - PUNCT american_scientific_journal-3571 60 4 a a PRON american_scientific_journal-3571 60 5 ) ) PUNCT american_scientific_journal-3571 60 6 shows show VERB american_scientific_journal-3571 60 7 the the DET american_scientific_journal-3571 60 8 quadruped quadruped NOUN american_scientific_journal-3571 60 9 robot robot NOUN american_scientific_journal-3571 60 10 main main ADJ american_scientific_journal-3571 60 11 parts part NOUN american_scientific_journal-3571 60 12 that that PRON american_scientific_journal-3571 60 13 is be AUX american_scientific_journal-3571 60 14 mimic mimic VERB american_scientific_journal-3571 60 15 the the DET american_scientific_journal-3571 60 16 natural natural ADJ american_scientific_journal-3571 60 17 anatomy anatomy NOUN american_scientific_journal-3571 60 18 of of ADP american_scientific_journal-3571 60 19 insects insect NOUN american_scientific_journal-3571 60 20 and and CCONJ american_scientific_journal-3571 60 21 labeling labeling NOUN american_scientific_journal-3571 60 22 of of ADP american_scientific_journal-3571 60 23 each each DET american_scientific_journal-3571 60 24 leg leg NOUN american_scientific_journal-3571 60 25 . . PUNCT american_scientific_journal-3571 61 1 in in ADP american_scientific_journal-3571 61 2 fig.(2 fig.(2 PROPN american_scientific_journal-3571 61 3 - - PUNCT american_scientific_journal-3571 61 4 b b NOUN american_scientific_journal-3571 61 5 ) ) PUNCT american_scientific_journal-3571 61 6 shows show VERB american_scientific_journal-3571 61 7 the the DET american_scientific_journal-3571 61 8 leg leg NOUN american_scientific_journal-3571 61 9 joints joint NOUN american_scientific_journal-3571 61 10 and and CCONJ american_scientific_journal-3571 61 11 the the DET american_scientific_journal-3571 61 12 link link NOUN american_scientific_journal-3571 61 13 name name NOUN american_scientific_journal-3571 61 14 of of ADP american_scientific_journal-3571 61 15 each each DET american_scientific_journal-3571 61 16 joint joint NOUN american_scientific_journal-3571 61 17 in in ADP american_scientific_journal-3571 61 18 the the DET american_scientific_journal-3571 61 19 quadruped quadruped NOUN american_scientific_journal-3571 61 20 leg leg NOUN american_scientific_journal-3571 61 21 . . PUNCT american_scientific_journal-3571 62 1 leg1 leg1 NOUN american_scientific_journal-3571 62 2 is be AUX american_scientific_journal-3571 62 3 the the DET american_scientific_journal-3571 62 4 right right ADJ american_scientific_journal-3571 62 5 front front NOUN american_scientific_journal-3571 62 6 ( ( PUNCT american_scientific_journal-3571 62 7 rf rf NOUN american_scientific_journal-3571 62 8 ) ) PUNCT american_scientific_journal-3571 62 9 side side NOUN american_scientific_journal-3571 62 10 and and CCONJ american_scientific_journal-3571 62 11 leg3 leg3 ADJ american_scientific_journal-3571 62 12 is be AUX american_scientific_journal-3571 62 13 the the DET american_scientific_journal-3571 62 14 right right ADJ american_scientific_journal-3571 62 15 rear rear NOUN american_scientific_journal-3571 62 16 ( ( PUNCT american_scientific_journal-3571 62 17 rr rr NOUN american_scientific_journal-3571 62 18 ) ) PUNCT american_scientific_journal-3571 62 19 side side NOUN american_scientific_journal-3571 62 20 and and CCONJ american_scientific_journal-3571 62 21 leg2 leg2 NOUN american_scientific_journal-3571 62 22 is be AUX american_scientific_journal-3571 62 23 the the DET american_scientific_journal-3571 62 24 left left ADJ american_scientific_journal-3571 62 25 front front NOUN american_scientific_journal-3571 62 26 ( ( PUNCT american_scientific_journal-3571 62 27 lf lf NOUN american_scientific_journal-3571 62 28 ) ) PUNCT american_scientific_journal-3571 62 29 american american ADJ american_scientific_journal-3571 62 30 scientific scientific ADJ american_scientific_journal-3571 62 31 research research NOUN american_scientific_journal-3571 62 32 journal journal NOUN american_scientific_journal-3571 62 33 for for ADP american_scientific_journal-3571 62 34 engineering engineering NOUN american_scientific_journal-3571 62 35 , , PUNCT american_scientific_journal-3571 62 36 technology technology NOUN american_scientific_journal-3571 62 37 , , PUNCT american_scientific_journal-3571 62 38 and and CCONJ american_scientific_journal-3571 62 39 sciences science NOUN american_scientific_journal-3571 62 40 ( ( PUNCT american_scientific_journal-3571 62 41 asrjets asrjet NOUN american_scientific_journal-3571 62 42 ) ) PUNCT american_scientific_journal-3571 62 43 ( ( PUNCT american_scientific_journal-3571 62 44 2017 2017 NUM american_scientific_journal-3571 62 45 ) ) PUNCT american_scientific_journal-3571 62 46 volume volume NOUN american_scientific_journal-3571 62 47 38 38 NUM american_scientific_journal-3571 62 48 , , PUNCT american_scientific_journal-3571 62 49 no no DET american_scientific_journal-3571 62 50 1 1 NUM american_scientific_journal-3571 62 51 , , PUNCT american_scientific_journal-3571 62 52 pp pp ADV american_scientific_journal-3571 62 53 17 17 NUM american_scientific_journal-3571 62 54 - - SYM american_scientific_journal-3571 62 55 32 32 NUM american_scientific_journal-3571 62 56 20 20 NUM american_scientific_journal-3571 62 57 side side NOUN american_scientific_journal-3571 62 58 and and CCONJ american_scientific_journal-3571 62 59 leg4 leg4 NOUN american_scientific_journal-3571 62 60 is be AUX american_scientific_journal-3571 62 61 the the DET american_scientific_journal-3571 62 62 left left ADJ american_scientific_journal-3571 62 63 rear rear NOUN american_scientific_journal-3571 62 64 ( ( PUNCT american_scientific_journal-3571 62 65 lr lr NOUN american_scientific_journal-3571 62 66 ) ) PUNCT american_scientific_journal-3571 62 67 side side NOUN american_scientific_journal-3571 62 68 . . PUNCT american_scientific_journal-3571 63 1 and and CCONJ american_scientific_journal-3571 63 2 as as SCONJ american_scientific_journal-3571 63 3 mentioned mention VERB american_scientific_journal-3571 63 4 before before ADV american_scientific_journal-3571 63 5 , , PUNCT american_scientific_journal-3571 63 6 the the DET american_scientific_journal-3571 63 7 forward forward ADJ american_scientific_journal-3571 63 8 direction direction NOUN american_scientific_journal-3571 63 9 of of ADP american_scientific_journal-3571 63 10 motion motion NOUN american_scientific_journal-3571 63 11 of of ADP american_scientific_journal-3571 63 12 the the DET american_scientific_journal-3571 63 13 quadruped quadruped NOUN american_scientific_journal-3571 63 14 robot robot NOUN american_scientific_journal-3571 63 15 , , PUNCT american_scientific_journal-3571 63 16 in in ADP american_scientific_journal-3571 63 17 case case NOUN american_scientific_journal-3571 63 18 of of ADP american_scientific_journal-3571 63 19 the the DET american_scientific_journal-3571 63 20 forward forward ADJ american_scientific_journal-3571 63 21 direction direction NOUN american_scientific_journal-3571 63 22 of of ADP american_scientific_journal-3571 63 23 motion motion NOUN american_scientific_journal-3571 63 24 is be AUX american_scientific_journal-3571 63 25 set set VERB american_scientific_journal-3571 63 26 to to PART american_scientific_journal-3571 63 27 be be AUX american_scientific_journal-3571 63 28 with with ADP american_scientific_journal-3571 63 29 the the DET american_scientific_journal-3571 63 30 x x ADJ american_scientific_journal-3571 63 31 - - ADJ american_scientific_journal-3571 63 32 axis axis ADJ american_scientific_journal-3571 63 33 direction direction NOUN american_scientific_journal-3571 63 34 and and CCONJ american_scientific_journal-3571 63 35 the the DET american_scientific_journal-3571 63 36 lateral lateral ADJ american_scientific_journal-3571 63 37 motion motion NOUN american_scientific_journal-3571 63 38 of of ADP american_scientific_journal-3571 63 39 the the DET american_scientific_journal-3571 63 40 quadruped quadruped NOUN american_scientific_journal-3571 63 41 robot robot NOUN american_scientific_journal-3571 63 42 will will AUX american_scientific_journal-3571 63 43 be be AUX american_scientific_journal-3571 63 44 in in ADP american_scientific_journal-3571 63 45 y y NOUN american_scientific_journal-3571 63 46 - - PUNCT american_scientific_journal-3571 63 47 axis axis NOUN american_scientific_journal-3571 63 48 . . PUNCT american_scientific_journal-3571 64 1 the the DET american_scientific_journal-3571 64 2 quadruped quadruped NOUN american_scientific_journal-3571 64 3 body body NOUN american_scientific_journal-3571 64 4 has have VERB american_scientific_journal-3571 64 5 a a DET american_scientific_journal-3571 64 6 symmetrical symmetrical ADJ american_scientific_journal-3571 64 7 dimension dimension NOUN american_scientific_journal-3571 64 8 in in ADP american_scientific_journal-3571 64 9 x x PROPN american_scientific_journal-3571 64 10 and and CCONJ american_scientific_journal-3571 64 11 y y PROPN american_scientific_journal-3571 64 12 axes axis NOUN american_scientific_journal-3571 64 13 . . PUNCT american_scientific_journal-3571 65 1 which which PRON american_scientific_journal-3571 65 2 giving give VERB american_scientific_journal-3571 65 3 the the DET american_scientific_journal-3571 65 4 robot robot NOUN american_scientific_journal-3571 65 5 better well ADJ american_scientific_journal-3571 65 6 stability stability NOUN american_scientific_journal-3571 65 7 during during ADP american_scientific_journal-3571 65 8 the the DET american_scientific_journal-3571 65 9 walking walking NOUN american_scientific_journal-3571 65 10 and and CCONJ american_scientific_journal-3571 65 11 making make VERB american_scientific_journal-3571 65 12 it it PRON american_scientific_journal-3571 65 13 statically statically ADV american_scientific_journal-3571 65 14 stable stable ADJ american_scientific_journal-3571 65 15 . . PUNCT american_scientific_journal-3571 66 1 ( ( PUNCT american_scientific_journal-3571 66 2 a a X american_scientific_journal-3571 66 3 ) ) PUNCT american_scientific_journal-3571 66 4 ( ( PUNCT american_scientific_journal-3571 66 5 b b X american_scientific_journal-3571 66 6 ) ) PUNCT american_scientific_journal-3571 66 7 figure figure NOUN american_scientific_journal-3571 66 8 2 2 NUM american_scientific_journal-3571 66 9 : : PUNCT american_scientific_journal-3571 66 10 quadruped quadruped NOUN american_scientific_journal-3571 66 11 robot robot NOUN american_scientific_journal-3571 66 12 simulation simulation NOUN american_scientific_journal-3571 66 13 using use VERB american_scientific_journal-3571 66 14 matlab matlab PROPN american_scientific_journal-3571 66 15 ( ( PUNCT american_scientific_journal-3571 66 16 a a NOUN american_scientific_journal-3571 66 17 ) ) PUNCT american_scientific_journal-3571 66 18 quadruped quadruped NOUN american_scientific_journal-3571 66 19 robot robot NOUN american_scientific_journal-3571 66 20 with with ADP american_scientific_journal-3571 66 21 four four NUM american_scientific_journal-3571 66 22 legs leg NOUN american_scientific_journal-3571 66 23 labeling labeling NOUN american_scientific_journal-3571 66 24 ( ( PUNCT american_scientific_journal-3571 66 25 b b NOUN american_scientific_journal-3571 66 26 ) ) PUNCT american_scientific_journal-3571 66 27 showing show VERB american_scientific_journal-3571 66 28 the the DET american_scientific_journal-3571 66 29 three three NUM american_scientific_journal-3571 66 30 joints joint NOUN american_scientific_journal-3571 66 31 ( ( PUNCT american_scientific_journal-3571 66 32 coxa coxa ADJ american_scientific_journal-3571 66 33 , , PUNCT american_scientific_journal-3571 66 34 femur femur ADJ american_scientific_journal-3571 66 35 , , PUNCT american_scientific_journal-3571 66 36 and and CCONJ american_scientific_journal-3571 66 37 tibia tibia NOUN american_scientific_journal-3571 66 38 ) ) PUNCT american_scientific_journal-3571 66 39 in in ADP american_scientific_journal-3571 66 40 each each DET american_scientific_journal-3571 66 41 legs leg NOUN american_scientific_journal-3571 66 42 . . PUNCT american_scientific_journal-3571 67 1 the the DET american_scientific_journal-3571 67 2 main main ADJ american_scientific_journal-3571 67 3 point point NOUN american_scientific_journal-3571 67 4 to to PART american_scientific_journal-3571 67 5 ensure ensure VERB american_scientific_journal-3571 67 6 the the DET american_scientific_journal-3571 67 7 stable stable ADJ american_scientific_journal-3571 67 8 walking walking NOUN american_scientific_journal-3571 67 9 in in ADP american_scientific_journal-3571 67 10 the the DET american_scientific_journal-3571 67 11 statically statically ADV american_scientific_journal-3571 67 12 stable stable ADJ american_scientific_journal-3571 67 13 gait gait NOUN american_scientific_journal-3571 67 14 , , PUNCT american_scientific_journal-3571 67 15 the the DET american_scientific_journal-3571 67 16 quadruped quadruped NOUN american_scientific_journal-3571 67 17 legs leg NOUN american_scientific_journal-3571 67 18 positions position NOUN american_scientific_journal-3571 67 19 are be AUX american_scientific_journal-3571 67 20 playing play VERB american_scientific_journal-3571 67 21 an an DET american_scientific_journal-3571 67 22 important important ADJ american_scientific_journal-3571 67 23 role role NOUN american_scientific_journal-3571 67 24 during during ADP american_scientific_journal-3571 67 25 the the DET american_scientific_journal-3571 67 26 walking walking NOUN american_scientific_journal-3571 67 27 of of ADP american_scientific_journal-3571 67 28 the the DET american_scientific_journal-3571 67 29 stability stability NOUN american_scientific_journal-3571 67 30 calculations calculation NOUN american_scientific_journal-3571 67 31 . . PUNCT american_scientific_journal-3571 68 1 the the DET american_scientific_journal-3571 68 2 legs leg NOUN american_scientific_journal-3571 68 3 tips tips NOUN american_scientific_journal-3571 68 4 positions position NOUN american_scientific_journal-3571 68 5 should should AUX american_scientific_journal-3571 68 6 be be AUX american_scientific_journal-3571 68 7 found find VERB american_scientific_journal-3571 68 8 by by ADP american_scientific_journal-3571 68 9 driving drive VERB american_scientific_journal-3571 68 10 the the DET american_scientific_journal-3571 68 11 forward forward ADJ american_scientific_journal-3571 68 12 kinematics kinematic NOUN american_scientific_journal-3571 68 13 and and CCONJ american_scientific_journal-3571 68 14 inverse inverse NOUN american_scientific_journal-3571 68 15 kinematics kinematic NOUN american_scientific_journal-3571 68 16 for for ADP american_scientific_journal-3571 68 17 the the DET american_scientific_journal-3571 68 18 quadruped quadruped NOUN american_scientific_journal-3571 68 19 robot robot NOUN american_scientific_journal-3571 68 20 . . PUNCT american_scientific_journal-3571 69 1 3 3 X american_scientific_journal-3571 69 2 . . X american_scientific_journal-3571 69 3 creeping creep VERB american_scientific_journal-3571 69 4 gait gait ADJ american_scientific_journal-3571 69 5 analysis analysis NOUN american_scientific_journal-3571 69 6 and and CCONJ american_scientific_journal-3571 69 7 sequence sequence NOUN american_scientific_journal-3571 69 8 description description NOUN american_scientific_journal-3571 69 9 the the DET american_scientific_journal-3571 69 10 quadruped quadruped NOUN american_scientific_journal-3571 69 11 robots robot NOUN american_scientific_journal-3571 69 12 have have VERB american_scientific_journal-3571 69 13 three three NUM american_scientific_journal-3571 69 14 main main ADJ american_scientific_journal-3571 69 15 gaits gait NOUN american_scientific_journal-3571 69 16 . . PUNCT american_scientific_journal-3571 70 1 this this DET american_scientific_journal-3571 70 2 gaits gait NOUN american_scientific_journal-3571 70 3 are be AUX american_scientific_journal-3571 70 4 classified classify VERB american_scientific_journal-3571 70 5 according accord VERB american_scientific_journal-3571 70 6 to to ADP american_scientific_journal-3571 70 7 its its PRON american_scientific_journal-3571 70 8 duty duty NOUN american_scientific_journal-3571 70 9 factor factor NOUN american_scientific_journal-3571 70 10 ( ( PUNCT american_scientific_journal-3571 70 11 𝛽𝛽𝑖𝑖 𝛽𝛽𝑖𝑖 INTJ american_scientific_journal-3571 70 12 ) ) PUNCT american_scientific_journal-3571 70 13 of of ADP american_scientific_journal-3571 70 14 each each DET american_scientific_journal-3571 70 15 leg leg NOUN american_scientific_journal-3571 70 16 , , PUNCT american_scientific_journal-3571 70 17 where where SCONJ american_scientific_journal-3571 70 18 i=1,,,4 i=1,,,4 ADJ american_scientific_journal-3571 70 19 . . PUNCT american_scientific_journal-3571 71 1 these these DET american_scientific_journal-3571 71 2 gaits gait NOUN american_scientific_journal-3571 71 3 are be AUX american_scientific_journal-3571 71 4 named name VERB american_scientific_journal-3571 71 5 from from ADP american_scientific_journal-3571 71 6 the the DET american_scientific_journal-3571 71 7 biological biological ADJ american_scientific_journal-3571 71 8 natural natural ADJ american_scientific_journal-3571 71 9 gaits gait NOUN american_scientific_journal-3571 71 10 of of ADP american_scientific_journal-3571 71 11 animals animal NOUN american_scientific_journal-3571 71 12 such such ADJ american_scientific_journal-3571 71 13 as as ADP american_scientific_journal-3571 71 14 crawl crawl NOUN american_scientific_journal-3571 71 15 gait gait NOUN american_scientific_journal-3571 71 16 , , PUNCT american_scientific_journal-3571 71 17 running run VERB american_scientific_journal-3571 71 18 gait gait NOUN american_scientific_journal-3571 71 19 , , PUNCT american_scientific_journal-3571 71 20 and and CCONJ american_scientific_journal-3571 71 21 the the DET american_scientific_journal-3571 71 22 galloping gallop VERB american_scientific_journal-3571 71 23 gait gait NOUN american_scientific_journal-3571 71 24 . . PUNCT american_scientific_journal-3571 72 1 the the DET american_scientific_journal-3571 72 2 quadruped quadruped NOUN american_scientific_journal-3571 72 3 robot robot NOUN american_scientific_journal-3571 72 4 locomotion locomotion NOUN american_scientific_journal-3571 72 5 has have VERB american_scientific_journal-3571 72 6 any any DET american_scientific_journal-3571 72 7 type type NOUN american_scientific_journal-3571 72 8 from from ADP american_scientific_journal-3571 72 9 these these DET american_scientific_journal-3571 72 10 gaits gait NOUN american_scientific_journal-3571 72 11 according accord VERB american_scientific_journal-3571 72 12 to to ADP american_scientific_journal-3571 72 13 its its PRON american_scientific_journal-3571 72 14 duty duty NOUN american_scientific_journal-3571 72 15 factor factor NOUN american_scientific_journal-3571 72 16 ( ( PUNCT american_scientific_journal-3571 72 17 𝛽𝛽𝑖𝑖 𝛽𝛽𝑖𝑖 INTJ american_scientific_journal-3571 72 18 ) ) PUNCT american_scientific_journal-3571 72 19 which which PRON american_scientific_journal-3571 72 20 is be AUX american_scientific_journal-3571 72 21 defined define VERB american_scientific_journal-3571 72 22 as as ADP american_scientific_journal-3571 72 23 the the DET american_scientific_journal-3571 72 24 ratio ratio NOUN american_scientific_journal-3571 72 25 of of ADP american_scientific_journal-3571 72 26 the the DET american_scientific_journal-3571 72 27 time time NOUN american_scientific_journal-3571 72 28 periods period NOUN american_scientific_journal-3571 72 29 between between ADP american_scientific_journal-3571 72 30 the the DET american_scientific_journal-3571 72 31 leg leg NOUN american_scientific_journal-3571 72 32 period period NOUN american_scientific_journal-3571 72 33 of of ADP american_scientific_journal-3571 72 34 swinging swinge VERB american_scientific_journal-3571 72 35 to to ADP american_scientific_journal-3571 72 36 the the DET american_scientific_journal-3571 72 37 period period NOUN american_scientific_journal-3571 72 38 that that PRON american_scientific_journal-3571 72 39 the the DET american_scientific_journal-3571 72 40 same same ADJ american_scientific_journal-3571 72 41 leg leg NOUN american_scientific_journal-3571 72 42 is be AUX american_scientific_journal-3571 72 43 contact contact NOUN american_scientific_journal-3571 72 44 with with ADP american_scientific_journal-3571 72 45 the the DET american_scientific_journal-3571 72 46 ground ground NOUN american_scientific_journal-3571 72 47 . . PUNCT american_scientific_journal-3571 73 1 when when SCONJ american_scientific_journal-3571 73 2 the the DET american_scientific_journal-3571 73 3 quadruped quadruped NOUN american_scientific_journal-3571 73 4 robot robot NOUN american_scientific_journal-3571 73 5 walks walk VERB american_scientific_journal-3571 73 6 using use VERB american_scientific_journal-3571 73 7 creeping creep VERB american_scientific_journal-3571 73 8 gait gait NOUN american_scientific_journal-3571 73 9 , , PUNCT american_scientific_journal-3571 73 10 the the DET american_scientific_journal-3571 73 11 value value NOUN american_scientific_journal-3571 73 12 of of ADP american_scientific_journal-3571 73 13 the the DET american_scientific_journal-3571 73 14 duty duty NOUN american_scientific_journal-3571 73 15 factor factor NOUN american_scientific_journal-3571 73 16 will will AUX american_scientific_journal-3571 73 17 equals equal VERB american_scientific_journal-3571 73 18 to to ADP american_scientific_journal-3571 73 19 0.75 0.75 NUM american_scientific_journal-3571 73 20 . . PUNCT american_scientific_journal-3571 74 1 when when SCONJ american_scientific_journal-3571 74 2 the the DET american_scientific_journal-3571 74 3 quadruped quadruped NOUN american_scientific_journal-3571 74 4 robot robot NOUN american_scientific_journal-3571 74 5 is be AUX american_scientific_journal-3571 74 6 running run VERB american_scientific_journal-3571 74 7 , , PUNCT american_scientific_journal-3571 74 8 it it PRON american_scientific_journal-3571 74 9 will will AUX american_scientific_journal-3571 74 10 have have VERB american_scientific_journal-3571 74 11 duty duty NOUN american_scientific_journal-3571 74 12 factor factor NOUN american_scientific_journal-3571 74 13 ranged range VERB american_scientific_journal-3571 74 14 between between ADP american_scientific_journal-3571 74 15 0.5 0.5 NUM american_scientific_journal-3571 74 16 - - SYM american_scientific_journal-3571 74 17 0.75 0.75 NUM american_scientific_journal-3571 74 18 . . PUNCT american_scientific_journal-3571 75 1 finally finally ADV american_scientific_journal-3571 75 2 when when SCONJ american_scientific_journal-3571 75 3 the the DET american_scientific_journal-3571 75 4 quadruped quadruped NOUN american_scientific_journal-3571 75 5 robot robot NOUN american_scientific_journal-3571 75 6 is be AUX american_scientific_journal-3571 75 7 galloping gallop VERB american_scientific_journal-3571 75 8 , , PUNCT american_scientific_journal-3571 75 9 it it PRON american_scientific_journal-3571 75 10 will will AUX american_scientific_journal-3571 75 11 have have VERB american_scientific_journal-3571 75 12 duty duty NOUN american_scientific_journal-3571 75 13 factor factor NOUN american_scientific_journal-3571 75 14 less less ADJ american_scientific_journal-3571 75 15 than than ADP american_scientific_journal-3571 75 16 0.5 0.5 NUM american_scientific_journal-3571 75 17 . . PUNCT american_scientific_journal-3571 76 1 these these DET american_scientific_journal-3571 76 2 main main ADJ american_scientific_journal-3571 76 3 gaits gait NOUN american_scientific_journal-3571 76 4 in in ADP american_scientific_journal-3571 76 5 the the DET american_scientific_journal-3571 76 6 robotics robotic NOUN american_scientific_journal-3571 76 7 field field NOUN american_scientific_journal-3571 76 8 have have AUX american_scientific_journal-3571 76 9 also also ADV american_scientific_journal-3571 76 10 been be AUX american_scientific_journal-3571 76 11 given give VERB american_scientific_journal-3571 76 12 a a DET american_scientific_journal-3571 76 13 name name NOUN american_scientific_journal-3571 76 14 , , PUNCT american_scientific_journal-3571 76 15 these these DET american_scientific_journal-3571 76 16 names name NOUN american_scientific_journal-3571 76 17 are be AUX american_scientific_journal-3571 76 18 called call VERB american_scientific_journal-3571 76 19 : : PUNCT american_scientific_journal-3571 76 20 creeping creep VERB american_scientific_journal-3571 76 21 gait gait NOUN american_scientific_journal-3571 76 22 , , PUNCT american_scientific_journal-3571 76 23 trotting trotting NOUN american_scientific_journal-3571 76 24 gait gait NOUN american_scientific_journal-3571 76 25 and and CCONJ american_scientific_journal-3571 76 26 the the DET american_scientific_journal-3571 76 27 bounding bounding NOUN american_scientific_journal-3571 76 28 gait gait NOUN american_scientific_journal-3571 77 1 [ [ X american_scientific_journal-3571 77 2 15 15 NUM american_scientific_journal-3571 77 3 ] ] PUNCT american_scientific_journal-3571 77 4 . . PUNCT american_scientific_journal-3571 78 1 hence hence ADV american_scientific_journal-3571 78 2 , , PUNCT american_scientific_journal-3571 78 3 these these DET american_scientific_journal-3571 78 4 gaits gait NOUN american_scientific_journal-3571 78 5 have have AUX american_scientific_journal-3571 78 6 been be AUX american_scientific_journal-3571 78 7 used use VERB american_scientific_journal-3571 78 8 by by ADP american_scientific_journal-3571 78 9 mammals mammal NOUN american_scientific_journal-3571 78 10 . . PUNCT american_scientific_journal-3571 79 1 for for ADP american_scientific_journal-3571 79 2 example example NOUN american_scientific_journal-3571 79 3 , , PUNCT american_scientific_journal-3571 79 4 cats cat NOUN american_scientific_journal-3571 79 5 are be AUX american_scientific_journal-3571 79 6 using use VERB american_scientific_journal-3571 79 7 the the DET american_scientific_journal-3571 79 8 creeping creep VERB american_scientific_journal-3571 79 9 gait gait NOUN american_scientific_journal-3571 79 10 for for ADP american_scientific_journal-3571 79 11 a a DET american_scientific_journal-3571 79 12 very very ADV american_scientific_journal-3571 79 13 slow slow ADJ american_scientific_journal-3571 79 14 walking walking NOUN american_scientific_journal-3571 79 15 . . PUNCT american_scientific_journal-3571 80 1 creeping creep VERB american_scientific_journal-3571 80 2 gait gait NOUN american_scientific_journal-3571 80 3 has have VERB american_scientific_journal-3571 80 4 some some DET american_scientific_journal-3571 80 5 advantages advantage NOUN american_scientific_journal-3571 80 6 , , PUNCT american_scientific_journal-3571 80 7 this this DET american_scientific_journal-3571 80 8 gait gait NOUN american_scientific_journal-3571 80 9 is be AUX american_scientific_journal-3571 80 10 ensure ensure VERB american_scientific_journal-3571 80 11 the the DET american_scientific_journal-3571 80 12 statically statically ADV american_scientific_journal-3571 80 13 stable stable ADJ american_scientific_journal-3571 80 14 movement movement NOUN american_scientific_journal-3571 80 15 which which PRON american_scientific_journal-3571 80 16 is be AUX american_scientific_journal-3571 80 17 used use VERB american_scientific_journal-3571 80 18 with with ADP american_scientific_journal-3571 80 19 the the DET american_scientific_journal-3571 80 20 range range NOUN american_scientific_journal-3571 80 21 of of ADP american_scientific_journal-3571 80 22 low low ADJ american_scientific_journal-3571 80 23 - - PUNCT american_scientific_journal-3571 80 24 speed speed NOUN american_scientific_journal-3571 80 25 walking walking NOUN american_scientific_journal-3571 80 26 . . PUNCT american_scientific_journal-3571 81 1 the the DET american_scientific_journal-3571 81 2 sequence sequence NOUN american_scientific_journal-3571 81 3 condition condition NOUN american_scientific_journal-3571 81 4 of of ADP american_scientific_journal-3571 81 5 the the DET american_scientific_journal-3571 81 6 creeping creep VERB american_scientific_journal-3571 81 7 gait gait NOUN american_scientific_journal-3571 81 8 is be AUX american_scientific_journal-3571 81 9 need need VERB american_scientific_journal-3571 81 10 a a DET american_scientific_journal-3571 81 11 three three NUM american_scientific_journal-3571 81 12 legs leg NOUN american_scientific_journal-3571 81 13 at at ADV american_scientific_journal-3571 81 14 least least ADJ american_scientific_journal-3571 81 15 are be AUX american_scientific_journal-3571 81 16 contact contact NOUN american_scientific_journal-3571 81 17 with with ADP american_scientific_journal-3571 81 18 the the DET american_scientific_journal-3571 81 19 ground ground NOUN american_scientific_journal-3571 81 20 when when SCONJ american_scientific_journal-3571 81 21 the the DET american_scientific_journal-3571 81 22 fourth fourth ADJ american_scientific_journal-3571 81 23 leg leg NOUN american_scientific_journal-3571 81 24 are be AUX american_scientific_journal-3571 81 25 swing swe VERB american_scientific_journal-3571 81 26 to to PART american_scientific_journal-3571 81 27 translate translate VERB american_scientific_journal-3571 81 28 to to ADP american_scientific_journal-3571 81 29 new new ADJ american_scientific_journal-3571 81 30 position position NOUN american_scientific_journal-3571 81 31 . . PUNCT american_scientific_journal-3571 82 1 this this DET american_scientific_journal-3571 82 2 sequence sequence NOUN american_scientific_journal-3571 82 3 condition condition NOUN american_scientific_journal-3571 82 4 is be AUX american_scientific_journal-3571 82 5 needed need VERB american_scientific_journal-3571 82 6 to to PART american_scientific_journal-3571 82 7 ensure ensure VERB american_scientific_journal-3571 82 8 the the DET american_scientific_journal-3571 82 9 statically statically ADV american_scientific_journal-3571 82 10 stable stable ADJ american_scientific_journal-3571 82 11 gait gait NOUN american_scientific_journal-3571 82 12 . . PUNCT american_scientific_journal-3571 83 1 the the DET american_scientific_journal-3571 83 2 quadruped quadruped NOUN american_scientific_journal-3571 83 3 robot robot NOUN american_scientific_journal-3571 83 4 creeping creeping NOUN american_scientific_journal-3571 83 5 gait gait PROPN american_scientific_journal-3571 83 6 sequence sequence NOUN american_scientific_journal-3571 83 7 has have VERB american_scientific_journal-3571 83 8 six six NUM american_scientific_journal-3571 83 9 types type NOUN american_scientific_journal-3571 83 10 of of ADP american_scientific_journal-3571 83 11 legs leg NOUN american_scientific_journal-3571 83 12 arrangement arrangement NOUN american_scientific_journal-3571 83 13 . . PUNCT american_scientific_journal-3571 84 1 in in ADP american_scientific_journal-3571 84 2 this this DET american_scientific_journal-3571 84 3 paper paper NOUN american_scientific_journal-3571 84 4 , , PUNCT american_scientific_journal-3571 84 5 quadruped quadrupe VERB american_scientific_journal-3571 84 6 robot robot NOUN american_scientific_journal-3571 84 7 leg leg NOUN american_scientific_journal-3571 84 8 sequence sequence NOUN american_scientific_journal-3571 84 9 is be AUX american_scientific_journal-3571 84 10 ( ( PUNCT american_scientific_journal-3571 84 11 rr rr NOUN american_scientific_journal-3571 84 12 , , PUNCT american_scientific_journal-3571 84 13 rf rf ADJ american_scientific_journal-3571 84 14 , , PUNCT american_scientific_journal-3571 84 15 lr lr NOUN american_scientific_journal-3571 84 16 , , PUNCT american_scientific_journal-3571 84 17 and and CCONJ american_scientific_journal-3571 84 18 lf lf INTJ american_scientific_journal-3571 84 19 ) ) PUNCT american_scientific_journal-3571 84 20 where where SCONJ american_scientific_journal-3571 84 21 ( ( PUNCT american_scientific_journal-3571 84 22 r r NOUN american_scientific_journal-3571 84 23 : : PUNCT american_scientific_journal-3571 84 24 right right ADJ american_scientific_journal-3571 84 25 , , PUNCT american_scientific_journal-3571 84 26 l l NOUN american_scientific_journal-3571 84 27 : : PUNCT american_scientific_journal-3571 84 28 left leave VERB american_scientific_journal-3571 84 29 , , PUNCT american_scientific_journal-3571 84 30 r r NOUN american_scientific_journal-3571 84 31 : : PUNCT american_scientific_journal-3571 84 32 rear rear ADJ american_scientific_journal-3571 84 33 , , PUNCT american_scientific_journal-3571 84 34 f f X american_scientific_journal-3571 84 35 : : PUNCT american_scientific_journal-3571 84 36 front front ADJ american_scientific_journal-3571 84 37 ) ) PUNCT american_scientific_journal-3571 84 38 . . PUNCT american_scientific_journal-3571 85 1 from from ADP american_scientific_journal-3571 85 2 the the DET american_scientific_journal-3571 85 3 labeling labeling NOUN american_scientific_journal-3571 85 4 fig.(2)-a fig.(2)-a NOUN american_scientific_journal-3571 85 5 , , PUNCT american_scientific_journal-3571 85 6 it it PRON american_scientific_journal-3571 85 7 can can AUX american_scientific_journal-3571 85 8 be be AUX american_scientific_journal-3571 85 9 seen see VERB american_scientific_journal-3571 85 10 that that SCONJ american_scientific_journal-3571 85 11 rr rr PROPN american_scientific_journal-3571 85 12 is be AUX american_scientific_journal-3571 85 13 leg4 leg4 NOUN american_scientific_journal-3571 85 14 , , PUNCT american_scientific_journal-3571 85 15 rf rf NOUN american_scientific_journal-3571 85 16 is be AUX american_scientific_journal-3571 85 17 leg2 leg2 PROPN american_scientific_journal-3571 85 18 , , PUNCT american_scientific_journal-3571 85 19 lr lr PROPN american_scientific_journal-3571 85 20 is be AUX american_scientific_journal-3571 85 21 leg3 leg3 ADJ american_scientific_journal-3571 85 22 , , PUNCT american_scientific_journal-3571 85 23 and and CCONJ american_scientific_journal-3571 85 24 lf lf PROPN american_scientific_journal-3571 85 25 is be AUX american_scientific_journal-3571 85 26 leg1 leg1 VERB american_scientific_journal-3571 85 27 . . PUNCT american_scientific_journal-3571 86 1 the the DET american_scientific_journal-3571 86 2 advantage advantage NOUN american_scientific_journal-3571 86 3 of of ADP american_scientific_journal-3571 86 4 choosing choose VERB american_scientific_journal-3571 86 5 this this DET american_scientific_journal-3571 86 6 leg leg NOUN american_scientific_journal-3571 86 7 sequence sequence NOUN american_scientific_journal-3571 86 8 arrangement arrangement NOUN american_scientific_journal-3571 86 9 to to PART american_scientific_journal-3571 86 10 have have VERB american_scientific_journal-3571 86 11 a a DET american_scientific_journal-3571 86 12 safety safety NOUN american_scientific_journal-3571 86 13 walking walking NOUN american_scientific_journal-3571 86 14 which which PRON american_scientific_journal-3571 86 15 is be AUX american_scientific_journal-3571 86 16 ensure ensure VERB american_scientific_journal-3571 86 17 that that SCONJ american_scientific_journal-3571 86 18 the the DET american_scientific_journal-3571 86 19 robot robot NOUN american_scientific_journal-3571 86 20 is be AUX american_scientific_journal-3571 86 21 body body NOUN american_scientific_journal-3571 86 22 moving move VERB american_scientific_journal-3571 86 23 forward forward ADV american_scientific_journal-3571 86 24 at at ADP american_scientific_journal-3571 86 25 the the DET american_scientific_journal-3571 86 26 instance instance NOUN american_scientific_journal-3571 86 27 time[12 time[12 PROPN american_scientific_journal-3571 86 28 ] ] PUNCT american_scientific_journal-3571 86 29 . . PUNCT american_scientific_journal-3571 87 1 there there PRON american_scientific_journal-3571 87 2 are be VERB american_scientific_journal-3571 87 3 two two NUM american_scientific_journal-3571 87 4 cartesian cartesian ADJ american_scientific_journal-3571 87 5 american american ADJ american_scientific_journal-3571 87 6 scientific scientific ADJ american_scientific_journal-3571 87 7 research research NOUN american_scientific_journal-3571 87 8 journal journal NOUN american_scientific_journal-3571 87 9 for for ADP american_scientific_journal-3571 87 10 engineering engineering NOUN american_scientific_journal-3571 87 11 , , PUNCT american_scientific_journal-3571 87 12 technology technology NOUN american_scientific_journal-3571 87 13 , , PUNCT american_scientific_journal-3571 87 14 and and CCONJ american_scientific_journal-3571 87 15 sciences science NOUN american_scientific_journal-3571 87 16 ( ( PUNCT american_scientific_journal-3571 87 17 asrjets asrjet NOUN american_scientific_journal-3571 87 18 ) ) PUNCT american_scientific_journal-3571 87 19 ( ( PUNCT american_scientific_journal-3571 87 20 2017 2017 NUM american_scientific_journal-3571 87 21 ) ) PUNCT american_scientific_journal-3571 87 22 volume volume NOUN american_scientific_journal-3571 87 23 38 38 NUM american_scientific_journal-3571 87 24 , , PUNCT american_scientific_journal-3571 87 25 no no DET american_scientific_journal-3571 87 26 1 1 NUM american_scientific_journal-3571 87 27 , , PUNCT american_scientific_journal-3571 87 28 pp pp ADV american_scientific_journal-3571 87 29 17 17 NUM american_scientific_journal-3571 87 30 - - SYM american_scientific_journal-3571 87 31 32 32 NUM american_scientific_journal-3571 87 32 21 21 NUM american_scientific_journal-3571 87 33 reference reference NOUN american_scientific_journal-3571 87 34 frames frame NOUN american_scientific_journal-3571 87 35 coordinate coordinate VERB american_scientific_journal-3571 87 36 when when SCONJ american_scientific_journal-3571 87 37 talking talk VERB american_scientific_journal-3571 87 38 about about ADP american_scientific_journal-3571 87 39 the the DET american_scientific_journal-3571 87 40 quadruped quadruped NOUN american_scientific_journal-3571 87 41 structure structure NOUN american_scientific_journal-3571 87 42 , , PUNCT american_scientific_journal-3571 87 43 the the DET american_scientific_journal-3571 87 44 first first ADJ american_scientific_journal-3571 87 45 coordinate coordinate NOUN american_scientific_journal-3571 87 46 frame frame NOUN american_scientific_journal-3571 87 47 is be AUX american_scientific_journal-3571 87 48 located locate VERB american_scientific_journal-3571 87 49 at at ADP american_scientific_journal-3571 87 50 the the DET american_scientific_journal-3571 87 51 coxa coxa NOUN american_scientific_journal-3571 87 52 joint joint NOUN american_scientific_journal-3571 87 53 and and CCONJ american_scientific_journal-3571 87 54 the the DET american_scientific_journal-3571 87 55 second second ADJ american_scientific_journal-3571 87 56 coordinate coordinate NOUN american_scientific_journal-3571 87 57 frame frame NOUN american_scientific_journal-3571 87 58 is be AUX american_scientific_journal-3571 87 59 located locate VERB american_scientific_journal-3571 87 60 on on ADP american_scientific_journal-3571 87 61 the the DET american_scientific_journal-3571 87 62 ground ground NOUN american_scientific_journal-3571 87 63 . . PUNCT american_scientific_journal-3571 88 1 in in ADP american_scientific_journal-3571 88 2 this this DET american_scientific_journal-3571 88 3 cartesian cartesian ADJ american_scientific_journal-3571 88 4 coordinate coordinate NOUN american_scientific_journal-3571 88 5 the the DET american_scientific_journal-3571 88 6 x x NOUN american_scientific_journal-3571 88 7 - - NOUN american_scientific_journal-3571 88 8 axis axis NOUN american_scientific_journal-3571 88 9 is be AUX american_scientific_journal-3571 88 10 referred refer VERB american_scientific_journal-3571 88 11 to to ADP american_scientific_journal-3571 88 12 the the DET american_scientific_journal-3571 88 13 front front ADJ american_scientific_journal-3571 88 14 side side NOUN american_scientific_journal-3571 88 15 direction direction NOUN american_scientific_journal-3571 88 16 of of ADP american_scientific_journal-3571 88 17 the the DET american_scientific_journal-3571 88 18 quadruped quadruped NOUN american_scientific_journal-3571 88 19 body body NOUN american_scientific_journal-3571 88 20 , , PUNCT american_scientific_journal-3571 88 21 and and CCONJ american_scientific_journal-3571 88 22 y y NOUN american_scientific_journal-3571 88 23 - - PUNCT american_scientific_journal-3571 88 24 axis axis NOUN american_scientific_journal-3571 88 25 is be AUX american_scientific_journal-3571 88 26 referred refer VERB american_scientific_journal-3571 88 27 to to ADP american_scientific_journal-3571 88 28 the the DET american_scientific_journal-3571 88 29 left left ADJ american_scientific_journal-3571 88 30 side side NOUN american_scientific_journal-3571 88 31 of of ADP american_scientific_journal-3571 88 32 the the DET american_scientific_journal-3571 88 33 quadruped quadruped NOUN american_scientific_journal-3571 88 34 body body NOUN american_scientific_journal-3571 88 35 . . PUNCT american_scientific_journal-3571 89 1 so so ADV american_scientific_journal-3571 89 2 , , PUNCT american_scientific_journal-3571 89 3 these these DET american_scientific_journal-3571 89 4 coordinates coordinate NOUN american_scientific_journal-3571 89 5 are be AUX american_scientific_journal-3571 89 6 very very ADV american_scientific_journal-3571 89 7 important important ADJ american_scientific_journal-3571 89 8 in in ADP american_scientific_journal-3571 89 9 the the DET american_scientific_journal-3571 89 10 analyzing analyzing NOUN american_scientific_journal-3571 89 11 and and CCONJ american_scientific_journal-3571 89 12 ensuring ensure VERB american_scientific_journal-3571 89 13 that that SCONJ american_scientific_journal-3571 89 14 vertical vertical ADJ american_scientific_journal-3571 89 15 projection projection NOUN american_scientific_journal-3571 89 16 of of ADP american_scientific_journal-3571 89 17 cog cog PROPN american_scientific_journal-3571 89 18 have have AUX american_scientific_journal-3571 89 19 been be AUX american_scientific_journal-3571 89 20 located locate VERB american_scientific_journal-3571 89 21 inside inside ADP american_scientific_journal-3571 89 22 the the DET american_scientific_journal-3571 89 23 supporting support VERB american_scientific_journal-3571 89 24 polygon polygon NOUN american_scientific_journal-3571 89 25 [ [ X american_scientific_journal-3571 89 26 13 13 NUM american_scientific_journal-3571 89 27 ] ] PUNCT american_scientific_journal-3571 89 28 . . PUNCT american_scientific_journal-3571 90 1 4 4 X american_scientific_journal-3571 90 2 . . X american_scientific_journal-3571 90 3 kinematics kinematic NOUN american_scientific_journal-3571 90 4 model model NOUN american_scientific_journal-3571 90 5 of of ADP american_scientific_journal-3571 90 6 a a DET american_scientific_journal-3571 90 7 quadruped quadruped NOUN american_scientific_journal-3571 90 8 robot robot NOUN american_scientific_journal-3571 90 9 4.1 4.1 NUM american_scientific_journal-3571 90 10 forward forward NOUN american_scientific_journal-3571 90 11 kinematics kinematic NOUN american_scientific_journal-3571 90 12 the the DET american_scientific_journal-3571 90 13 quadruped quadruped NOUN american_scientific_journal-3571 90 14 robot robot NOUN american_scientific_journal-3571 90 15 is be AUX american_scientific_journal-3571 90 16 depending depend VERB american_scientific_journal-3571 90 17 on on ADP american_scientific_journal-3571 90 18 the the DET american_scientific_journal-3571 90 19 configuration configuration NOUN american_scientific_journal-3571 90 20 of of ADP american_scientific_journal-3571 90 21 each each DET american_scientific_journal-3571 90 22 leg leg NOUN american_scientific_journal-3571 90 23 , , PUNCT american_scientific_journal-3571 90 24 because because SCONJ american_scientific_journal-3571 90 25 its its PRON american_scientific_journal-3571 90 26 represent represent NOUN american_scientific_journal-3571 90 27 as as ADP american_scientific_journal-3571 90 28 the the DET american_scientific_journal-3571 90 29 physical physical ADJ american_scientific_journal-3571 90 30 constraints constraint NOUN american_scientific_journal-3571 90 31 of of ADP american_scientific_journal-3571 90 32 the the DET american_scientific_journal-3571 90 33 robot robot NOUN american_scientific_journal-3571 90 34 walking walk VERB american_scientific_journal-3571 90 35 . . PUNCT american_scientific_journal-3571 91 1 in in ADP american_scientific_journal-3571 91 2 this this DET american_scientific_journal-3571 91 3 paper paper NOUN american_scientific_journal-3571 91 4 , , PUNCT american_scientific_journal-3571 91 5 the the DET american_scientific_journal-3571 91 6 robot robot NOUN american_scientific_journal-3571 91 7 leg leg NOUN american_scientific_journal-3571 91 8 has have VERB american_scientific_journal-3571 91 9 three three NUM american_scientific_journal-3571 91 10 - - PUNCT american_scientific_journal-3571 91 11 revolute revolute NOUN american_scientific_journal-3571 91 12 joints joint NOUN american_scientific_journal-3571 91 13 which which PRON american_scientific_journal-3571 91 14 are be AUX american_scientific_journal-3571 91 15 labeled label VERB american_scientific_journal-3571 91 16 in in ADP american_scientific_journal-3571 91 17 the the DET american_scientific_journal-3571 91 18 kinematical kinematical ADJ american_scientific_journal-3571 91 19 chain chain NOUN american_scientific_journal-3571 91 20 as as ADP american_scientific_journal-3571 91 21 ( ( PUNCT american_scientific_journal-3571 91 22 πœƒπœƒ1,πœƒπœƒ2 πœƒπœƒ1,πœƒπœƒ2 X american_scientific_journal-3571 91 23 and and CCONJ american_scientific_journal-3571 91 24 πœƒπœƒ3 πœƒπœƒ3 NUM american_scientific_journal-3571 91 25 ) ) PUNCT american_scientific_journal-3571 91 26 . . PUNCT american_scientific_journal-3571 92 1 every every DET american_scientific_journal-3571 92 2 leg leg NOUN american_scientific_journal-3571 92 3 has have VERB american_scientific_journal-3571 92 4 a a DET american_scientific_journal-3571 92 5 mechanism mechanism NOUN american_scientific_journal-3571 92 6 that that PRON american_scientific_journal-3571 92 7 is be AUX american_scientific_journal-3571 92 8 choosing choose VERB american_scientific_journal-3571 92 9 according accord VERB american_scientific_journal-3571 92 10 to to ADP american_scientific_journal-3571 92 11 these these DET american_scientific_journal-3571 92 12 revolute revolute ADJ american_scientific_journal-3571 92 13 joints joint NOUN american_scientific_journal-3571 92 14 . . PUNCT american_scientific_journal-3571 93 1 modeling modeling NOUN american_scientific_journal-3571 93 2 of of ADP american_scientific_journal-3571 93 3 the the DET american_scientific_journal-3571 93 4 leg leg NOUN american_scientific_journal-3571 93 5 structure structure NOUN american_scientific_journal-3571 93 6 is be AUX american_scientific_journal-3571 93 7 to to PART american_scientific_journal-3571 93 8 mimic mimic VERB american_scientific_journal-3571 93 9 the the DET american_scientific_journal-3571 93 10 biological biological ADJ american_scientific_journal-3571 93 11 structures structure NOUN american_scientific_journal-3571 93 12 for for ADP american_scientific_journal-3571 93 13 animals animal NOUN american_scientific_journal-3571 93 14 and and CCONJ american_scientific_journal-3571 93 15 insects insect NOUN american_scientific_journal-3571 93 16 . . PUNCT american_scientific_journal-3571 94 1 to to PART american_scientific_journal-3571 94 2 drive drive VERB american_scientific_journal-3571 94 3 the the DET american_scientific_journal-3571 94 4 geometrical geometrical ADJ american_scientific_journal-3571 94 5 model model NOUN american_scientific_journal-3571 94 6 to to ADP american_scientific_journal-3571 94 7 each each DET american_scientific_journal-3571 94 8 leg leg NOUN american_scientific_journal-3571 94 9 which which PRON american_scientific_journal-3571 94 10 is be AUX american_scientific_journal-3571 94 11 related relate VERB american_scientific_journal-3571 94 12 to to ADP american_scientific_journal-3571 94 13 the the DET american_scientific_journal-3571 94 14 robot robot NOUN american_scientific_journal-3571 94 15 center center NOUN american_scientific_journal-3571 94 16 body body NOUN american_scientific_journal-3571 94 17 , , PUNCT american_scientific_journal-3571 94 18 thus thus ADV american_scientific_journal-3571 94 19 forward forward ADP american_scientific_journal-3571 94 20 kinematics kinematic NOUN american_scientific_journal-3571 94 21 must must AUX american_scientific_journal-3571 94 22 be be AUX american_scientific_journal-3571 94 23 applied apply VERB american_scientific_journal-3571 94 24 to to PART american_scientific_journal-3571 94 25 find find VERB american_scientific_journal-3571 94 26 the the DET american_scientific_journal-3571 94 27 position position NOUN american_scientific_journal-3571 94 28 and and CCONJ american_scientific_journal-3571 94 29 orientation orientation NOUN american_scientific_journal-3571 94 30 for for ADP american_scientific_journal-3571 94 31 each each DET american_scientific_journal-3571 94 32 leg leg NOUN american_scientific_journal-3571 94 33 tip tip NOUN american_scientific_journal-3571 94 34 which which PRON american_scientific_journal-3571 94 35 is be AUX american_scientific_journal-3571 94 36 here here ADV american_scientific_journal-3571 94 37 named name VERB american_scientific_journal-3571 94 38 as as ADP american_scientific_journal-3571 94 39 ( ( PUNCT american_scientific_journal-3571 94 40 xi xi PROPN american_scientific_journal-3571 94 41 , , PUNCT american_scientific_journal-3571 94 42 yi yi PROPN american_scientific_journal-3571 94 43 , , PUNCT american_scientific_journal-3571 94 44 zi zi NOUN american_scientific_journal-3571 94 45 ) ) PUNCT american_scientific_journal-3571 94 46 , , PUNCT american_scientific_journal-3571 94 47 i=1,2,3,and i=1,2,3,and NOUN american_scientific_journal-3571 94 48 4 4 NUM american_scientific_journal-3571 94 49 . . PUNCT american_scientific_journal-3571 95 1 in in ADP american_scientific_journal-3571 95 2 the the DET american_scientific_journal-3571 95 3 fig.(3 fig.(3 NOUN american_scientific_journal-3571 95 4 ) ) PUNCT american_scientific_journal-3571 95 5 the the DET american_scientific_journal-3571 95 6 kinematical kinematical ADJ american_scientific_journal-3571 95 7 chains chain NOUN american_scientific_journal-3571 95 8 for for ADP american_scientific_journal-3571 95 9 any any DET american_scientific_journal-3571 95 10 leg leg NOUN american_scientific_journal-3571 95 11 is be AUX american_scientific_journal-3571 95 12 showing show VERB american_scientific_journal-3571 95 13 . . PUNCT american_scientific_journal-3571 96 1 figure figure NOUN american_scientific_journal-3571 96 2 3 3 NUM american_scientific_journal-3571 96 3 : : PUNCT american_scientific_journal-3571 96 4 coordinate coordinate NOUN american_scientific_journal-3571 96 5 frames frame NOUN american_scientific_journal-3571 96 6 for for ADP american_scientific_journal-3571 96 7 one one NUM american_scientific_journal-3571 96 8 leg leg NOUN american_scientific_journal-3571 96 9 of of ADP american_scientific_journal-3571 96 10 quadruped quadruped NOUN american_scientific_journal-3571 96 11 robot robot NOUN american_scientific_journal-3571 96 12 forward forward PROPN american_scientific_journal-3571 96 13 kinematics kinematics PROPN american_scientific_journal-3571 96 14 is be AUX american_scientific_journal-3571 96 15 depending depend VERB american_scientific_journal-3571 96 16 on on ADP american_scientific_journal-3571 96 17 the the DET american_scientific_journal-3571 96 18 d d PROPN american_scientific_journal-3571 96 19 - - NOUN american_scientific_journal-3571 96 20 h h ADJ american_scientific_journal-3571 96 21 ( ( PUNCT american_scientific_journal-3571 96 22 denavit denavit PROPN american_scientific_journal-3571 96 23 - - PUNCT american_scientific_journal-3571 96 24 hartenberg hartenberg PROPN american_scientific_journal-3571 96 25 ) ) PUNCT american_scientific_journal-3571 96 26 parameters parameter NOUN american_scientific_journal-3571 96 27 of of ADP american_scientific_journal-3571 96 28 the the DET american_scientific_journal-3571 96 29 leg leg NOUN american_scientific_journal-3571 96 30 structure structure NOUN american_scientific_journal-3571 96 31 design design NOUN american_scientific_journal-3571 96 32 ; ; PUNCT american_scientific_journal-3571 96 33 these these DET american_scientific_journal-3571 96 34 parameters parameter NOUN american_scientific_journal-3571 96 35 are be AUX american_scientific_journal-3571 96 36 showing show VERB american_scientific_journal-3571 96 37 in in ADP american_scientific_journal-3571 96 38 table table NOUN american_scientific_journal-3571 96 39 1 1 NUM american_scientific_journal-3571 96 40 . . PUNCT american_scientific_journal-3571 96 41 table table NOUN american_scientific_journal-3571 96 42 1 1 NUM american_scientific_journal-3571 96 43 : : PUNCT american_scientific_journal-3571 96 44 the the DET american_scientific_journal-3571 96 45 denavit denavit PROPN american_scientific_journal-3571 96 46 - - PUNCT american_scientific_journal-3571 96 47 hartenberg hartenberg PROPN american_scientific_journal-3571 96 48 parameters parameter NOUN american_scientific_journal-3571 96 49 table table VERB american_scientific_journal-3571 96 50 for for ADP american_scientific_journal-3571 96 51 one one NUM american_scientific_journal-3571 96 52 leg leg NOUN american_scientific_journal-3571 96 53 in in ADP american_scientific_journal-3571 96 54 our our PRON american_scientific_journal-3571 96 55 quadruped quadruped NOUN american_scientific_journal-3571 96 56 robot robot NOUN american_scientific_journal-3571 96 57 link link NOUN american_scientific_journal-3571 96 58 no no INTJ american_scientific_journal-3571 96 59 . . PUNCT american_scientific_journal-3571 97 1 link link PROPN american_scientific_journal-3571 97 2 name name PROPN american_scientific_journal-3571 97 3 πœΆπœΆπ’Šπ’Š πœΆπœΆπ’Šπ’Š PROPN american_scientific_journal-3571 97 4 ( ( PUNCT american_scientific_journal-3571 97 5 deg deg PROPN american_scientific_journal-3571 97 6 ) ) PUNCT american_scientific_journal-3571 97 7 π’‚π’‚π’Šπ’Š π’‚π’‚π’Šπ’Š PROPN american_scientific_journal-3571 97 8 ( ( PUNCT american_scientific_journal-3571 97 9 cm cm NOUN american_scientific_journal-3571 97 10 ) ) PUNCT american_scientific_journal-3571 97 11 π’…π’…π’Šπ’Š π’…π’…π’Šπ’Š NOUN american_scientific_journal-3571 97 12 ( ( PUNCT american_scientific_journal-3571 97 13 cm cm NOUN american_scientific_journal-3571 97 14 ) ) PUNCT american_scientific_journal-3571 97 15 πœ½πœ½π’Šπ’Š πœ½πœ½π’Šπ’Š NOUN american_scientific_journal-3571 97 16 ( ( PUNCT american_scientific_journal-3571 97 17 deg deg PROPN american_scientific_journal-3571 97 18 ) ) PUNCT american_scientific_journal-3571 97 19 1 1 NUM american_scientific_journal-3571 97 20 coxa coxa VERB american_scientific_journal-3571 97 21 90 90 NUM american_scientific_journal-3571 97 22 π‘Žπ‘Ž1 π‘Žπ‘Ž1 NOUN american_scientific_journal-3571 97 23 0 0 PUNCT american_scientific_journal-3571 97 24 πœƒπœƒ1 πœƒπœƒ1 NOUN american_scientific_journal-3571 97 25 2 2 NUM american_scientific_journal-3571 97 26 femur femur NOUN american_scientific_journal-3571 97 27 0 0 PUNCT american_scientific_journal-3571 97 28 π‘Žπ‘Ž2 π‘Žπ‘Ž2 NOUN american_scientific_journal-3571 97 29 0 0 NUM american_scientific_journal-3571 97 30 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 97 31 3 3 NUM american_scientific_journal-3571 97 32 tibia tibia NOUN american_scientific_journal-3571 97 33 0 0 NUM american_scientific_journal-3571 98 1 π‘Žπ‘Ž3 π‘Žπ‘Ž3 NOUN american_scientific_journal-3571 98 2 0 0 NUM american_scientific_journal-3571 98 3 πœƒπœƒ3 πœƒπœƒ3 NOUN american_scientific_journal-3571 98 4 american american PROPN american_scientific_journal-3571 98 5 scientific scientific ADJ american_scientific_journal-3571 98 6 research research PROPN american_scientific_journal-3571 98 7 journal journal NOUN american_scientific_journal-3571 98 8 for for ADP american_scientific_journal-3571 98 9 engineering engineering NOUN american_scientific_journal-3571 98 10 , , PUNCT american_scientific_journal-3571 98 11 technology technology NOUN american_scientific_journal-3571 98 12 , , PUNCT american_scientific_journal-3571 98 13 and and CCONJ american_scientific_journal-3571 98 14 sciences science NOUN american_scientific_journal-3571 98 15 ( ( PUNCT american_scientific_journal-3571 98 16 asrjets asrjet NOUN american_scientific_journal-3571 98 17 ) ) PUNCT american_scientific_journal-3571 98 18 ( ( PUNCT american_scientific_journal-3571 98 19 2017 2017 NUM american_scientific_journal-3571 98 20 ) ) PUNCT american_scientific_journal-3571 98 21 volume volume NOUN american_scientific_journal-3571 98 22 38 38 NUM american_scientific_journal-3571 98 23 , , PUNCT american_scientific_journal-3571 98 24 no no DET american_scientific_journal-3571 98 25 1 1 NUM american_scientific_journal-3571 98 26 , , PUNCT american_scientific_journal-3571 98 27 pp pp ADV american_scientific_journal-3571 98 28 17 17 NUM american_scientific_journal-3571 98 29 - - SYM american_scientific_journal-3571 98 30 32 32 NUM american_scientific_journal-3571 98 31 22 22 NUM american_scientific_journal-3571 98 32 where where SCONJ american_scientific_journal-3571 98 33 the the DET american_scientific_journal-3571 98 34 links link NOUN american_scientific_journal-3571 99 1 parameter:π‘Žπ‘Ž1=2.5 parameter:π‘Žπ‘Ž1=2.5 VERB american_scientific_journal-3571 99 2 cm cm NOUN american_scientific_journal-3571 99 3 π‘Žπ‘Ž2= π‘Žπ‘Ž2= NOUN american_scientific_journal-3571 99 4 5 5 NUM american_scientific_journal-3571 99 5 cm cm NOUN american_scientific_journal-3571 99 6 , , PUNCT american_scientific_journal-3571 99 7 and and CCONJ american_scientific_journal-3571 99 8 π‘Žπ‘Ž3= π‘Žπ‘Ž3= VERB american_scientific_journal-3571 99 9 9 9 NUM american_scientific_journal-3571 99 10 cm cm NOUN american_scientific_journal-3571 99 11 . . PUNCT american_scientific_journal-3571 100 1 π‘Žπ‘Žπ‘–π‘– π‘Žπ‘Žπ‘–π‘– NOUN american_scientific_journal-3571 100 2 are be AUX american_scientific_journal-3571 100 3 the the DET american_scientific_journal-3571 100 4 lengths length NOUN american_scientific_journal-3571 100 5 of of ADP american_scientific_journal-3571 100 6 the the DET american_scientific_journal-3571 100 7 leg leg NOUN american_scientific_journal-3571 100 8 links link NOUN american_scientific_journal-3571 100 9 . . PUNCT american_scientific_journal-3571 101 1 the the DET american_scientific_journal-3571 101 2 leg leg NOUN american_scientific_journal-3571 101 3 structure structure NOUN american_scientific_journal-3571 101 4 is be AUX american_scientific_journal-3571 101 5 symmetric symmetric ADJ american_scientific_journal-3571 101 6 on on ADP american_scientific_journal-3571 101 7 the the DET american_scientific_journal-3571 101 8 coordinate coordinate NOUN american_scientific_journal-3571 101 9 axis axis NOUN american_scientific_journal-3571 101 10 and and CCONJ american_scientific_journal-3571 101 11 the the DET american_scientific_journal-3571 101 12 walking walking NOUN american_scientific_journal-3571 101 13 is be AUX american_scientific_journal-3571 101 14 set set VERB american_scientific_journal-3571 101 15 towards towards ADP american_scientific_journal-3571 101 16 the the DET american_scientific_journal-3571 101 17 x x NOUN american_scientific_journal-3571 101 18 - - NOUN american_scientific_journal-3571 101 19 axis axis NOUN american_scientific_journal-3571 101 20 . . PUNCT american_scientific_journal-3571 102 1 the the DET american_scientific_journal-3571 102 2 transformation transformation NOUN american_scientific_journal-3571 102 3 matrix matrix NOUN american_scientific_journal-3571 102 4 used use VERB american_scientific_journal-3571 102 5 to to PART american_scientific_journal-3571 102 6 translate translate VERB american_scientific_journal-3571 102 7 from from ADP american_scientific_journal-3571 102 8 one one NUM american_scientific_journal-3571 102 9 link link NOUN american_scientific_journal-3571 102 10 named name VERB american_scientific_journal-3571 102 11 i i PRON american_scientific_journal-3571 102 12 to to ADP american_scientific_journal-3571 102 13 another another DET american_scientific_journal-3571 102 14 link link NOUN american_scientific_journal-3571 102 15 named name VERB american_scientific_journal-3571 102 16 i-1 i-1 NOUN american_scientific_journal-3571 102 17 by by ADP american_scientific_journal-3571 102 18 using use VERB american_scientific_journal-3571 102 19 the the DET american_scientific_journal-3571 102 20 d d PROPN american_scientific_journal-3571 102 21 - - ADJ american_scientific_journal-3571 102 22 h h ADJ american_scientific_journal-3571 102 23 parameters parameter NOUN american_scientific_journal-3571 102 24 table table NOUN american_scientific_journal-3571 102 25 . . PUNCT american_scientific_journal-3571 103 1 equ equ PROPN american_scientific_journal-3571 103 2 . . PROPN american_scientific_journal-3571 103 3 2 2 NUM american_scientific_journal-3571 103 4 , , PUNCT american_scientific_journal-3571 103 5 the the DET american_scientific_journal-3571 103 6 general general ADJ american_scientific_journal-3571 103 7 matrix matrix NOUN american_scientific_journal-3571 103 8 is be AUX american_scientific_journal-3571 103 9 given give VERB american_scientific_journal-3571 103 10 : : PUNCT american_scientific_journal-3571 103 11 π‘‡π‘‡π‘–π‘–π‘–π‘–βˆ’1 π‘‡π‘‡π‘–π‘–π‘–π‘–βˆ’1 NOUN american_scientific_journal-3571 103 12 = = SYM american_scientific_journal-3571 103 13 οΏ½ οΏ½ PROPN american_scientific_journal-3571 103 14 π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– NOUN american_scientific_journal-3571 103 15 βˆ’π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘–π‘π‘π‘π‘π‘π‘π‘π‘π‘–π‘– βˆ’π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘–π‘π‘π‘π‘π‘π‘π‘π‘π‘–π‘– PROPN american_scientific_journal-3571 103 16 π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ π‘π‘π‘–π‘– π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ π‘π‘π‘–π‘– INTJ american_scientific_journal-3571 103 17 π‘Žπ‘Žπ‘–π‘–π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– π‘Žπ‘Žπ‘–π‘–π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– PROPN american_scientific_journal-3571 103 18 π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– PROPN american_scientific_journal-3571 104 1 π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘–π‘π‘π‘π‘π‘π‘π‘π‘π‘–π‘– π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘–π‘π‘π‘π‘π‘π‘π‘π‘π‘–π‘– PROPN american_scientific_journal-3571 104 2 βˆ’π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ π‘π‘π‘–π‘– βˆ’π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ π‘π‘π‘–π‘– INTJ american_scientific_journal-3571 105 1 π‘Žπ‘Žπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– π‘Žπ‘Žπ‘–π‘–π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– NOUN american_scientific_journal-3571 105 2 0 0 NUM american_scientific_journal-3571 105 3 0 0 NUM american_scientific_journal-3571 106 1 𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐𝑖𝑖 𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐𝑖𝑖 ADJ american_scientific_journal-3571 106 2 0 0 NUM american_scientific_journal-3571 106 3 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖 ADJ american_scientific_journal-3571 106 4 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 NOUN american_scientific_journal-3571 106 5 0 0 NUM american_scientific_journal-3571 106 6 1 1 NUM american_scientific_journal-3571 106 7 οΏ½ οΏ½ PROPN american_scientific_journal-3571 106 8 ( ( PUNCT american_scientific_journal-3571 106 9 2 2 NUM american_scientific_journal-3571 106 10 ) ) PUNCT american_scientific_journal-3571 106 11 by by ADP american_scientific_journal-3571 106 12 multiplying multiply VERB american_scientific_journal-3571 106 13 each each DET american_scientific_journal-3571 106 14 joint joint ADJ american_scientific_journal-3571 106 15 transformation transformation NOUN american_scientific_journal-3571 106 16 matrix matrix NOUN american_scientific_journal-3571 106 17 , , PUNCT american_scientific_journal-3571 106 18 the the DET american_scientific_journal-3571 106 19 overall overall ADJ american_scientific_journal-3571 106 20 transformation transformation NOUN american_scientific_journal-3571 106 21 matrix matrix NOUN american_scientific_journal-3571 106 22 can can AUX american_scientific_journal-3571 106 23 be be AUX american_scientific_journal-3571 106 24 obtained obtain VERB american_scientific_journal-3571 106 25 as as ADP american_scientific_journal-3571 106 26 the the DET american_scientific_journal-3571 106 27 following following NOUN american_scientific_journal-3571 106 28 eq eq NOUN american_scientific_journal-3571 106 29 . . PROPN american_scientific_journal-3571 107 1 3 3 NUM american_scientific_journal-3571 107 2 : : PUNCT american_scientific_journal-3571 108 1 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏 PROPN american_scientific_journal-3571 108 2 = = SYM american_scientific_journal-3571 108 3 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 108 4 𝑓𝑓𝑏𝑏𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓𝑏𝑏𝑓𝑓𝑓𝑓𝑓𝑓 NOUN american_scientific_journal-3571 108 5 βˆ— βˆ— PROPN american_scientific_journal-3571 108 6 𝑇𝑇𝑓𝑓𝑏𝑏𝑓𝑓𝑓𝑓𝑓𝑓 𝑇𝑇𝑓𝑓𝑏𝑏𝑓𝑓𝑓𝑓𝑓𝑓 PROPN american_scientific_journal-3571 108 7 𝑑𝑑𝑖𝑖𝑏𝑏𝑖𝑖𝑐𝑐 𝑑𝑑𝑖𝑖𝑏𝑏𝑖𝑖𝑐𝑐 ADV american_scientific_journal-3571 108 8 ( ( PUNCT american_scientific_journal-3571 108 9 3 3 X american_scientific_journal-3571 108 10 ) ) PUNCT american_scientific_journal-3571 108 11 the the DET american_scientific_journal-3571 108 12 transformation transformation NOUN american_scientific_journal-3571 108 13 matrix matrix NOUN american_scientific_journal-3571 108 14 for for ADP american_scientific_journal-3571 108 15 each each DET american_scientific_journal-3571 108 16 joint joint NOUN american_scientific_journal-3571 108 17 in in ADP american_scientific_journal-3571 108 18 the the DET american_scientific_journal-3571 108 19 quadruped quadruped NOUN american_scientific_journal-3571 108 20 robot robot NOUN american_scientific_journal-3571 108 21 leg leg NOUN american_scientific_journal-3571 108 22 is be AUX american_scientific_journal-3571 108 23 given give VERB american_scientific_journal-3571 108 24 by by ADP american_scientific_journal-3571 108 25 the the DET american_scientific_journal-3571 108 26 following follow VERB american_scientific_journal-3571 108 27 equations equation NOUN american_scientific_journal-3571 108 28 : : PUNCT american_scientific_journal-3571 108 29 𝑇𝑇10 𝑇𝑇10 PROPN american_scientific_journal-3571 108 30 = = SYM american_scientific_journal-3571 108 31 οΏ½ οΏ½ PROPN american_scientific_journal-3571 108 32 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 108 33 0 0 PUNCT american_scientific_journal-3571 109 1 𝑐𝑐1 𝑐𝑐1 INTJ american_scientific_journal-3571 109 2 π‘Žπ‘Ž1𝑐𝑐1 π‘Žπ‘Ž1𝑐𝑐1 PROPN american_scientific_journal-3571 110 1 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 110 2 0 0 NUM american_scientific_journal-3571 111 1 βˆ’π‘π‘1 βˆ’π‘π‘1 PROPN american_scientific_journal-3571 112 1 π‘Žπ‘Ž1𝑐𝑐1 π‘Žπ‘Ž1𝑐𝑐1 PROPN american_scientific_journal-3571 112 2 0 0 NUM american_scientific_journal-3571 112 3 0 0 NUM american_scientific_journal-3571 112 4 1 1 NUM american_scientific_journal-3571 112 5 0 0 NUM american_scientific_journal-3571 112 6 0 0 NUM american_scientific_journal-3571 112 7 𝑑𝑑1 𝑑𝑑1 NOUN american_scientific_journal-3571 112 8 0 0 NUM american_scientific_journal-3571 112 9 1 1 NUM american_scientific_journal-3571 112 10 οΏ½ οΏ½ PROPN american_scientific_journal-3571 112 11 ( ( PUNCT american_scientific_journal-3571 112 12 4 4 NUM american_scientific_journal-3571 112 13 ) ) PUNCT american_scientific_journal-3571 112 14 𝑇𝑇21 𝑇𝑇21 PROPN american_scientific_journal-3571 112 15 = = SYM american_scientific_journal-3571 112 16 οΏ½ οΏ½ PROPN american_scientific_journal-3571 112 17 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 112 18 βˆ’π‘π‘2 βˆ’π‘π‘2 PROPN american_scientific_journal-3571 112 19 0 0 PROPN american_scientific_journal-3571 112 20 π‘Žπ‘Ž2𝑐𝑐2 π‘Žπ‘Ž2𝑐𝑐2 PROPN american_scientific_journal-3571 112 21 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 112 22 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 112 23 0 0 PUNCT american_scientific_journal-3571 112 24 π‘Žπ‘Ž2𝑐𝑐2 π‘Žπ‘Ž2𝑐𝑐2 NOUN american_scientific_journal-3571 112 25 0 0 NUM american_scientific_journal-3571 112 26 0 0 NUM american_scientific_journal-3571 112 27 0 0 NUM american_scientific_journal-3571 112 28 0 0 NUM american_scientific_journal-3571 112 29 1 1 NUM american_scientific_journal-3571 112 30 0 0 NUM american_scientific_journal-3571 112 31 0 0 NUM american_scientific_journal-3571 112 32 1 1 NUM american_scientific_journal-3571 112 33 οΏ½ οΏ½ PROPN american_scientific_journal-3571 112 34 ( ( PUNCT american_scientific_journal-3571 112 35 5 5 NUM american_scientific_journal-3571 112 36 ) ) PUNCT american_scientific_journal-3571 112 37 𝑇𝑇32 𝑇𝑇32 PROPN american_scientific_journal-3571 112 38 = = SYM american_scientific_journal-3571 112 39 οΏ½ οΏ½ PROPN american_scientific_journal-3571 112 40 𝑐𝑐3 𝑐𝑐3 PROPN american_scientific_journal-3571 112 41 βˆ’π‘π‘3 βˆ’π‘π‘3 PROPN american_scientific_journal-3571 112 42 0 0 NUM american_scientific_journal-3571 112 43 π‘Žπ‘Ž3𝑐𝑐3 π‘Žπ‘Ž3𝑐𝑐3 PROPN american_scientific_journal-3571 112 44 𝑐𝑐3 𝑐𝑐3 PROPN american_scientific_journal-3571 112 45 𝑐𝑐3 𝑐𝑐3 PROPN american_scientific_journal-3571 112 46 0 0 NUM american_scientific_journal-3571 112 47 π‘Žπ‘Ž3𝑐𝑐3 π‘Žπ‘Ž3𝑐𝑐3 NOUN american_scientific_journal-3571 112 48 0 0 NUM american_scientific_journal-3571 112 49 0 0 NUM american_scientific_journal-3571 112 50 0 0 NUM american_scientific_journal-3571 112 51 0 0 NUM american_scientific_journal-3571 112 52 1 1 NUM american_scientific_journal-3571 112 53 0 0 NUM american_scientific_journal-3571 112 54 0 0 NUM american_scientific_journal-3571 112 55 1 1 NUM american_scientific_journal-3571 112 56 οΏ½ οΏ½ PROPN american_scientific_journal-3571 112 57 ( ( PUNCT american_scientific_journal-3571 112 58 6 6 NUM american_scientific_journal-3571 112 59 ) ) PUNCT american_scientific_journal-3571 112 60 multiplications multiplication NOUN american_scientific_journal-3571 112 61 of of ADP american_scientific_journal-3571 112 62 these these DET american_scientific_journal-3571 112 63 matrixes matrix NOUN american_scientific_journal-3571 112 64 produce produce VERB american_scientific_journal-3571 112 65 the the DET american_scientific_journal-3571 112 66 final final ADJ american_scientific_journal-3571 112 67 matrix matrix NOUN american_scientific_journal-3571 112 68 that that PRON american_scientific_journal-3571 112 69 it it PRON american_scientific_journal-3571 112 70 used use VERB american_scientific_journal-3571 112 71 to to PART american_scientific_journal-3571 112 72 describe describe VERB american_scientific_journal-3571 112 73 the the DET american_scientific_journal-3571 112 74 leg leg NOUN american_scientific_journal-3571 112 75 - - PUNCT american_scientific_journal-3571 112 76 tip tip NOUN american_scientific_journal-3571 112 77 position position NOUN american_scientific_journal-3571 112 78 and and CCONJ american_scientific_journal-3571 112 79 orientation orientation NOUN american_scientific_journal-3571 112 80 . . PUNCT american_scientific_journal-3571 113 1 this this DET american_scientific_journal-3571 113 2 matrix matrix NOUN american_scientific_journal-3571 113 3 is be AUX american_scientific_journal-3571 113 4 given give VERB american_scientific_journal-3571 113 5 as as ADP american_scientific_journal-3571 113 6 the the DET american_scientific_journal-3571 113 7 following follow VERB american_scientific_journal-3571 113 8 : : PUNCT american_scientific_journal-3571 113 9 οΏ½ οΏ½ PROPN american_scientific_journal-3571 113 10 c1(c2 c1(c2 SYM american_scientific_journal-3571 113 11 + + NOUN american_scientific_journal-3571 113 12 3 3 NUM american_scientific_journal-3571 113 13 ) ) PUNCT american_scientific_journal-3571 113 14 βˆ’c1s2βˆ’3 βˆ’c1s2βˆ’3 PROPN american_scientific_journal-3571 113 15 s1 s1 NOUN american_scientific_journal-3571 113 16 a3c1(c2 a3c1(c2 VERB american_scientific_journal-3571 113 17 + + NOUN american_scientific_journal-3571 113 18 3 3 NUM american_scientific_journal-3571 113 19 ) ) PUNCT american_scientific_journal-3571 113 20 + + CCONJ american_scientific_journal-3571 113 21 c1(a2c2+a1 c1(a2c2+a1 PROPN american_scientific_journal-3571 113 22 ) ) PUNCT american_scientific_journal-3571 114 1 s1(c2 s1(c2 ADP american_scientific_journal-3571 114 2 + + NOUN american_scientific_journal-3571 114 3 3 3 NUM american_scientific_journal-3571 114 4 ) ) PUNCT american_scientific_journal-3571 114 5 βˆ’s1(s2βˆ’3 βˆ’s1(s2βˆ’3 NOUN american_scientific_journal-3571 114 6 ) ) PUNCT american_scientific_journal-3571 115 1 βˆ’c1 βˆ’c1 NOUN american_scientific_journal-3571 115 2 a3s1(c2 a3s1(c2 VERB american_scientific_journal-3571 115 3 + + ADJ american_scientific_journal-3571 115 4 3 3 NUM american_scientific_journal-3571 115 5 ) ) PUNCT american_scientific_journal-3571 115 6 + + CCONJ american_scientific_journal-3571 115 7 s1(a2c2+a1 s1(a2c2+a1 NOUN american_scientific_journal-3571 115 8 ) ) PUNCT american_scientific_journal-3571 115 9 s2 s2 NOUN american_scientific_journal-3571 115 10 + + PROPN american_scientific_journal-3571 115 11 3 3 NUM american_scientific_journal-3571 115 12 0 0 NUM american_scientific_journal-3571 115 13 ( ( PUNCT american_scientific_journal-3571 115 14 c2 c2 PROPN american_scientific_journal-3571 115 15 + + PROPN american_scientific_journal-3571 115 16 3 3 NUM american_scientific_journal-3571 115 17 ) ) PUNCT american_scientific_journal-3571 115 18 0 0 NUM american_scientific_journal-3571 115 19 0 0 NUM american_scientific_journal-3571 115 20 a3(s2βˆ’3 a3(s2βˆ’3 NOUN american_scientific_journal-3571 115 21 ) ) PUNCT american_scientific_journal-3571 116 1 + + CCONJ american_scientific_journal-3571 116 2 a2s2 a2s2 NOUN american_scientific_journal-3571 116 3 0 0 NUM american_scientific_journal-3571 116 4 1 1 NUM american_scientific_journal-3571 116 5 οΏ½ οΏ½ PROPN american_scientific_journal-3571 116 6 ( ( PUNCT american_scientific_journal-3571 116 7 7 7 NUM american_scientific_journal-3571 116 8 ) ) PUNCT american_scientific_journal-3571 116 9 where where SCONJ american_scientific_journal-3571 116 10 : : PUNCT american_scientific_journal-3571 116 11 𝑐𝑐𝑖𝑖 𝑐𝑐𝑖𝑖 NOUN american_scientific_journal-3571 116 12 = = PUNCT american_scientific_journal-3571 116 13 π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– π‘π‘π‘π‘π‘π‘πœƒπœƒπ‘–π‘– NOUN american_scientific_journal-3571 116 14 and and CCONJ american_scientific_journal-3571 116 15 𝑐𝑐𝑖𝑖 𝑐𝑐𝑖𝑖 NOUN american_scientific_journal-3571 116 16 = = PUNCT american_scientific_journal-3571 116 17 π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– π‘π‘π‘ π‘ π‘ π‘ πœƒπœƒπ‘–π‘– NOUN american_scientific_journal-3571 116 18 , , PUNCT american_scientific_journal-3571 116 19 for for ADP american_scientific_journal-3571 116 20 i=1,2 i=1,2 ADJ american_scientific_journal-3571 116 21 , , PUNCT american_scientific_journal-3571 116 22 and and CCONJ american_scientific_journal-3571 116 23 3 3 X american_scientific_journal-3571 116 24 . . X american_scientific_journal-3571 116 25 american american PROPN american_scientific_journal-3571 116 26 scientific scientific ADJ american_scientific_journal-3571 116 27 research research PROPN american_scientific_journal-3571 116 28 journal journal NOUN american_scientific_journal-3571 116 29 for for ADP american_scientific_journal-3571 116 30 engineering engineering NOUN american_scientific_journal-3571 116 31 , , PUNCT american_scientific_journal-3571 116 32 technology technology NOUN american_scientific_journal-3571 116 33 , , PUNCT american_scientific_journal-3571 116 34 and and CCONJ american_scientific_journal-3571 116 35 sciences science NOUN american_scientific_journal-3571 116 36 ( ( PUNCT american_scientific_journal-3571 116 37 asrjets asrjet NOUN american_scientific_journal-3571 116 38 ) ) PUNCT american_scientific_journal-3571 116 39 ( ( PUNCT american_scientific_journal-3571 116 40 2017 2017 NUM american_scientific_journal-3571 116 41 ) ) PUNCT american_scientific_journal-3571 116 42 volume volume NOUN american_scientific_journal-3571 116 43 38 38 NUM american_scientific_journal-3571 116 44 , , PUNCT american_scientific_journal-3571 116 45 no no DET american_scientific_journal-3571 116 46 1 1 NUM american_scientific_journal-3571 116 47 , , PUNCT american_scientific_journal-3571 116 48 pp pp ADV american_scientific_journal-3571 116 49 17 17 NUM american_scientific_journal-3571 116 50 - - SYM american_scientific_journal-3571 116 51 32 32 NUM american_scientific_journal-3571 116 52 23 23 NUM american_scientific_journal-3571 116 53 ( ( PUNCT american_scientific_journal-3571 116 54 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 116 55 + + PROPN american_scientific_journal-3571 116 56 3)= 3)= NUM american_scientific_journal-3571 116 57 cos cos X american_scientific_journal-3571 116 58 ( ( PUNCT american_scientific_journal-3571 116 59 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 116 60 + + X american_scientific_journal-3571 116 61 πœƒπœƒ3 πœƒπœƒ3 ADV american_scientific_journal-3571 116 62 ) ) PUNCT american_scientific_journal-3571 116 63 ( ( PUNCT american_scientific_journal-3571 116 64 𝑐𝑐2βˆ’3)= 𝑐𝑐2βˆ’3)= NOUN american_scientific_journal-3571 116 65 sin sin NOUN american_scientific_journal-3571 116 66 ( ( PUNCT american_scientific_journal-3571 116 67 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 116 68 βˆ’ βˆ’ PROPN american_scientific_journal-3571 116 69 πœƒπœƒ3 πœƒπœƒ3 NOUN american_scientific_journal-3571 116 70 ) ) PUNCT american_scientific_journal-3571 116 71 thus thus ADV american_scientific_journal-3571 116 72 , , PUNCT american_scientific_journal-3571 116 73 the the DET american_scientific_journal-3571 116 74 final final ADJ american_scientific_journal-3571 116 75 position position NOUN american_scientific_journal-3571 116 76 of of ADP american_scientific_journal-3571 116 77 the the DET american_scientific_journal-3571 116 78 leg leg NOUN american_scientific_journal-3571 116 79 tip tip NOUN american_scientific_journal-3571 116 80 can can AUX american_scientific_journal-3571 116 81 be be AUX american_scientific_journal-3571 116 82 obtained obtain VERB american_scientific_journal-3571 116 83 as as ADP american_scientific_journal-3571 116 84 : : PUNCT american_scientific_journal-3571 116 85 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-3571 116 86 = = PUNCT american_scientific_journal-3571 116 87 π‘Žπ‘Ž1𝑐𝑐1 π‘Žπ‘Ž1𝑐𝑐1 PROPN american_scientific_journal-3571 116 88 + + CCONJ american_scientific_journal-3571 116 89 π‘Žπ‘Ž2𝑐𝑐1𝑐𝑐2 π‘Žπ‘Ž2𝑐𝑐1𝑐𝑐2 PROPN american_scientific_journal-3571 116 90 + + CCONJ american_scientific_journal-3571 116 91 π‘Žπ‘Ž3𝑐𝑐1 π‘Žπ‘Ž3𝑐𝑐1 X american_scientific_journal-3571 116 92 ( ( PUNCT american_scientific_journal-3571 116 93 8) 8) NUM american_scientific_journal-3571 116 94 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-3571 116 95 = = PUNCT american_scientific_journal-3571 116 96 π‘Žπ‘Ž1𝑐𝑐1 π‘Žπ‘Ž1𝑐𝑐1 PROPN american_scientific_journal-3571 116 97 + + CCONJ american_scientific_journal-3571 116 98 π‘Žπ‘Ž2𝑐𝑐1𝑐𝑐2 π‘Žπ‘Ž2𝑐𝑐1𝑐𝑐2 PROPN american_scientific_journal-3571 116 99 + + CCONJ american_scientific_journal-3571 116 100 π‘Žπ‘Ž3𝑐𝑐1𝑐𝑐2 π‘Žπ‘Ž3𝑐𝑐1𝑐𝑐2 NUM american_scientific_journal-3571 116 101 + + NOUN american_scientific_journal-3571 116 102 3 3 NUM american_scientific_journal-3571 116 103 ( ( PUNCT american_scientific_journal-3571 116 104 9 9 NUM american_scientific_journal-3571 116 105 ) ) PUNCT american_scientific_journal-3571 116 106 𝑧𝑧𝑖𝑖 𝑧𝑧𝑖𝑖 NOUN american_scientific_journal-3571 116 107 = = PUNCT american_scientific_journal-3571 116 108 π‘Žπ‘Ž2𝑐𝑐2 π‘Žπ‘Ž2𝑐𝑐2 PROPN american_scientific_journal-3571 117 1 + + CCONJ american_scientific_journal-3571 117 2 π‘Žπ‘Ž3 π‘Žπ‘Ž3 PRON american_scientific_journal-3571 117 3 𝑐𝑐2βˆ’3 𝑐𝑐2βˆ’3 NOUN american_scientific_journal-3571 117 4 ( ( PUNCT american_scientific_journal-3571 117 5 10 10 NUM american_scientific_journal-3571 117 6 ) ) PUNCT american_scientific_journal-3571 117 7 where where SCONJ american_scientific_journal-3571 117 8 : : PUNCT american_scientific_journal-3571 117 9 ( ( PUNCT american_scientific_journal-3571 117 10 π‘₯π‘₯𝑖𝑖,𝑦𝑦𝑖𝑖 π‘₯π‘₯𝑖𝑖,𝑦𝑦𝑖𝑖 X american_scientific_journal-3571 117 11 , , PUNCT american_scientific_journal-3571 117 12 𝑧𝑧𝑖𝑖 𝑧𝑧𝑖𝑖 NOUN american_scientific_journal-3571 117 13 ) ) PUNCT american_scientific_journal-3571 117 14 is be AUX american_scientific_journal-3571 117 15 the the DET american_scientific_journal-3571 117 16 leg leg NOUN american_scientific_journal-3571 117 17 - - PUNCT american_scientific_journal-3571 117 18 tip tip NOUN american_scientific_journal-3571 117 19 coordinates coordinate NOUN american_scientific_journal-3571 117 20 , , PUNCT american_scientific_journal-3571 117 21 i=1 i=1 X american_scientific_journal-3571 117 22 … … SYM american_scientific_journal-3571 117 23 4 4 NUM american_scientific_journal-3571 117 24 . . NOUN american_scientific_journal-3571 117 25 4.2 4.2 NUM american_scientific_journal-3571 117 26 inverse inverse NOUN american_scientific_journal-3571 117 27 kinematics kinematic NOUN american_scientific_journal-3571 117 28 the the DET american_scientific_journal-3571 117 29 inverse inverse NOUN american_scientific_journal-3571 117 30 kinematics kinematic NOUN american_scientific_journal-3571 117 31 is be AUX american_scientific_journal-3571 117 32 used use VERB american_scientific_journal-3571 117 33 to to PART american_scientific_journal-3571 117 34 formulate formulate VERB american_scientific_journal-3571 117 35 and and CCONJ american_scientific_journal-3571 117 36 achieve achieve VERB american_scientific_journal-3571 117 37 the the DET american_scientific_journal-3571 117 38 joint joint ADJ american_scientific_journal-3571 117 39 angles angle NOUN american_scientific_journal-3571 117 40 from from ADP american_scientific_journal-3571 117 41 the the DET american_scientific_journal-3571 117 42 leg leg NOUN american_scientific_journal-3571 117 43 tip tip NOUN american_scientific_journal-3571 117 44 position position NOUN american_scientific_journal-3571 117 45 and and CCONJ american_scientific_journal-3571 117 46 orientation orientation NOUN american_scientific_journal-3571 117 47 which which PRON american_scientific_journal-3571 117 48 has have AUX american_scientific_journal-3571 117 49 been be AUX american_scientific_journal-3571 117 50 calculated calculate VERB american_scientific_journal-3571 117 51 from from ADP american_scientific_journal-3571 117 52 the the DET american_scientific_journal-3571 117 53 forward forward ADJ american_scientific_journal-3571 117 54 kinematics kinematic NOUN american_scientific_journal-3571 118 1 [ [ X american_scientific_journal-3571 118 2 14 14 NUM american_scientific_journal-3571 118 3 ] ] PUNCT american_scientific_journal-3571 118 4 . . PUNCT american_scientific_journal-3571 119 1 in in ADP american_scientific_journal-3571 119 2 this this DET american_scientific_journal-3571 119 3 paper paper NOUN american_scientific_journal-3571 119 4 , , PUNCT american_scientific_journal-3571 119 5 the the DET american_scientific_journal-3571 119 6 goal goal NOUN american_scientific_journal-3571 119 7 of of ADP american_scientific_journal-3571 119 8 inverse inverse NOUN american_scientific_journal-3571 119 9 kinematics kinematic NOUN american_scientific_journal-3571 119 10 is be AUX american_scientific_journal-3571 119 11 to to PART american_scientific_journal-3571 119 12 find find VERB american_scientific_journal-3571 119 13 joint joint ADJ american_scientific_journal-3571 119 14 angles angle NOUN american_scientific_journal-3571 119 15 of of ADP american_scientific_journal-3571 119 16 each each DET american_scientific_journal-3571 119 17 leg leg NOUN american_scientific_journal-3571 119 18 , , PUNCT american_scientific_journal-3571 119 19 πœƒπœƒ1,πœƒπœƒ2 πœƒπœƒ1,πœƒπœƒ2 X american_scientific_journal-3571 119 20 and and CCONJ american_scientific_journal-3571 119 21 πœƒπœƒ3 πœƒπœƒ3 ADV american_scientific_journal-3571 119 22 , , PUNCT american_scientific_journal-3571 119 23 from from ADP american_scientific_journal-3571 119 24 the the DET american_scientific_journal-3571 119 25 leg leg NOUN american_scientific_journal-3571 119 26 position position NOUN american_scientific_journal-3571 119 27 . . PUNCT american_scientific_journal-3571 120 1 the the DET american_scientific_journal-3571 120 2 leg leg NOUN american_scientific_journal-3571 120 3 configuration configuration NOUN american_scientific_journal-3571 120 4 assumed assume VERB american_scientific_journal-3571 120 5 to to PART american_scientific_journal-3571 120 6 be be AUX american_scientific_journal-3571 120 7 similar similar ADJ american_scientific_journal-3571 120 8 with with ADP american_scientific_journal-3571 120 9 the the DET american_scientific_journal-3571 120 10 natural natural ADJ american_scientific_journal-3571 120 11 biological biological ADJ american_scientific_journal-3571 120 12 insect insect NOUN american_scientific_journal-3571 120 13 as as SCONJ american_scientific_journal-3571 120 14 illustrated illustrate VERB american_scientific_journal-3571 120 15 in in ADP american_scientific_journal-3571 120 16 fig.(4 fig.(4 PROPN american_scientific_journal-3571 120 17 ) ) PUNCT american_scientific_journal-3571 120 18 . . PUNCT american_scientific_journal-3571 121 1 figure figure VERB american_scientific_journal-3571 121 2 4 4 NUM american_scientific_journal-3571 121 3 : : PUNCT american_scientific_journal-3571 121 4 shows show VERB american_scientific_journal-3571 121 5 one one NUM american_scientific_journal-3571 121 6 leg leg NOUN american_scientific_journal-3571 121 7 of of ADP american_scientific_journal-3571 121 8 insect insect NOUN american_scientific_journal-3571 121 9 and and CCONJ american_scientific_journal-3571 121 10 its its PRON american_scientific_journal-3571 121 11 links link NOUN american_scientific_journal-3571 121 12 ( ( PUNCT american_scientific_journal-3571 121 13 coxa coxa ADJ american_scientific_journal-3571 121 14 , , PUNCT american_scientific_journal-3571 121 15 femur femur NOUN american_scientific_journal-3571 121 16 , , PUNCT american_scientific_journal-3571 121 17 tibia tibia NOUN american_scientific_journal-3571 121 18 ) ) PUNCT american_scientific_journal-3571 122 1 [ [ X american_scientific_journal-3571 122 2 16 16 NUM american_scientific_journal-3571 122 3 ] ] PUNCT american_scientific_journal-3571 122 4 to to PART american_scientific_journal-3571 122 5 solve solve VERB american_scientific_journal-3571 122 6 inverse inverse ADJ american_scientific_journal-3571 122 7 kinematics kinematic NOUN american_scientific_journal-3571 122 8 for for ADP american_scientific_journal-3571 122 9 every every DET american_scientific_journal-3571 122 10 legs leg NOUN american_scientific_journal-3571 122 11 , , PUNCT american_scientific_journal-3571 122 12 its its PRON american_scientific_journal-3571 122 13 need need NOUN american_scientific_journal-3571 122 14 to to PART american_scientific_journal-3571 122 15 use use VERB american_scientific_journal-3571 122 16 the the DET american_scientific_journal-3571 122 17 geometrical geometrical ADJ american_scientific_journal-3571 122 18 methods method NOUN american_scientific_journal-3571 122 19 . . PUNCT american_scientific_journal-3571 123 1 firstly firstly ADV american_scientific_journal-3571 123 2 , , PUNCT american_scientific_journal-3571 123 3 its its PRON american_scientific_journal-3571 123 4 need need NOUN american_scientific_journal-3571 123 5 to to PART american_scientific_journal-3571 123 6 simple simple VERB american_scientific_journal-3571 123 7 the the DET american_scientific_journal-3571 123 8 geometrical geometrical ADJ american_scientific_journal-3571 123 9 figure figure NOUN american_scientific_journal-3571 123 10 of of ADP american_scientific_journal-3571 123 11 the the DET american_scientific_journal-3571 123 12 leg leg NOUN american_scientific_journal-3571 123 13 from from ADP american_scientific_journal-3571 123 14 ( ( PUNCT american_scientific_journal-3571 123 15 3d 3d NOUN american_scientific_journal-3571 123 16 ) ) PUNCT american_scientific_journal-3571 123 17 views view NOUN american_scientific_journal-3571 123 18 to to ADP american_scientific_journal-3571 123 19 ( ( PUNCT american_scientific_journal-3571 123 20 2d 2d NOUN american_scientific_journal-3571 123 21 ) ) PUNCT american_scientific_journal-3571 123 22 view view NOUN american_scientific_journal-3571 123 23 . . PUNCT american_scientific_journal-3571 124 1 secondly secondly ADV american_scientific_journal-3571 124 2 , , PUNCT american_scientific_journal-3571 124 3 finding find VERB american_scientific_journal-3571 124 4 each each DET american_scientific_journal-3571 124 5 joint joint ADJ american_scientific_journal-3571 124 6 angle angle NOUN american_scientific_journal-3571 124 7 by by ADP american_scientific_journal-3571 124 8 using use VERB american_scientific_journal-3571 124 9 the the DET american_scientific_journal-3571 124 10 geometrical geometrical ADJ american_scientific_journal-3571 124 11 analysis analysis NOUN american_scientific_journal-3571 124 12 to to PART american_scientific_journal-3571 124 13 find find VERB american_scientific_journal-3571 124 14 ( ( PUNCT american_scientific_journal-3571 124 15 πœƒπœƒ1,πœƒπœƒ2 πœƒπœƒ1,πœƒπœƒ2 X american_scientific_journal-3571 124 16 and and CCONJ american_scientific_journal-3571 124 17 πœƒπœƒ3 πœƒπœƒ3 ADP american_scientific_journal-3571 124 18 ) ) PUNCT american_scientific_journal-3571 124 19 as as SCONJ american_scientific_journal-3571 124 20 shown show VERB american_scientific_journal-3571 124 21 in in ADP american_scientific_journal-3571 124 22 fig.(5 fig.(5 PROPN american_scientific_journal-3571 124 23 ) ) PUNCT american_scientific_journal-3571 124 24 . . PUNCT american_scientific_journal-3571 125 1 figure figure VERB american_scientific_journal-3571 125 2 5 5 NUM american_scientific_journal-3571 125 3 : : PUNCT american_scientific_journal-3571 125 4 quadruped quadrupe VERB american_scientific_journal-3571 125 5 top top ADJ american_scientific_journal-3571 125 6 view view NOUN american_scientific_journal-3571 125 7 showing show VERB american_scientific_journal-3571 125 8 leg leg NOUN american_scientific_journal-3571 125 9 angle angle NOUN american_scientific_journal-3571 125 10 πœƒπœƒ1 πœƒπœƒ1 PROPN american_scientific_journal-3571 125 11 american american PROPN american_scientific_journal-3571 125 12 scientific scientific PROPN american_scientific_journal-3571 125 13 research research PROPN american_scientific_journal-3571 125 14 journal journal NOUN american_scientific_journal-3571 125 15 for for ADP american_scientific_journal-3571 125 16 engineering engineering NOUN american_scientific_journal-3571 125 17 , , PUNCT american_scientific_journal-3571 125 18 technology technology NOUN american_scientific_journal-3571 125 19 , , PUNCT american_scientific_journal-3571 125 20 and and CCONJ american_scientific_journal-3571 125 21 sciences science NOUN american_scientific_journal-3571 125 22 ( ( PUNCT american_scientific_journal-3571 125 23 asrjets asrjet NOUN american_scientific_journal-3571 125 24 ) ) PUNCT american_scientific_journal-3571 125 25 ( ( PUNCT american_scientific_journal-3571 125 26 2017 2017 NUM american_scientific_journal-3571 125 27 ) ) PUNCT american_scientific_journal-3571 125 28 volume volume NOUN american_scientific_journal-3571 125 29 38 38 NUM american_scientific_journal-3571 125 30 , , PUNCT american_scientific_journal-3571 125 31 no no DET american_scientific_journal-3571 125 32 1 1 NUM american_scientific_journal-3571 125 33 , , PUNCT american_scientific_journal-3571 125 34 pp pp ADV american_scientific_journal-3571 125 35 17 17 NUM american_scientific_journal-3571 125 36 - - SYM american_scientific_journal-3571 125 37 32 32 NUM american_scientific_journal-3571 125 38 24 24 NUM american_scientific_journal-3571 125 39 πœƒπœƒ1 πœƒπœƒ1 NOUN american_scientific_journal-3571 125 40 can can AUX american_scientific_journal-3571 125 41 be be AUX american_scientific_journal-3571 125 42 directly directly ADV american_scientific_journal-3571 125 43 calculated calculate VERB american_scientific_journal-3571 125 44 as as ADP american_scientific_journal-3571 125 45 : : PUNCT american_scientific_journal-3571 125 46 πœƒπœƒ1 πœƒπœƒ1 NOUN american_scientific_journal-3571 125 47 = = SYM american_scientific_journal-3571 125 48 π‘‘π‘‘π‘Žπ‘Žπ‘ π‘ βˆ’1(𝑋𝑋 π‘‘π‘‘π‘Žπ‘Žπ‘ π‘ βˆ’1(𝑋𝑋 NOUN american_scientific_journal-3571 125 49 𝑑𝑑𝑖𝑖𝑑𝑑 𝑑𝑑𝑖𝑖𝑑𝑑 NOUN american_scientific_journal-3571 125 50 π‘Œπ‘Œ π‘Œπ‘Œ PROPN american_scientific_journal-3571 125 51 𝑑𝑑𝑖𝑖𝑑𝑑 𝑑𝑑𝑖𝑖𝑑𝑑 NOUN american_scientific_journal-3571 125 52 ) ) PUNCT american_scientific_journal-3571 125 53 ( ( PUNCT american_scientific_journal-3571 125 54 11 11 NUM american_scientific_journal-3571 125 55 ) ) PUNCT american_scientific_journal-3571 125 56 after after ADP american_scientific_journal-3571 125 57 finding find VERB american_scientific_journal-3571 125 58 πœƒπœƒ1 πœƒπœƒ1 PROPN american_scientific_journal-3571 125 59 , , PUNCT american_scientific_journal-3571 125 60 the the DET american_scientific_journal-3571 125 61 other other ADJ american_scientific_journal-3571 125 62 angelsπœƒπœƒ2 angelsπœƒπœƒ2 NOUN american_scientific_journal-3571 125 63 and and CCONJ american_scientific_journal-3571 125 64 πœƒπœƒ3 πœƒπœƒ3 NOUN american_scientific_journal-3571 125 65 are be AUX american_scientific_journal-3571 125 66 in in ADP american_scientific_journal-3571 125 67 the the DET american_scientific_journal-3571 125 68 same same ADJ american_scientific_journal-3571 125 69 ( ( PUNCT american_scientific_journal-3571 125 70 y y PROPN american_scientific_journal-3571 125 71 - - PUNCT american_scientific_journal-3571 125 72 z z NOUN american_scientific_journal-3571 125 73 ) ) PUNCT american_scientific_journal-3571 125 74 plane plane NOUN american_scientific_journal-3571 125 75 . . PUNCT american_scientific_journal-3571 126 1 firstly firstly ADV american_scientific_journal-3571 126 2 , , PUNCT american_scientific_journal-3571 126 3 finding find VERB american_scientific_journal-3571 126 4 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 126 5 by by ADP american_scientific_journal-3571 126 6 dividing divide VERB american_scientific_journal-3571 126 7 it it PRON american_scientific_journal-3571 126 8 into into ADP american_scientific_journal-3571 126 9 two two NUM american_scientific_journal-3571 126 10 parts part NOUN american_scientific_journal-3571 126 11 𝑐𝑐1and 𝑐𝑐1and VERB american_scientific_journal-3571 126 12 𝑐𝑐2 𝑐𝑐2 NOUN american_scientific_journal-3571 126 13 to to PART american_scientific_journal-3571 126 14 simplify simplify VERB american_scientific_journal-3571 126 15 the the DET american_scientific_journal-3571 126 16 problem problem NOUN american_scientific_journal-3571 126 17 . . PUNCT american_scientific_journal-3571 127 1 from from ADP american_scientific_journal-3571 127 2 fig.(6 fig.(6 PROPN american_scientific_journal-3571 127 3 ) ) PUNCT american_scientific_journal-3571 127 4 , , PUNCT american_scientific_journal-3571 127 5 it it PRON american_scientific_journal-3571 127 6 can can AUX american_scientific_journal-3571 127 7 be be AUX american_scientific_journal-3571 127 8 seen see VERB american_scientific_journal-3571 127 9 that that SCONJ american_scientific_journal-3571 127 10 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 127 11 is be AUX american_scientific_journal-3571 127 12 depending depend VERB american_scientific_journal-3571 127 13 on on ADP american_scientific_journal-3571 127 14 the the DET american_scientific_journal-3571 127 15 distance distance NOUN american_scientific_journal-3571 127 16 l l NOUN american_scientific_journal-3571 127 17 which which PRON american_scientific_journal-3571 127 18 equals equal VERB american_scientific_journal-3571 127 19 to to ADP american_scientific_journal-3571 127 20 : : PUNCT american_scientific_journal-3571 128 1 𝐿𝐿 𝐿𝐿 PROPN american_scientific_journal-3571 128 2 = = PUNCT american_scientific_journal-3571 128 3 οΏ½ οΏ½ PROPN american_scientific_journal-3571 128 4 𝑧𝑧𝑐𝑐𝑓𝑓𝑓𝑓𝑏𝑏𝑏𝑏𝑑𝑑2 𝑧𝑧𝑐𝑐𝑓𝑓𝑓𝑓𝑏𝑏𝑏𝑏𝑑𝑑2 NOUN american_scientific_journal-3571 128 5 + + CCONJ american_scientific_journal-3571 128 6 ( ( PUNCT american_scientific_journal-3571 128 7 𝐿𝐿1 𝐿𝐿1 PROPN american_scientific_journal-3571 128 8 βˆ’ βˆ’ PROPN american_scientific_journal-3571 128 9 𝑐𝑐)22 𝑐𝑐)22 NOUN american_scientific_journal-3571 128 10 ( ( PUNCT american_scientific_journal-3571 128 11 12 12 NUM american_scientific_journal-3571 128 12 ) ) PUNCT american_scientific_journal-3571 128 13 where where SCONJ american_scientific_journal-3571 128 14 : : PUNCT american_scientific_journal-3571 128 15 c c NOUN american_scientific_journal-3571 128 16 is be AUX american_scientific_journal-3571 128 17 the the DET american_scientific_journal-3571 128 18 length length NOUN american_scientific_journal-3571 128 19 of of ADP american_scientific_journal-3571 128 20 coxa coxa PROPN american_scientific_journal-3571 128 21 link link NOUN american_scientific_journal-3571 128 22 . . PUNCT american_scientific_journal-3571 129 1 so so ADV american_scientific_journal-3571 129 2 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 129 3 can can AUX american_scientific_journal-3571 129 4 be be AUX american_scientific_journal-3571 129 5 calculated calculate VERB american_scientific_journal-3571 129 6 as as ADP american_scientific_journal-3571 129 7 : : PUNCT american_scientific_journal-3571 129 8 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 129 9 = = PUNCT american_scientific_journal-3571 130 1 π‘π‘π‘π‘π‘π‘βˆ’1(π‘§π‘§π‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ π‘π‘π‘π‘π‘π‘βˆ’1(π‘§π‘§π‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ PROPN american_scientific_journal-3571 130 2 𝐿𝐿 𝐿𝐿 PROPN american_scientific_journal-3571 130 3 ) ) PUNCT american_scientific_journal-3571 130 4 ( ( PUNCT american_scientific_journal-3571 130 5 13 13 NUM american_scientific_journal-3571 130 6 ) ) PUNCT american_scientific_journal-3571 130 7 from from ADP american_scientific_journal-3571 130 8 the the DET american_scientific_journal-3571 130 9 cosine cosine NOUN american_scientific_journal-3571 130 10 rules rule NOUN american_scientific_journal-3571 130 11 and and CCONJ american_scientific_journal-3571 130 12 from from ADP american_scientific_journal-3571 130 13 fig.(6 fig.(6 PROPN american_scientific_journal-3571 130 14 ) ) PUNCT american_scientific_journal-3571 130 15 , , PUNCT american_scientific_journal-3571 130 16 𝑐𝑐2will 𝑐𝑐2will PRON american_scientific_journal-3571 130 17 be be AUX american_scientific_journal-3571 130 18 found find VERB american_scientific_journal-3571 130 19 as as ADP american_scientific_journal-3571 130 20 : : PUNCT american_scientific_journal-3571 130 21 𝑇𝑇2 𝑇𝑇2 PROPN american_scientific_journal-3571 130 22 = = SYM american_scientific_journal-3571 130 23 𝐹𝐹2 𝐹𝐹2 PROPN american_scientific_journal-3571 130 24 + + PROPN american_scientific_journal-3571 130 25 𝐿𝐿2 𝐿𝐿2 PROPN american_scientific_journal-3571 130 26 βˆ’ βˆ’ PROPN american_scientific_journal-3571 130 27 ( ( PUNCT american_scientific_journal-3571 130 28 2 2 NUM american_scientific_journal-3571 130 29 βˆ— βˆ— NOUN american_scientific_journal-3571 130 30 𝐹𝐹 𝐹𝐹 PROPN american_scientific_journal-3571 130 31 βˆ— βˆ— NOUN american_scientific_journal-3571 130 32 𝐿𝐿)cos 𝐿𝐿)cos X american_scientific_journal-3571 130 33 ( ( PUNCT american_scientific_journal-3571 130 34 𝑐𝑐2 𝑐𝑐2 NOUN american_scientific_journal-3571 130 35 ) ) PUNCT american_scientific_journal-3571 130 36 thus thus ADV american_scientific_journal-3571 130 37 : : PUNCT american_scientific_journal-3571 130 38 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 130 39 = = PUNCT american_scientific_journal-3571 130 40 π‘π‘π‘π‘π‘π‘βˆ’1 π‘π‘π‘π‘π‘π‘βˆ’1 NOUN american_scientific_journal-3571 130 41 οΏ½ οΏ½ NOUN american_scientific_journal-3571 130 42 𝐹𝐹 𝐹𝐹 ADJ american_scientific_journal-3571 130 43 2+𝐿𝐿2βˆ’π‘‡π‘‡2 2+𝐿𝐿2βˆ’π‘‡π‘‡2 NUM american_scientific_journal-3571 130 44 2βˆ—πΉπΉβˆ—πΏπΏ 2βˆ—πΉπΉβˆ—πΏπΏ NUM american_scientific_journal-3571 130 45 οΏ½ οΏ½ PROPN american_scientific_journal-3571 130 46 ( ( PUNCT american_scientific_journal-3571 130 47 14 14 NUM american_scientific_journal-3571 130 48 ) ) PUNCT american_scientific_journal-3571 130 49 where where SCONJ american_scientific_journal-3571 130 50 : : PUNCT american_scientific_journal-3571 130 51 f f PROPN american_scientific_journal-3571 130 52 is be AUX american_scientific_journal-3571 130 53 the the DET american_scientific_journal-3571 130 54 femur femur ADJ american_scientific_journal-3571 130 55 link link NOUN american_scientific_journal-3571 130 56 length length NOUN american_scientific_journal-3571 130 57 and and CCONJ american_scientific_journal-3571 130 58 t t PROPN american_scientific_journal-3571 130 59 is be AUX american_scientific_journal-3571 130 60 the the DET american_scientific_journal-3571 130 61 tibia tibia NOUN american_scientific_journal-3571 130 62 link link NOUN american_scientific_journal-3571 130 63 length length NOUN american_scientific_journal-3571 130 64 . . PUNCT american_scientific_journal-3571 131 1 figure figure VERB american_scientific_journal-3571 131 2 6 6 NUM american_scientific_journal-3571 131 3 : : PUNCT american_scientific_journal-3571 131 4 quadruped quadruped NOUN american_scientific_journal-3571 131 5 robot robot NOUN american_scientific_journal-3571 131 6 leg leg NOUN american_scientific_journal-3571 131 7 and and CCONJ american_scientific_journal-3571 131 8 its its PRON american_scientific_journal-3571 131 9 links link NOUN american_scientific_journal-3571 131 10 ( ( PUNCT american_scientific_journal-3571 131 11 coxa coxa ADJ american_scientific_journal-3571 131 12 , , PUNCT american_scientific_journal-3571 131 13 femur femur NOUN american_scientific_journal-3571 131 14 , , PUNCT american_scientific_journal-3571 131 15 tibia tibia NOUN american_scientific_journal-3571 131 16 ) ) PUNCT american_scientific_journal-3571 131 17 , , PUNCT american_scientific_journal-3571 131 18 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 131 19 andπœƒπœƒ3 andπœƒπœƒ3 X american_scientific_journal-3571 132 1 [ [ X american_scientific_journal-3571 132 2 14 14 NUM american_scientific_journal-3571 132 3 ] ] PUNCT american_scientific_journal-3571 132 4 from from ADP american_scientific_journal-3571 132 5 fig.(6),πœƒπœƒ2 fig.(6),πœƒπœƒ2 PROPN american_scientific_journal-3571 132 6 equals equal VERB american_scientific_journal-3571 132 7 to to ADP american_scientific_journal-3571 132 8 : : PUNCT american_scientific_journal-3571 132 9 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 132 10 = = PUNCT american_scientific_journal-3571 132 11 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-3571 132 12 + + CCONJ american_scientific_journal-3571 132 13 𝑐𝑐2 𝑐𝑐2 PROPN american_scientific_journal-3571 132 14 american american ADJ american_scientific_journal-3571 132 15 scientific scientific ADJ american_scientific_journal-3571 132 16 research research NOUN american_scientific_journal-3571 132 17 journal journal NOUN american_scientific_journal-3571 132 18 for for ADP american_scientific_journal-3571 132 19 engineering engineering NOUN american_scientific_journal-3571 132 20 , , PUNCT american_scientific_journal-3571 132 21 technology technology NOUN american_scientific_journal-3571 132 22 , , PUNCT american_scientific_journal-3571 132 23 and and CCONJ american_scientific_journal-3571 132 24 sciences science NOUN american_scientific_journal-3571 132 25 ( ( PUNCT american_scientific_journal-3571 132 26 asrjets asrjet NOUN american_scientific_journal-3571 132 27 ) ) PUNCT american_scientific_journal-3571 132 28 ( ( PUNCT american_scientific_journal-3571 132 29 2017 2017 NUM american_scientific_journal-3571 132 30 ) ) PUNCT american_scientific_journal-3571 132 31 volume volume NOUN american_scientific_journal-3571 132 32 38 38 NUM american_scientific_journal-3571 132 33 , , PUNCT american_scientific_journal-3571 132 34 no no DET american_scientific_journal-3571 132 35 1 1 NUM american_scientific_journal-3571 132 36 , , PUNCT american_scientific_journal-3571 132 37 pp pp ADV american_scientific_journal-3571 132 38 17 17 NUM american_scientific_journal-3571 132 39 - - SYM american_scientific_journal-3571 132 40 32 32 NUM american_scientific_journal-3571 132 41 25 25 NUM american_scientific_journal-3571 132 42 πœƒπœƒ2 πœƒπœƒ2 X american_scientific_journal-3571 132 43 = = PUNCT american_scientific_journal-3571 132 44 π‘π‘π‘π‘π‘π‘βˆ’1 π‘π‘π‘π‘π‘π‘βˆ’1 PROPN american_scientific_journal-3571 132 45 οΏ½ οΏ½ NOUN american_scientific_journal-3571 132 46 π‘§π‘§π‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ π‘§π‘§π‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ NOUN american_scientific_journal-3571 132 47 𝐿𝐿 𝐿𝐿 PROPN american_scientific_journal-3571 132 48 οΏ½ οΏ½ PROPN american_scientific_journal-3571 132 49 + + CCONJ american_scientific_journal-3571 132 50 π‘π‘π‘π‘π‘π‘βˆ’1 π‘π‘π‘π‘π‘π‘βˆ’1 PROPN american_scientific_journal-3571 132 51 οΏ½ οΏ½ NOUN american_scientific_journal-3571 132 52 𝐹𝐹 𝐹𝐹 ADJ american_scientific_journal-3571 132 53 2+𝐿𝐿2βˆ’π‘‡π‘‡2 2+𝐿𝐿2βˆ’π‘‡π‘‡2 NUM american_scientific_journal-3571 132 54 2βˆ—πΉπΉβˆ—πΏπΏ 2βˆ—πΉπΉβˆ—πΏπΏ NUM american_scientific_journal-3571 132 55 οΏ½ οΏ½ PROPN american_scientific_journal-3571 132 56 ( ( PUNCT american_scientific_journal-3571 132 57 15 15 NUM american_scientific_journal-3571 132 58 ) ) PUNCT american_scientific_journal-3571 132 59 by by ADP american_scientific_journal-3571 132 60 the the DET american_scientific_journal-3571 132 61 same same ADJ american_scientific_journal-3571 132 62 method method NOUN american_scientific_journal-3571 132 63 , , PUNCT american_scientific_journal-3571 132 64 πœƒπœƒ3 πœƒπœƒ3 X american_scientific_journal-3571 132 65 is be AUX american_scientific_journal-3571 132 66 calculated calculate VERB american_scientific_journal-3571 132 67 as as ADP american_scientific_journal-3571 132 68 : : PUNCT american_scientific_journal-3571 132 69 πœƒπœƒ3 πœƒπœƒ3 NOUN american_scientific_journal-3571 132 70 = = PUNCT american_scientific_journal-3571 132 71 π‘π‘π‘π‘π‘π‘βˆ’1 π‘π‘π‘π‘π‘π‘βˆ’1 PROPN american_scientific_journal-3571 132 72 οΏ½ οΏ½ NOUN american_scientific_journal-3571 132 73 𝐹𝐹 𝐹𝐹 ADJ american_scientific_journal-3571 132 74 2+𝑇𝑇2βˆ’πΏπΏ2 2+𝑇𝑇2βˆ’πΏπΏ2 PROPN american_scientific_journal-3571 132 75 2βˆ—πΉπΉβˆ—π‘‡π‘‡ 2βˆ—πΉπΉβˆ—π‘‡π‘‡ NUM american_scientific_journal-3571 132 76 οΏ½ οΏ½ PROPN american_scientific_journal-3571 132 77 ( ( PUNCT american_scientific_journal-3571 132 78 16 16 NUM american_scientific_journal-3571 132 79 ) ) PUNCT american_scientific_journal-3571 132 80 5 5 NUM american_scientific_journal-3571 132 81 . . PUNCT american_scientific_journal-3571 132 82 stability stability NOUN american_scientific_journal-3571 132 83 margins margin VERB american_scientific_journal-3571 132 84 analysis analysis NOUN american_scientific_journal-3571 132 85 for for ADP american_scientific_journal-3571 132 86 quadruped quadruped NOUN american_scientific_journal-3571 132 87 robot robot NOUN american_scientific_journal-3571 132 88 creeping creeping NOUN american_scientific_journal-3571 132 89 gait gait NOUN american_scientific_journal-3571 132 90 the the DET american_scientific_journal-3571 132 91 quadruped quadruped NOUN american_scientific_journal-3571 132 92 robot robot NOUN american_scientific_journal-3571 132 93 walks walk VERB american_scientific_journal-3571 132 94 with with ADP american_scientific_journal-3571 132 95 a a DET american_scientific_journal-3571 132 96 specific specific ADJ american_scientific_journal-3571 132 97 goal goal NOUN american_scientific_journal-3571 132 98 to to PART american_scientific_journal-3571 132 99 have have AUX american_scientific_journal-3571 132 100 a a DET american_scientific_journal-3571 132 101 statically statically ADV american_scientific_journal-3571 132 102 stable stable ADJ american_scientific_journal-3571 132 103 movement movement NOUN american_scientific_journal-3571 132 104 . . PUNCT american_scientific_journal-3571 133 1 during during ADP american_scientific_journal-3571 133 2 the the DET american_scientific_journal-3571 133 3 robot robot NOUN american_scientific_journal-3571 133 4 walking walk VERB american_scientific_journal-3571 133 5 the the DET american_scientific_journal-3571 133 6 vertical vertical ADJ american_scientific_journal-3571 133 7 projection projection NOUN american_scientific_journal-3571 133 8 of of ADP american_scientific_journal-3571 133 9 cog cog PROPN american_scientific_journal-3571 133 10 on on ADP american_scientific_journal-3571 133 11 the the DET american_scientific_journal-3571 133 12 ground ground NOUN american_scientific_journal-3571 133 13 must must AUX american_scientific_journal-3571 133 14 be be AUX american_scientific_journal-3571 133 15 inside inside ADP american_scientific_journal-3571 133 16 the the DET american_scientific_journal-3571 133 17 supporting support VERB american_scientific_journal-3571 133 18 polygon polygon NOUN american_scientific_journal-3571 133 19 . . PUNCT american_scientific_journal-3571 134 1 this this PRON american_scientific_journal-3571 134 2 is be AUX american_scientific_journal-3571 134 3 the the DET american_scientific_journal-3571 134 4 main main ADJ american_scientific_journal-3571 134 5 criterion criterion NOUN american_scientific_journal-3571 134 6 which which PRON american_scientific_journal-3571 134 7 is be AUX american_scientific_journal-3571 134 8 conditioned condition VERB american_scientific_journal-3571 134 9 for for ADP american_scientific_journal-3571 134 10 the the DET american_scientific_journal-3571 134 11 statically statically ADV american_scientific_journal-3571 134 12 stable stable ADJ american_scientific_journal-3571 134 13 walking walking NOUN american_scientific_journal-3571 134 14 . . PUNCT american_scientific_journal-3571 135 1 the the DET american_scientific_journal-3571 135 2 quadruped quadruped NOUN american_scientific_journal-3571 135 3 robot robot NOUN american_scientific_journal-3571 135 4 is be AUX american_scientific_journal-3571 135 5 stable stable ADJ american_scientific_journal-3571 135 6 and and CCONJ american_scientific_journal-3571 135 7 will will AUX american_scientific_journal-3571 135 8 not not PART american_scientific_journal-3571 135 9 turn turn VERB american_scientific_journal-3571 135 10 down down ADP american_scientific_journal-3571 135 11 when when SCONJ american_scientific_journal-3571 135 12 it it PRON american_scientific_journal-3571 135 13 satisfied satisfy VERB american_scientific_journal-3571 135 14 these these DET american_scientific_journal-3571 135 15 conditions condition NOUN american_scientific_journal-3571 135 16 of of ADP american_scientific_journal-3571 135 17 the the DET american_scientific_journal-3571 135 18 statically statically ADV american_scientific_journal-3571 135 19 stable stable ADJ american_scientific_journal-3571 135 20 walking walking NOUN american_scientific_journal-3571 135 21 . . PUNCT american_scientific_journal-3571 136 1 the the DET american_scientific_journal-3571 136 2 main main ADJ american_scientific_journal-3571 136 3 advantage advantage NOUN american_scientific_journal-3571 136 4 of of ADP american_scientific_journal-3571 136 5 the the DET american_scientific_journal-3571 136 6 quadruped quadruped NOUN american_scientific_journal-3571 136 7 robot robot NOUN american_scientific_journal-3571 136 8 walking walk VERB american_scientific_journal-3571 136 9 in in ADP american_scientific_journal-3571 136 10 periodically periodically ADV american_scientific_journal-3571 136 11 repeated repeat VERB american_scientific_journal-3571 136 12 locomotion locomotion NOUN american_scientific_journal-3571 136 13 is be AUX american_scientific_journal-3571 136 14 to to PART american_scientific_journal-3571 136 15 produce produce VERB american_scientific_journal-3571 136 16 a a DET american_scientific_journal-3571 136 17 constant constant ADJ american_scientific_journal-3571 136 18 speed speed NOUN american_scientific_journal-3571 136 19 . . PUNCT american_scientific_journal-3571 137 1 this this DET american_scientific_journal-3571 137 2 property property NOUN american_scientific_journal-3571 137 3 is be AUX american_scientific_journal-3571 137 4 leading lead VERB american_scientific_journal-3571 137 5 to to ADP american_scientific_journal-3571 137 6 the the DET american_scientific_journal-3571 137 7 fact fact NOUN american_scientific_journal-3571 137 8 that that SCONJ american_scientific_journal-3571 137 9 the the DET american_scientific_journal-3571 137 10 accelerations acceleration NOUN american_scientific_journal-3571 137 11 on on ADP american_scientific_journal-3571 137 12 the the DET american_scientific_journal-3571 137 13 robot robot NOUN american_scientific_journal-3571 137 14 body body NOUN american_scientific_journal-3571 137 15 are be AUX american_scientific_journal-3571 137 16 equal equal ADJ american_scientific_journal-3571 137 17 to to ADP american_scientific_journal-3571 137 18 zero zero NUM american_scientific_journal-3571 137 19 , , PUNCT american_scientific_journal-3571 137 20 and and CCONJ american_scientific_journal-3571 137 21 the the DET american_scientific_journal-3571 137 22 disturbances disturbance NOUN american_scientific_journal-3571 137 23 on on ADP american_scientific_journal-3571 137 24 the the DET american_scientific_journal-3571 137 25 legs leg NOUN american_scientific_journal-3571 137 26 will will AUX american_scientific_journal-3571 137 27 be be AUX american_scientific_journal-3571 137 28 reduced reduce VERB american_scientific_journal-3571 137 29 . . PUNCT american_scientific_journal-3571 138 1 when when SCONJ american_scientific_journal-3571 138 2 the the DET american_scientific_journal-3571 138 3 quadruped quadruped NOUN american_scientific_journal-3571 138 4 robot robot NOUN american_scientific_journal-3571 138 5 walking walk VERB american_scientific_journal-3571 138 6 using use VERB american_scientific_journal-3571 138 7 creeping creep VERB american_scientific_journal-3571 138 8 gait gait NOUN american_scientific_journal-3571 138 9 , , PUNCT american_scientific_journal-3571 138 10 the the DET american_scientific_journal-3571 138 11 static static ADJ american_scientific_journal-3571 138 12 stability stability NOUN american_scientific_journal-3571 138 13 walking walk VERB american_scientific_journal-3571 138 14 is be AUX american_scientific_journal-3571 138 15 depending depend VERB american_scientific_journal-3571 138 16 on on ADP american_scientific_journal-3571 138 17 the the DET american_scientific_journal-3571 138 18 stability stability NOUN american_scientific_journal-3571 138 19 margins margin NOUN american_scientific_journal-3571 138 20 . . PUNCT american_scientific_journal-3571 139 1 these these DET american_scientific_journal-3571 139 2 margins margin NOUN american_scientific_journal-3571 139 3 are be AUX american_scientific_journal-3571 139 4 defined define VERB american_scientific_journal-3571 139 5 as as ADP american_scientific_journal-3571 139 6 shortest short ADJ american_scientific_journal-3571 139 7 distance distance NOUN american_scientific_journal-3571 139 8 between between ADP american_scientific_journal-3571 139 9 the the DET american_scientific_journal-3571 139 10 vertical vertical ADJ american_scientific_journal-3571 139 11 projection projection NOUN american_scientific_journal-3571 139 12 of of ADP american_scientific_journal-3571 139 13 cog cog PROPN american_scientific_journal-3571 139 14 to to ADP american_scientific_journal-3571 139 15 the the DET american_scientific_journal-3571 139 16 boundaries boundary NOUN american_scientific_journal-3571 139 17 of of ADP american_scientific_journal-3571 139 18 the the DET american_scientific_journal-3571 139 19 supporting support VERB american_scientific_journal-3571 139 20 pattern pattern NOUN american_scientific_journal-3571 139 21 [ [ X american_scientific_journal-3571 139 22 13 13 NUM american_scientific_journal-3571 139 23 ] ] PUNCT american_scientific_journal-3571 139 24 . . PUNCT american_scientific_journal-3571 140 1 the the DET american_scientific_journal-3571 140 2 next next ADJ american_scientific_journal-3571 140 3 figures figure NOUN american_scientific_journal-3571 140 4 are be AUX american_scientific_journal-3571 140 5 showing show VERB american_scientific_journal-3571 140 6 and and CCONJ american_scientific_journal-3571 140 7 explaining explain VERB american_scientific_journal-3571 140 8 the the DET american_scientific_journal-3571 140 9 quadruped quadruped NOUN american_scientific_journal-3571 140 10 robot robot NOUN american_scientific_journal-3571 140 11 model model NOUN american_scientific_journal-3571 140 12 , , PUNCT american_scientific_journal-3571 140 13 and and CCONJ american_scientific_journal-3571 140 14 the the DET american_scientific_journal-3571 140 15 stability stability NOUN american_scientific_journal-3571 140 16 margins margin VERB american_scientific_journal-3571 140 17 mathematically mathematically ADV american_scientific_journal-3571 140 18 analysis analysis NOUN american_scientific_journal-3571 140 19 to to PART american_scientific_journal-3571 140 20 find find VERB american_scientific_journal-3571 140 21 and and CCONJ american_scientific_journal-3571 140 22 calculate calculate VERB american_scientific_journal-3571 140 23 the the DET american_scientific_journal-3571 140 24 stability stability NOUN american_scientific_journal-3571 140 25 margins margin NOUN american_scientific_journal-3571 140 26 as as ADP american_scientific_journal-3571 140 27 the the DET american_scientific_journal-3571 140 28 following following ADJ american_scientific_journal-3571 140 29 cases case NOUN american_scientific_journal-3571 140 30 : : PUNCT american_scientific_journal-3571 140 31 figure figure VERB american_scientific_journal-3571 140 32 7 7 NUM american_scientific_journal-3571 140 33 : : PUNCT american_scientific_journal-3571 140 34 quadruped quadruped NOUN american_scientific_journal-3571 140 35 robot robot NOUN american_scientific_journal-3571 140 36 ( ( PUNCT american_scientific_journal-3571 140 37 top top ADJ american_scientific_journal-3571 140 38 - - PUNCT american_scientific_journal-3571 140 39 view view NOUN american_scientific_journal-3571 140 40 ) ) PUNCT american_scientific_journal-3571 140 41 showing show VERB american_scientific_journal-3571 140 42 the the DET american_scientific_journal-3571 140 43 support support NOUN american_scientific_journal-3571 140 44 triangle triangle NOUN american_scientific_journal-3571 140 45 when when SCONJ american_scientific_journal-3571 140 46 leg4 leg4 PROPN american_scientific_journal-3571 140 47 is be AUX american_scientific_journal-3571 140 48 swinging swinge VERB american_scientific_journal-3571 140 49 and and CCONJ american_scientific_journal-3571 140 50 other other ADJ american_scientific_journal-3571 140 51 legs leg NOUN american_scientific_journal-3571 140 52 are be AUX american_scientific_journal-3571 140 53 fixed fix VERB american_scientific_journal-3571 140 54 on on ADP american_scientific_journal-3571 140 55 the the DET american_scientific_journal-3571 140 56 ground ground NOUN american_scientific_journal-3571 140 57 case case NOUN american_scientific_journal-3571 140 58 one one NUM american_scientific_journal-3571 140 59 : : PUNCT american_scientific_journal-3571 140 60 when when SCONJ american_scientific_journal-3571 140 61 the the DET american_scientific_journal-3571 140 62 quadruped quadruped NOUN american_scientific_journal-3571 140 63 robot robot NOUN american_scientific_journal-3571 140 64 leg4 leg4 PROPN american_scientific_journal-3571 140 65 is be AUX american_scientific_journal-3571 140 66 swing swe VERB american_scientific_journal-3571 140 67 and and CCONJ american_scientific_journal-3571 140 68 the the DET american_scientific_journal-3571 140 69 other other ADJ american_scientific_journal-3571 140 70 legs leg NOUN american_scientific_journal-3571 140 71 ( ( PUNCT american_scientific_journal-3571 140 72 1 1 NUM american_scientific_journal-3571 140 73 , , PUNCT american_scientific_journal-3571 140 74 2 2 NUM american_scientific_journal-3571 140 75 , , PUNCT american_scientific_journal-3571 140 76 and and CCONJ american_scientific_journal-3571 140 77 3 3 X american_scientific_journal-3571 140 78 ) ) PUNCT american_scientific_journal-3571 140 79 are be AUX american_scientific_journal-3571 140 80 fixed fix VERB american_scientific_journal-3571 140 81 on on ADP american_scientific_journal-3571 140 82 the the DET american_scientific_journal-3571 140 83 ground ground NOUN american_scientific_journal-3571 140 84 as as ADP american_scientific_journal-3571 140 85 showing show VERB american_scientific_journal-3571 140 86 in in ADP american_scientific_journal-3571 140 87 fig fig NOUN american_scientific_journal-3571 140 88 . . PUNCT american_scientific_journal-3571 141 1 ( ( PUNCT american_scientific_journal-3571 141 2 7 7 NUM american_scientific_journal-3571 141 3 ) ) PUNCT american_scientific_journal-3571 141 4 . . PUNCT american_scientific_journal-3571 142 1 the the DET american_scientific_journal-3571 142 2 supporting support VERB american_scientific_journal-3571 142 3 area area NOUN american_scientific_journal-3571 142 4 will will AUX american_scientific_journal-3571 142 5 be be AUX american_scientific_journal-3571 142 6 divided divide VERB american_scientific_journal-3571 142 7 into into ADP american_scientific_journal-3571 142 8 three three NUM american_scientific_journal-3571 142 9 areas area NOUN american_scientific_journal-3571 142 10 called call VERB american_scientific_journal-3571 142 11 ( ( PUNCT american_scientific_journal-3571 142 12 area1 area1 NOUN american_scientific_journal-3571 142 13 , , PUNCT american_scientific_journal-3571 142 14 area2 area2 NOUN american_scientific_journal-3571 142 15 , , PUNCT american_scientific_journal-3571 142 16 and and CCONJ american_scientific_journal-3571 142 17 area3 area3 NUM american_scientific_journal-3571 142 18 ) ) PUNCT american_scientific_journal-3571 142 19 . . PUNCT american_scientific_journal-3571 143 1 the the DET american_scientific_journal-3571 143 2 blue blue ADJ american_scientific_journal-3571 143 3 lines line NOUN american_scientific_journal-3571 143 4 are be AUX american_scientific_journal-3571 143 5 the the DET american_scientific_journal-3571 143 6 lines line NOUN american_scientific_journal-3571 143 7 of of ADP american_scientific_journal-3571 143 8 the the DET american_scientific_journal-3571 143 9 stability stability NOUN american_scientific_journal-3571 143 10 margins margin NOUN american_scientific_journal-3571 143 11 which which PRON american_scientific_journal-3571 143 12 are be AUX american_scientific_journal-3571 143 13 needed need VERB american_scientific_journal-3571 143 14 to to PART american_scientific_journal-3571 143 15 be be AUX american_scientific_journal-3571 143 16 the the DET american_scientific_journal-3571 143 17 minimum minimum NOUN american_scientific_journal-3571 143 18 from from ADP american_scientific_journal-3571 143 19 the the DET american_scientific_journal-3571 143 20 vertical vertical ADJ american_scientific_journal-3571 143 21 projection projection NOUN american_scientific_journal-3571 143 22 of of ADP american_scientific_journal-3571 143 23 cog cog PROPN american_scientific_journal-3571 143 24 to to ADP american_scientific_journal-3571 143 25 the the DET american_scientific_journal-3571 143 26 supporting support VERB american_scientific_journal-3571 143 27 lines line NOUN american_scientific_journal-3571 143 28 ( ( PUNCT american_scientific_journal-3571 143 29 l1 l1 PROPN american_scientific_journal-3571 143 30 , , PUNCT american_scientific_journal-3571 143 31 l2 l2 NOUN american_scientific_journal-3571 143 32 , , PUNCT american_scientific_journal-3571 143 33 and and CCONJ american_scientific_journal-3571 143 34 l3 l3 NOUN american_scientific_journal-3571 143 35 ) ) PUNCT american_scientific_journal-3571 143 36 . . PUNCT american_scientific_journal-3571 144 1 these these DET american_scientific_journal-3571 144 2 blue blue ADJ american_scientific_journal-3571 144 3 lines line NOUN american_scientific_journal-3571 144 4 are be AUX american_scientific_journal-3571 144 5 denoted denote VERB american_scientific_journal-3571 144 6 as as ADP american_scientific_journal-3571 144 7 ( ( PUNCT american_scientific_journal-3571 144 8 t1 t1 NOUN american_scientific_journal-3571 144 9 , , PUNCT american_scientific_journal-3571 144 10 t2 t2 NOUN american_scientific_journal-3571 144 11 , , PUNCT american_scientific_journal-3571 144 12 and and CCONJ american_scientific_journal-3571 144 13 t3 t3 PROPN american_scientific_journal-3571 144 14 ) ) PUNCT american_scientific_journal-3571 144 15 . . PUNCT american_scientific_journal-3571 145 1 after after SCONJ american_scientific_journal-3571 145 2 this this DET american_scientific_journal-3571 145 3 method method NOUN american_scientific_journal-3571 145 4 is be AUX american_scientific_journal-3571 145 5 applied apply VERB american_scientific_journal-3571 145 6 , , PUNCT american_scientific_journal-3571 145 7 the the DET american_scientific_journal-3571 145 8 stability stability NOUN american_scientific_journal-3571 145 9 margins margin NOUN american_scientific_journal-3571 145 10 will will AUX american_scientific_journal-3571 145 11 be be AUX american_scientific_journal-3571 145 12 found find VERB american_scientific_journal-3571 145 13 as as ADP american_scientific_journal-3571 145 14 : : PUNCT american_scientific_journal-3571 145 15 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1 PROPN american_scientific_journal-3571 145 16 = = SYM american_scientific_journal-3571 145 17 1 1 NUM american_scientific_journal-3571 145 18 2 2 NUM american_scientific_journal-3571 145 19 οΏ½ οΏ½ NOUN american_scientific_journal-3571 145 20 1 1 NUM american_scientific_journal-3571 145 21 1 1 NUM american_scientific_journal-3571 145 22 1 1 NUM american_scientific_journal-3571 145 23 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 NOUN american_scientific_journal-3571 145 24 π‘₯π‘₯1 π‘₯π‘₯1 NOUN american_scientific_journal-3571 145 25 π‘₯π‘₯3 π‘₯π‘₯3 PROPN american_scientific_journal-3571 145 26 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 NOUN american_scientific_journal-3571 145 27 𝑦𝑦1 𝑦𝑦1 PROPN american_scientific_journal-3571 145 28 𝑦𝑦3 𝑦𝑦3 VERB american_scientific_journal-3571 145 29 οΏ½ οΏ½ PROPN american_scientific_journal-3571 145 30 where where SCONJ american_scientific_journal-3571 145 31 , , PUNCT american_scientific_journal-3571 145 32 ( ( PUNCT american_scientific_journal-3571 145 33 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 NOUN american_scientific_journal-3571 145 34 , , PUNCT american_scientific_journal-3571 145 35 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 NOUN american_scientific_journal-3571 145 36 ) ) PUNCT american_scientific_journal-3571 145 37 is be AUX american_scientific_journal-3571 145 38 the the DET american_scientific_journal-3571 145 39 center center NOUN american_scientific_journal-3571 145 40 of of ADP american_scientific_journal-3571 145 41 gravity gravity NOUN american_scientific_journal-3571 145 42 coordinate coordinate NOUN american_scientific_journal-3571 145 43 of of ADP american_scientific_journal-3571 145 44 the the DET american_scientific_journal-3571 145 45 quadruped quadruped NOUN american_scientific_journal-3571 145 46 robot robot NOUN american_scientific_journal-3571 145 47 on on ADP american_scientific_journal-3571 145 48 the the DET american_scientific_journal-3571 145 49 ground ground NOUN american_scientific_journal-3571 145 50 . . PUNCT american_scientific_journal-3571 146 1 ( ( PUNCT american_scientific_journal-3571 146 2 π‘₯π‘₯1,𝑦𝑦1 π‘₯π‘₯1,𝑦𝑦1 PROPN american_scientific_journal-3571 146 3 ) ) PUNCT american_scientific_journal-3571 146 4 is be AUX american_scientific_journal-3571 146 5 the the DET american_scientific_journal-3571 146 6 leg1 leg1 NOUN american_scientific_journal-3571 146 7 50 50 NUM american_scientific_journal-3571 146 8 40 40 NUM american_scientific_journal-3571 146 9 x x SYM american_scientific_journal-3571 146 10 30 30 NUM american_scientific_journal-3571 146 11 20 20 NUM american_scientific_journal-3571 146 12 10 10 NUM american_scientific_journal-3571 146 13 0 0 NUM american_scientific_journal-3571 146 14 10 10 NUM american_scientific_journal-3571 146 15 0 0 NUM american_scientific_journal-3571 146 16 10 10 NUM american_scientific_journal-3571 146 17 20 20 NUM american_scientific_journal-3571 146 18 y y NOUN american_scientific_journal-3571 146 19 30 30 NUM american_scientific_journal-3571 146 20 40 40 NUM american_scientific_journal-3571 146 21 leg leg NOUN american_scientific_journal-3571 146 22 4 4 NUM american_scientific_journal-3571 146 23 swing swing NOUN american_scientific_journal-3571 146 24 support support NOUN american_scientific_journal-3571 146 25 triangle triangle NOUN american_scientific_journal-3571 146 26 american american ADJ american_scientific_journal-3571 146 27 scientific scientific ADJ american_scientific_journal-3571 146 28 research research NOUN american_scientific_journal-3571 146 29 journal journal NOUN american_scientific_journal-3571 146 30 for for ADP american_scientific_journal-3571 146 31 engineering engineering NOUN american_scientific_journal-3571 146 32 , , PUNCT american_scientific_journal-3571 146 33 technology technology NOUN american_scientific_journal-3571 146 34 , , PUNCT american_scientific_journal-3571 146 35 and and CCONJ american_scientific_journal-3571 146 36 sciences science NOUN american_scientific_journal-3571 146 37 ( ( PUNCT american_scientific_journal-3571 146 38 asrjets asrjet NOUN american_scientific_journal-3571 146 39 ) ) PUNCT american_scientific_journal-3571 146 40 ( ( PUNCT american_scientific_journal-3571 146 41 2017 2017 NUM american_scientific_journal-3571 146 42 ) ) PUNCT american_scientific_journal-3571 146 43 volume volume NOUN american_scientific_journal-3571 146 44 38 38 NUM american_scientific_journal-3571 146 45 , , PUNCT american_scientific_journal-3571 146 46 no no DET american_scientific_journal-3571 146 47 1 1 NUM american_scientific_journal-3571 146 48 , , PUNCT american_scientific_journal-3571 146 49 pp pp ADV american_scientific_journal-3571 146 50 17 17 NUM american_scientific_journal-3571 146 51 - - SYM american_scientific_journal-3571 146 52 32 32 NUM american_scientific_journal-3571 146 53 26 26 NUM american_scientific_journal-3571 146 54 coordinate coordinate NOUN american_scientific_journal-3571 146 55 of of ADP american_scientific_journal-3571 146 56 tip tip NOUN american_scientific_journal-3571 146 57 position position NOUN american_scientific_journal-3571 146 58 . . PUNCT american_scientific_journal-3571 147 1 ( ( PUNCT american_scientific_journal-3571 147 2 π‘₯π‘₯3,𝑦𝑦3 π‘₯π‘₯3,𝑦𝑦3 NOUN american_scientific_journal-3571 147 3 ) ) PUNCT american_scientific_journal-3571 147 4 is be AUX american_scientific_journal-3571 147 5 the the DET american_scientific_journal-3571 147 6 leg3 leg3 ADJ american_scientific_journal-3571 147 7 coordinate coordinate NOUN american_scientific_journal-3571 147 8 of of ADP american_scientific_journal-3571 147 9 tip tip NOUN american_scientific_journal-3571 147 10 position position NOUN american_scientific_journal-3571 147 11 . . PUNCT american_scientific_journal-3571 148 1 by by ADP american_scientific_journal-3571 148 2 expanding expand VERB american_scientific_journal-3571 148 3 and and CCONJ american_scientific_journal-3571 148 4 simplify simplify VERB american_scientific_journal-3571 148 5 this this DET american_scientific_journal-3571 148 6 matrix matrix NOUN american_scientific_journal-3571 148 7 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1can π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1can VERB american_scientific_journal-3571 148 8 be be AUX american_scientific_journal-3571 148 9 calculated calculate VERB american_scientific_journal-3571 148 10 as as ADP american_scientific_journal-3571 148 11 the the DET american_scientific_journal-3571 148 12 following following NOUN american_scientific_journal-3571 148 13 : : PUNCT american_scientific_journal-3571 148 14 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž1 PROPN american_scientific_journal-3571 148 15 = = SYM american_scientific_journal-3571 148 16 1 1 NUM american_scientific_journal-3571 148 17 2 2 NUM american_scientific_journal-3571 148 18 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 19 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 20 π‘₯π‘₯1 π‘₯π‘₯1 NOUN american_scientific_journal-3571 148 21 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 22 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 23 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 24 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 25 𝑦𝑦3 𝑦𝑦3 NOUN american_scientific_journal-3571 148 26 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 27 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 28 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 29 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 30 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 31 π‘₯π‘₯3 π‘₯π‘₯3 PROPN american_scientific_journal-3571 148 32 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 33 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 34 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 35 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 36 𝑦𝑦1 𝑦𝑦1 PROPN american_scientific_journal-3571 148 37 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 38 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 39 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 40 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 41 𝐿𝐿1 𝐿𝐿1 PROPN american_scientific_journal-3571 148 42 = = SYM american_scientific_journal-3571 148 43 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 44 ( ( PUNCT american_scientific_journal-3571 148 45 π‘₯π‘₯1 π‘₯π‘₯1 NOUN american_scientific_journal-3571 148 46 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 47 π‘₯π‘₯3)2 π‘₯π‘₯3)2 PROPN american_scientific_journal-3571 148 48 + + CCONJ american_scientific_journal-3571 148 49 ( ( PUNCT american_scientific_journal-3571 148 50 𝑦𝑦1 𝑦𝑦1 PROPN american_scientific_journal-3571 148 51 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 52 𝑦𝑦3)2 𝑦𝑦3)2 PROPN american_scientific_journal-3571 148 53 𝑑𝑑1 𝑑𝑑1 NOUN american_scientific_journal-3571 148 54 = = SYM american_scientific_journal-3571 148 55 2 2 NUM american_scientific_journal-3571 148 56 βˆ— βˆ— NOUN american_scientific_journal-3571 148 57 ( ( PUNCT american_scientific_journal-3571 148 58 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐1 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐1 PROPN american_scientific_journal-3571 148 59 𝐿𝐿1 𝐿𝐿1 PROPN american_scientific_journal-3571 148 60 ) ) PUNCT american_scientific_journal-3571 148 61 ( ( PUNCT american_scientific_journal-3571 148 62 17 17 NUM american_scientific_journal-3571 148 63 ) ) PUNCT american_scientific_journal-3571 148 64 by by ADP american_scientific_journal-3571 148 65 the the DET american_scientific_journal-3571 148 66 same same ADJ american_scientific_journal-3571 148 67 way way NOUN american_scientific_journal-3571 148 68 , , PUNCT american_scientific_journal-3571 148 69 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 PROPN american_scientific_journal-3571 148 70 and and CCONJ american_scientific_journal-3571 148 71 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž3 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž3 NOUN american_scientific_journal-3571 148 72 will will AUX american_scientific_journal-3571 148 73 be be AUX american_scientific_journal-3571 148 74 found find VERB american_scientific_journal-3571 148 75 as as ADP american_scientific_journal-3571 148 76 : : PUNCT american_scientific_journal-3571 148 77 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 X american_scientific_journal-3571 148 78 = = SYM american_scientific_journal-3571 148 79 1 1 NUM american_scientific_journal-3571 148 80 2 2 NUM american_scientific_journal-3571 148 81 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 82 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 83 π‘₯π‘₯1 π‘₯π‘₯1 NOUN american_scientific_journal-3571 148 84 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 85 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 86 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 87 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 88 𝑦𝑦2 𝑦𝑦2 ADJ american_scientific_journal-3571 148 89 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 90 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 NOUN american_scientific_journal-3571 148 91 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 92 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 93 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 94 π‘₯π‘₯2 π‘₯π‘₯2 NOUN american_scientific_journal-3571 148 95 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 96 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 97 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 98 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 99 𝑦𝑦1 𝑦𝑦1 PROPN american_scientific_journal-3571 148 100 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 101 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 102 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 103 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 104 𝐿𝐿2 𝐿𝐿2 PROPN american_scientific_journal-3571 148 105 = = PUNCT american_scientific_journal-3571 148 106 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 107 ( ( PUNCT american_scientific_journal-3571 148 108 π‘₯π‘₯1 π‘₯π‘₯1 NOUN american_scientific_journal-3571 148 109 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 110 π‘₯π‘₯2)2 π‘₯π‘₯2)2 PUNCT american_scientific_journal-3571 148 111 + + CCONJ american_scientific_journal-3571 148 112 ( ( PUNCT american_scientific_journal-3571 148 113 𝑦𝑦1 𝑦𝑦1 NOUN american_scientific_journal-3571 148 114 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 115 𝑦𝑦2)2 𝑦𝑦2)2 PUNCT american_scientific_journal-3571 148 116 𝑑𝑑2 𝑑𝑑2 NOUN american_scientific_journal-3571 148 117 = = SYM american_scientific_journal-3571 148 118 2 2 NUM american_scientific_journal-3571 148 119 βˆ— βˆ— NOUN american_scientific_journal-3571 148 120 ( ( PUNCT american_scientific_journal-3571 148 121 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐2 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐2 PROPN american_scientific_journal-3571 148 122 𝐿𝐿2 𝐿𝐿2 PROPN american_scientific_journal-3571 148 123 ) ) PUNCT american_scientific_journal-3571 148 124 ( ( PUNCT american_scientific_journal-3571 148 125 18 18 NUM american_scientific_journal-3571 148 126 ) ) PUNCT american_scientific_journal-3571 148 127 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 π΄π΄π΄π΄π΄π΄π‘Žπ‘Ž2 NOUN american_scientific_journal-3571 148 128 = = SYM american_scientific_journal-3571 148 129 1 1 NUM american_scientific_journal-3571 148 130 2 2 NUM american_scientific_journal-3571 148 131 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 132 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 133 π‘₯π‘₯2 π‘₯π‘₯2 NOUN american_scientific_journal-3571 148 134 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 135 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 136 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 137 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 138 𝑦𝑦3 𝑦𝑦3 NOUN american_scientific_journal-3571 148 139 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 140 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 141 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 142 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 143 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 144 π‘₯π‘₯2 π‘₯π‘₯2 NOUN american_scientific_journal-3571 148 145 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 146 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 π‘₯π‘₯𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 147 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 148 οΏ½ οΏ½ NOUN american_scientific_journal-3571 148 149 𝑦𝑦3 𝑦𝑦3 NOUN american_scientific_journal-3571 148 150 βˆ’ βˆ’ NOUN american_scientific_journal-3571 148 151 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦𝑐𝑐𝑐𝑐𝑐𝑐 PROPN american_scientific_journal-3571 148 152 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 153 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 154 𝐿𝐿3 𝐿𝐿3 PROPN american_scientific_journal-3571 148 155 = = SYM american_scientific_journal-3571 148 156 οΏ½ οΏ½ PROPN american_scientific_journal-3571 148 157 ( ( PUNCT american_scientific_journal-3571 148 158 π‘₯π‘₯2 π‘₯π‘₯2 X american_scientific_journal-3571 148 159 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 160 π‘₯π‘₯3)2 π‘₯π‘₯3)2 PROPN american_scientific_journal-3571 148 161 + + CCONJ american_scientific_journal-3571 148 162 ( ( PUNCT american_scientific_journal-3571 148 163 𝑦𝑦2 𝑦𝑦2 VERB american_scientific_journal-3571 148 164 βˆ’ βˆ’ PROPN american_scientific_journal-3571 148 165 𝑦𝑦3)2 𝑦𝑦3)2 PROPN american_scientific_journal-3571 148 166 𝑑𝑑3 𝑑𝑑3 NOUN american_scientific_journal-3571 148 167 = = NOUN american_scientific_journal-3571 148 168 2 2 NUM american_scientific_journal-3571 148 169 βˆ— βˆ— NOUN american_scientific_journal-3571 148 170 ( ( PUNCT american_scientific_journal-3571 148 171 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐3 𝐴𝐴𝑓𝑓𝑏𝑏𝑐𝑐3 PROPN american_scientific_journal-3571 148 172 𝐿𝐿3 𝐿𝐿3 PROPN american_scientific_journal-3571 148 173 ) ) PUNCT american_scientific_journal-3571 148 174 ( ( PUNCT american_scientific_journal-3571 148 175 19 19 NUM american_scientific_journal-3571 148 176 ) ) PUNCT american_scientific_journal-3571 148 177 finally finally ADV american_scientific_journal-3571 148 178 , , PUNCT american_scientific_journal-3571 148 179 the the DET american_scientific_journal-3571 148 180 first first ADJ american_scientific_journal-3571 148 181 stability stability NOUN american_scientific_journal-3571 148 182 margin margin NOUN american_scientific_journal-3571 148 183 𝑐𝑐𝑠𝑠1is 𝑐𝑐𝑠𝑠1i VERB american_scientific_journal-3571 148 184 the the DET american_scientific_journal-3571 148 185 minimum minimum ADJ american_scientific_journal-3571 148 186 distance distance NOUN american_scientific_journal-3571 148 187 from from ADP american_scientific_journal-3571 148 188 these these DET american_scientific_journal-3571 148 189 three three NUM american_scientific_journal-3571 148 190 margins margin NOUN american_scientific_journal-3571 148 191 : : PUNCT american_scientific_journal-3571 148 192 𝑐𝑐𝑠𝑠1 𝑐𝑐𝑠𝑠1 X american_scientific_journal-3571 148 193 = = PUNCT american_scientific_journal-3571 149 1 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 NOUN american_scientific_journal-3571 149 2 ( ( PUNCT american_scientific_journal-3571 149 3 𝑑𝑑1,𝑑𝑑2,𝑑𝑑3 𝑑𝑑1,𝑑𝑑2,𝑑𝑑3 PROPN american_scientific_journal-3571 149 4 ) ) PUNCT american_scientific_journal-3571 149 5 ( ( PUNCT american_scientific_journal-3571 149 6 20 20 NUM american_scientific_journal-3571 149 7 ) ) PUNCT american_scientific_journal-3571 149 8 the the DET american_scientific_journal-3571 149 9 other other ADJ american_scientific_journal-3571 149 10 stability stability NOUN american_scientific_journal-3571 149 11 margins margin NOUN american_scientific_journal-3571 149 12 have have AUX american_scientific_journal-3571 149 13 been be AUX american_scientific_journal-3571 149 14 calculated calculate VERB american_scientific_journal-3571 149 15 in in ADP american_scientific_journal-3571 149 16 each each DET american_scientific_journal-3571 149 17 period period NOUN american_scientific_journal-3571 149 18 when when SCONJ american_scientific_journal-3571 149 19 the the DET american_scientific_journal-3571 149 20 other other ADJ american_scientific_journal-3571 149 21 legs leg NOUN american_scientific_journal-3571 149 22 are be AUX american_scientific_journal-3571 149 23 swinging swinge VERB american_scientific_journal-3571 149 24 respectively respectively ADV american_scientific_journal-3571 149 25 . . PUNCT american_scientific_journal-3571 150 1 as as SCONJ american_scientific_journal-3571 150 2 𝑐𝑐𝑠𝑠1 𝑐𝑐𝑠𝑠1 PROPN american_scientific_journal-3571 150 3 analyzed analyze VERB american_scientific_journal-3571 150 4 , , PUNCT american_scientific_journal-3571 150 5 the the DET american_scientific_journal-3571 150 6 other other ADJ american_scientific_journal-3571 150 7 margins margin NOUN american_scientific_journal-3571 150 8 are be AUX american_scientific_journal-3571 150 9 equals equal VERB american_scientific_journal-3571 150 10 to to PART american_scientific_journal-3571 150 11 : : PUNCT american_scientific_journal-3571 150 12 𝑐𝑐𝑠𝑠2 𝑐𝑐𝑠𝑠2 X american_scientific_journal-3571 151 1 = = SYM american_scientific_journal-3571 151 2 min min PROPN american_scientific_journal-3571 151 3 ( ( PUNCT american_scientific_journal-3571 151 4 𝑑𝑑4,𝑑𝑑5,𝑑𝑑6 𝑑𝑑4,𝑑𝑑5,𝑑𝑑6 NOUN american_scientific_journal-3571 151 5 ) ) PUNCT american_scientific_journal-3571 151 6 ( ( PUNCT american_scientific_journal-3571 151 7 21 21 NUM american_scientific_journal-3571 151 8 ) ) PUNCT american_scientific_journal-3571 151 9 𝑐𝑐𝑠𝑠3 𝑐𝑐𝑠𝑠3 X american_scientific_journal-3571 152 1 = = PUNCT american_scientific_journal-3571 152 2 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 NOUN american_scientific_journal-3571 152 3 ( ( PUNCT american_scientific_journal-3571 152 4 𝑑𝑑7,𝑑𝑑8,𝑑𝑑9 𝑑𝑑7,𝑑𝑑8,𝑑𝑑9 PROPN american_scientific_journal-3571 152 5 ) ) PUNCT american_scientific_journal-3571 152 6 ( ( PUNCT american_scientific_journal-3571 152 7 22 22 NUM american_scientific_journal-3571 152 8 ) ) PUNCT american_scientific_journal-3571 152 9 𝑐𝑐𝑠𝑠4 𝑐𝑐𝑠𝑠4 X american_scientific_journal-3571 153 1 = = PRON american_scientific_journal-3571 154 1 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 NOUN american_scientific_journal-3571 154 2 ( ( PUNCT american_scientific_journal-3571 154 3 𝑑𝑑10,𝑑𝑑11,𝑑𝑑12 𝑑𝑑10,𝑑𝑑11,𝑑𝑑12 PROPN american_scientific_journal-3571 154 4 ) ) PUNCT american_scientific_journal-3571 154 5 ( ( PUNCT american_scientific_journal-3571 154 6 23 23 NUM american_scientific_journal-3571 154 7 ) ) PUNCT american_scientific_journal-3571 154 8 where where SCONJ american_scientific_journal-3571 154 9 ( ( PUNCT american_scientific_journal-3571 154 10 𝑐𝑐𝑠𝑠2,𝑐𝑐𝑠𝑠3 𝑐𝑐𝑠𝑠2,𝑐𝑐𝑠𝑠3 ADJ american_scientific_journal-3571 154 11 , , PUNCT american_scientific_journal-3571 154 12 π‘Žπ‘Žπ‘ π‘ π‘‘π‘‘ π‘Žπ‘Žπ‘ π‘ π‘‘π‘‘ PROPN american_scientific_journal-3571 154 13 𝑐𝑐𝑠𝑠4 𝑐𝑐𝑠𝑠4 PROPN american_scientific_journal-3571 154 14 ) ) PUNCT american_scientific_journal-3571 154 15 have have AUX american_scientific_journal-3571 154 16 been be AUX american_scientific_journal-3571 154 17 calculated calculate VERB american_scientific_journal-3571 154 18 corresponding correspond VERB american_scientific_journal-3571 154 19 to to ADP american_scientific_journal-3571 154 20 the the DET american_scientific_journal-3571 154 21 other other ADJ american_scientific_journal-3571 154 22 cases case NOUN american_scientific_journal-3571 154 23 when when SCONJ american_scientific_journal-3571 154 24 the the DET american_scientific_journal-3571 154 25 legs leg NOUN american_scientific_journal-3571 154 26 are be AUX american_scientific_journal-3571 154 27 swinging swinge VERB american_scientific_journal-3571 154 28 sequence sequence NOUN american_scientific_journal-3571 154 29 during during ADP american_scientific_journal-3571 154 30 the the DET american_scientific_journal-3571 154 31 robot robot NOUN american_scientific_journal-3571 154 32 creeping creep VERB american_scientific_journal-3571 154 33 gait gait NOUN american_scientific_journal-3571 154 34 . . PUNCT american_scientific_journal-3571 155 1 and and CCONJ american_scientific_journal-3571 155 2 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 PROPN american_scientific_journal-3571 155 3 ( ( PUNCT american_scientific_journal-3571 155 4 i=4, i=4, NOUN american_scientific_journal-3571 155 5 ... ... PUNCT american_scientific_journal-3571 155 6 ,12 ,12 PUNCT american_scientific_journal-3571 155 7 ) ) PUNCT american_scientific_journal-3571 155 8 are be AUX american_scientific_journal-3571 155 9 the the DET american_scientific_journal-3571 155 10 distances distance NOUN american_scientific_journal-3571 155 11 between between ADP american_scientific_journal-3571 155 12 the the DET american_scientific_journal-3571 155 13 robot robot NOUN american_scientific_journal-3571 155 14 center center NOUN american_scientific_journal-3571 155 15 and and CCONJ american_scientific_journal-3571 155 16 the the DET american_scientific_journal-3571 155 17 legs leg NOUN american_scientific_journal-3571 155 18 tips tip NOUN american_scientific_journal-3571 155 19 , , PUNCT american_scientific_journal-3571 155 20 when when SCONJ american_scientific_journal-3571 155 21 all all DET american_scientific_journal-3571 155 22 the the DET american_scientific_journal-3571 155 23 legs leg NOUN american_scientific_journal-3571 155 24 had have AUX american_scientific_journal-3571 155 25 been be AUX american_scientific_journal-3571 155 26 swing swing NOUN american_scientific_journal-3571 155 27 as as ADP american_scientific_journal-3571 155 28 𝑙𝑙𝐴𝐴𝑙𝑙2 𝑙𝑙𝐴𝐴𝑙𝑙2 PROPN american_scientific_journal-3571 155 29 , , PUNCT american_scientific_journal-3571 155 30 𝑙𝑙𝐴𝐴𝑙𝑙3 𝑙𝑙𝐴𝐴𝑙𝑙3 PROPN american_scientific_journal-3571 155 31 , , PUNCT american_scientific_journal-3571 155 32 and and CCONJ american_scientific_journal-3571 155 33 𝑙𝑙𝐴𝐴𝑙𝑙1 𝑙𝑙𝐴𝐴𝑙𝑙1 PROPN american_scientific_journal-3571 155 34 respectively respectively ADV american_scientific_journal-3571 155 35 . . PUNCT american_scientific_journal-3571 156 1 american american PROPN american_scientific_journal-3571 156 2 scientific scientific ADJ american_scientific_journal-3571 156 3 research research PROPN american_scientific_journal-3571 156 4 journal journal NOUN american_scientific_journal-3571 156 5 for for ADP american_scientific_journal-3571 156 6 engineering engineering NOUN american_scientific_journal-3571 156 7 , , PUNCT american_scientific_journal-3571 156 8 technology technology NOUN american_scientific_journal-3571 156 9 , , PUNCT american_scientific_journal-3571 156 10 and and CCONJ american_scientific_journal-3571 156 11 sciences science NOUN american_scientific_journal-3571 156 12 ( ( PUNCT american_scientific_journal-3571 156 13 asrjets asrjet NOUN american_scientific_journal-3571 156 14 ) ) PUNCT american_scientific_journal-3571 156 15 ( ( PUNCT american_scientific_journal-3571 156 16 2017 2017 NUM american_scientific_journal-3571 156 17 ) ) PUNCT american_scientific_journal-3571 156 18 volume volume NOUN american_scientific_journal-3571 156 19 38 38 NUM american_scientific_journal-3571 156 20 , , PUNCT american_scientific_journal-3571 156 21 no no DET american_scientific_journal-3571 156 22 1 1 NUM american_scientific_journal-3571 156 23 , , PUNCT american_scientific_journal-3571 156 24 pp pp ADV american_scientific_journal-3571 156 25 17 17 NUM american_scientific_journal-3571 156 26 - - SYM american_scientific_journal-3571 156 27 32 32 NUM american_scientific_journal-3571 156 28 27 27 NUM american_scientific_journal-3571 156 29 6 6 NUM american_scientific_journal-3571 156 30 . . PUNCT american_scientific_journal-3571 157 1 stability stability NOUN american_scientific_journal-3571 157 2 margins margin VERB american_scientific_journal-3571 157 3 optimization optimization NOUN american_scientific_journal-3571 157 4 using use VERB american_scientific_journal-3571 157 5 pso pso NOUN american_scientific_journal-3571 157 6 the the DET american_scientific_journal-3571 157 7 stability stability NOUN american_scientific_journal-3571 157 8 margins margin NOUN american_scientific_journal-3571 157 9 of of ADP american_scientific_journal-3571 157 10 each each DET american_scientific_journal-3571 157 11 leg leg NOUN american_scientific_journal-3571 157 12 sequence sequence NOUN american_scientific_journal-3571 157 13 when when SCONJ american_scientific_journal-3571 157 14 the the DET american_scientific_journal-3571 157 15 quadruped quadruped NOUN american_scientific_journal-3571 157 16 robot robot NOUN american_scientific_journal-3571 157 17 walking walk VERB american_scientific_journal-3571 157 18 with with ADP american_scientific_journal-3571 157 19 creeping creep VERB american_scientific_journal-3571 157 20 gait gait NOUN american_scientific_journal-3571 157 21 is be AUX american_scientific_journal-3571 157 22 analyzed analyze VERB american_scientific_journal-3571 157 23 . . PUNCT american_scientific_journal-3571 158 1 these these DET american_scientific_journal-3571 158 2 margins margin NOUN american_scientific_journal-3571 158 3 are be AUX american_scientific_journal-3571 158 4 varying vary VERB american_scientific_journal-3571 158 5 between between ADP american_scientific_journal-3571 158 6 a a DET american_scientific_journal-3571 158 7 range range NOUN american_scientific_journal-3571 158 8 of of ADP american_scientific_journal-3571 158 9 values value NOUN american_scientific_journal-3571 158 10 , , PUNCT american_scientific_journal-3571 158 11 and and CCONJ american_scientific_journal-3571 158 12 its its PRON american_scientific_journal-3571 158 13 need need NOUN american_scientific_journal-3571 158 14 to to PART american_scientific_journal-3571 158 15 achieving achieve VERB american_scientific_journal-3571 158 16 the the DET american_scientific_journal-3571 158 17 optimal optimal ADJ american_scientific_journal-3571 158 18 value value NOUN american_scientific_journal-3571 158 19 of of ADP american_scientific_journal-3571 158 20 each each DET american_scientific_journal-3571 158 21 stability stability NOUN american_scientific_journal-3571 158 22 margin margin NOUN american_scientific_journal-3571 158 23 . . PUNCT american_scientific_journal-3571 159 1 in in ADP american_scientific_journal-3571 159 2 this this DET american_scientific_journal-3571 159 3 section section NOUN american_scientific_journal-3571 159 4 an an DET american_scientific_journal-3571 159 5 optimization optimization NOUN american_scientific_journal-3571 159 6 method method NOUN american_scientific_journal-3571 159 7 called call VERB american_scientific_journal-3571 159 8 particle particle NOUN american_scientific_journal-3571 159 9 swarm swarm NOUN american_scientific_journal-3571 159 10 optimization optimization NOUN american_scientific_journal-3571 159 11 is be AUX american_scientific_journal-3571 159 12 used use VERB american_scientific_journal-3571 159 13 to to PART american_scientific_journal-3571 159 14 optimize optimize VERB american_scientific_journal-3571 159 15 the the DET american_scientific_journal-3571 159 16 stability stability NOUN american_scientific_journal-3571 159 17 margins margin NOUN american_scientific_journal-3571 159 18 to to PART american_scientific_journal-3571 159 19 have have VERB american_scientific_journal-3571 159 20 the the DET american_scientific_journal-3571 159 21 best good ADJ american_scientific_journal-3571 159 22 stability stability NOUN american_scientific_journal-3571 159 23 margin margin NOUN american_scientific_journal-3571 159 24 during during ADP american_scientific_journal-3571 159 25 the the DET american_scientific_journal-3571 159 26 quadruped quadruped NOUN american_scientific_journal-3571 159 27 robot robot NOUN american_scientific_journal-3571 159 28 walking walk VERB american_scientific_journal-3571 159 29 using use VERB american_scientific_journal-3571 159 30 creeping creep VERB american_scientific_journal-3571 159 31 gait gait ADJ american_scientific_journal-3571 159 32 locomotion locomotion NOUN american_scientific_journal-3571 159 33 . . PUNCT american_scientific_journal-3571 160 1 the the DET american_scientific_journal-3571 160 2 pso pso NOUN american_scientific_journal-3571 160 3 optimization optimization NOUN american_scientific_journal-3571 160 4 algorithm algorithm NOUN american_scientific_journal-3571 160 5 is be AUX american_scientific_journal-3571 160 6 based base VERB american_scientific_journal-3571 160 7 on on ADP american_scientific_journal-3571 160 8 some some DET american_scientific_journal-3571 160 9 features feature NOUN american_scientific_journal-3571 160 10 such such ADJ american_scientific_journal-3571 160 11 as as ADP american_scientific_journal-3571 160 12 : : PUNCT american_scientific_journal-3571 160 13 1the 1the NUM american_scientific_journal-3571 160 14 cost cost NOUN american_scientific_journal-3571 160 15 function function NOUN american_scientific_journal-3571 160 16 : : PUNCT american_scientific_journal-3571 160 17 this this PRON american_scientific_journal-3571 160 18 is be AUX american_scientific_journal-3571 160 19 the the DET american_scientific_journal-3571 160 20 main main ADJ american_scientific_journal-3571 160 21 function function NOUN american_scientific_journal-3571 160 22 of of ADP american_scientific_journal-3571 160 23 the the DET american_scientific_journal-3571 160 24 problem problem NOUN american_scientific_journal-3571 160 25 that that PRON american_scientific_journal-3571 160 26 it it PRON american_scientific_journal-3571 160 27 needs need VERB american_scientific_journal-3571 160 28 to to PART american_scientific_journal-3571 160 29 be be AUX american_scientific_journal-3571 160 30 optimized optimize VERB american_scientific_journal-3571 160 31 . . PUNCT american_scientific_journal-3571 161 1 in in ADP american_scientific_journal-3571 161 2 this this DET american_scientific_journal-3571 161 3 paper paper NOUN american_scientific_journal-3571 161 4 , , PUNCT american_scientific_journal-3571 161 5 the the DET american_scientific_journal-3571 161 6 main main ADJ american_scientific_journal-3571 161 7 parameters parameter NOUN american_scientific_journal-3571 161 8 that that PRON american_scientific_journal-3571 161 9 will will AUX american_scientific_journal-3571 161 10 pass pass VERB american_scientific_journal-3571 161 11 to to ADP american_scientific_journal-3571 161 12 the the DET american_scientific_journal-3571 161 13 cost cost NOUN american_scientific_journal-3571 161 14 function function NOUN american_scientific_journal-3571 161 15 are be AUX american_scientific_journal-3571 161 16 the the DET american_scientific_journal-3571 161 17 robot robot NOUN american_scientific_journal-3571 161 18 body body NOUN american_scientific_journal-3571 161 19 center center NOUN american_scientific_journal-3571 161 20 in in ADP american_scientific_journal-3571 161 21 x x ADJ american_scientific_journal-3571 161 22 - - NOUN american_scientific_journal-3571 161 23 axis axis ADJ american_scientific_journal-3571 161 24 and and CCONJ american_scientific_journal-3571 161 25 y y NOUN american_scientific_journal-3571 161 26 - - PUNCT american_scientific_journal-3571 161 27 axis axis NOUN american_scientific_journal-3571 161 28 and and CCONJ american_scientific_journal-3571 161 29 the the DET american_scientific_journal-3571 161 30 leg leg NOUN american_scientific_journal-3571 161 31 tips tip NOUN american_scientific_journal-3571 161 32 which which PRON american_scientific_journal-3571 161 33 are be AUX american_scientific_journal-3571 161 34 presented present VERB american_scientific_journal-3571 161 35 as as ADP american_scientific_journal-3571 161 36 the the DET american_scientific_journal-3571 161 37 constraint constraint NOUN american_scientific_journal-3571 161 38 of of ADP american_scientific_journal-3571 161 39 the the DET american_scientific_journal-3571 161 40 cost cost NOUN american_scientific_journal-3571 161 41 function function NOUN american_scientific_journal-3571 161 42 . . PUNCT american_scientific_journal-3571 162 1 2the 2the DET american_scientific_journal-3571 162 2 minimum minimum ADJ american_scientific_journal-3571 162 3 and and CCONJ american_scientific_journal-3571 162 4 maximum maximum ADJ american_scientific_journal-3571 162 5 values value NOUN american_scientific_journal-3571 162 6 of of ADP american_scientific_journal-3571 162 7 variables variable NOUN american_scientific_journal-3571 162 8 : : PUNCT american_scientific_journal-3571 162 9 in in ADP american_scientific_journal-3571 162 10 this this DET american_scientific_journal-3571 162 11 paper paper NOUN american_scientific_journal-3571 162 12 , , PUNCT american_scientific_journal-3571 162 13 the the DET american_scientific_journal-3571 162 14 stability stability NOUN american_scientific_journal-3571 162 15 margin margin NOUN american_scientific_journal-3571 162 16 limiting limit VERB american_scientific_journal-3571 162 17 values value NOUN american_scientific_journal-3571 162 18 are be AUX american_scientific_journal-3571 162 19 presented present VERB american_scientific_journal-3571 162 20 as as ADP american_scientific_journal-3571 162 21 varmin varmin NOUN american_scientific_journal-3571 162 22 and and CCONJ american_scientific_journal-3571 162 23 varmax varmax VERB american_scientific_journal-3571 162 24 3number 3number NUM american_scientific_journal-3571 162 25 of of ADP american_scientific_journal-3571 162 26 iteration iteration NOUN american_scientific_journal-3571 162 27 : : PUNCT american_scientific_journal-3571 162 28 in in ADP american_scientific_journal-3571 162 29 this this DET american_scientific_journal-3571 162 30 paper paper NOUN american_scientific_journal-3571 162 31 the the DET american_scientific_journal-3571 162 32 number number NOUN american_scientific_journal-3571 162 33 of of ADP american_scientific_journal-3571 162 34 iteration iteration NOUN american_scientific_journal-3571 162 35 is be AUX american_scientific_journal-3571 162 36 : : PUNCT american_scientific_journal-3571 162 37 500 500 NUM american_scientific_journal-3571 162 38 iteration iteration NOUN american_scientific_journal-3571 162 39 4number 4number NUM american_scientific_journal-3571 162 40 of of ADP american_scientific_journal-3571 162 41 population population NOUN american_scientific_journal-3571 162 42 : : PUNCT american_scientific_journal-3571 162 43 in in ADP american_scientific_journal-3571 162 44 this this DET american_scientific_journal-3571 162 45 paper paper NOUN american_scientific_journal-3571 162 46 the the DET american_scientific_journal-3571 162 47 number number NOUN american_scientific_journal-3571 162 48 of of ADP american_scientific_journal-3571 162 49 population population NOUN american_scientific_journal-3571 162 50 equals equal VERB american_scientific_journal-3571 162 51 to to ADP american_scientific_journal-3571 162 52 5 5 NUM american_scientific_journal-3571 162 53 . . PUNCT american_scientific_journal-3571 162 54 5the 5the PRON american_scientific_journal-3571 162 55 initial initial ADJ american_scientific_journal-3571 162 56 weight weight NOUN american_scientific_journal-3571 162 57 : : PUNCT american_scientific_journal-3571 162 58 in in ADP american_scientific_journal-3571 162 59 this this DET american_scientific_journal-3571 162 60 paper paper NOUN american_scientific_journal-3571 162 61 the the DET american_scientific_journal-3571 162 62 initial initial ADJ american_scientific_journal-3571 162 63 weight weight NOUN american_scientific_journal-3571 162 64 π‘Šπ‘Šπ‘–π‘–π‘–π‘–π‘–π‘–π‘‘π‘‘π‘–π‘–π‘π‘π‘–π‘– π‘Šπ‘Šπ‘–π‘–π‘–π‘–π‘–π‘–π‘‘π‘‘π‘–π‘–π‘π‘π‘–π‘– NOUN american_scientific_journal-3571 162 65 = = SYM american_scientific_journal-3571 162 66 1 1 NUM american_scientific_journal-3571 162 67 , , PUNCT american_scientific_journal-3571 162 68 and and CCONJ american_scientific_journal-3571 162 69 the the DET american_scientific_journal-3571 162 70 damping damp VERB american_scientific_journal-3571 162 71 weight weight NOUN american_scientific_journal-3571 162 72 π‘Šπ‘Šπ‘‘π‘‘π‘π‘π‘“π‘“π‘‘π‘‘ π‘Šπ‘Šπ‘‘π‘‘π‘π‘π‘“π‘“π‘‘π‘‘ PROPN american_scientific_journal-3571 162 73 = = PUNCT american_scientific_journal-3571 162 74 0.99 0.99 NUM american_scientific_journal-3571 162 75 6the 6the NUM american_scientific_journal-3571 162 76 constant constant ADJ american_scientific_journal-3571 162 77 values value NOUN american_scientific_journal-3571 162 78 𝐢𝐢1and𝐢𝐢2 𝐢𝐢1and𝐢𝐢2 VERB american_scientific_journal-3571 162 79 : : PUNCT american_scientific_journal-3571 162 80 in in ADP american_scientific_journal-3571 162 81 this this DET american_scientific_journal-3571 162 82 paper paper NOUN american_scientific_journal-3571 162 83 𝐢𝐢1=3.999 𝐢𝐢1=3.999 NOUN american_scientific_journal-3571 162 84 and𝐢𝐢2 and𝐢𝐢2 NOUN american_scientific_journal-3571 162 85 = = SYM american_scientific_journal-3571 162 86 0.0001 0.0001 NUM american_scientific_journal-3571 162 87 . . PUNCT american_scientific_journal-3571 163 1 all all DET american_scientific_journal-3571 163 2 these these DET american_scientific_journal-3571 163 3 parameters parameter NOUN american_scientific_journal-3571 163 4 are be AUX american_scientific_journal-3571 163 5 playing play VERB american_scientific_journal-3571 163 6 a a DET american_scientific_journal-3571 163 7 very very ADV american_scientific_journal-3571 163 8 important important ADJ american_scientific_journal-3571 163 9 role role NOUN american_scientific_journal-3571 163 10 for for ADP american_scientific_journal-3571 163 11 enhancement enhancement NOUN american_scientific_journal-3571 163 12 the the DET american_scientific_journal-3571 163 13 optimization optimization NOUN american_scientific_journal-3571 163 14 method method NOUN american_scientific_journal-3571 163 15 working work VERB american_scientific_journal-3571 163 16 . . PUNCT american_scientific_journal-3571 164 1 the the DET american_scientific_journal-3571 164 2 pso pso NOUN american_scientific_journal-3571 164 3 optimization optimization NOUN american_scientific_journal-3571 164 4 results result NOUN american_scientific_journal-3571 164 5 of of ADP american_scientific_journal-3571 164 6 the the DET american_scientific_journal-3571 164 7 stability stability NOUN american_scientific_journal-3571 164 8 margins margin NOUN american_scientific_journal-3571 164 9 are be AUX american_scientific_journal-3571 164 10 showing show VERB american_scientific_journal-3571 164 11 in in ADP american_scientific_journal-3571 164 12 section section NOUN american_scientific_journal-3571 164 13 7 7 NUM american_scientific_journal-3571 164 14 . . NOUN american_scientific_journal-3571 164 15 7 7 NUM american_scientific_journal-3571 164 16 . . X american_scientific_journal-3571 164 17 simulation simulation NOUN american_scientific_journal-3571 164 18 and and CCONJ american_scientific_journal-3571 164 19 results result NOUN american_scientific_journal-3571 164 20 in in ADP american_scientific_journal-3571 164 21 this this DET american_scientific_journal-3571 164 22 section section NOUN american_scientific_journal-3571 164 23 , , PUNCT american_scientific_journal-3571 164 24 the the DET american_scientific_journal-3571 164 25 quadruped quadruped NOUN american_scientific_journal-3571 164 26 robot robot NOUN american_scientific_journal-3571 164 27 walking walk VERB american_scientific_journal-3571 164 28 according accord VERB american_scientific_journal-3571 164 29 to to ADP american_scientific_journal-3571 164 30 the the DET american_scientific_journal-3571 164 31 creeping creep VERB american_scientific_journal-3571 164 32 gait gait NOUN american_scientific_journal-3571 164 33 sequence sequence NOUN american_scientific_journal-3571 164 34 locomotion locomotion NOUN american_scientific_journal-3571 164 35 is be AUX american_scientific_journal-3571 164 36 shown show VERB american_scientific_journal-3571 164 37 . . PUNCT american_scientific_journal-3571 165 1 each each DET american_scientific_journal-3571 165 2 gait gait NOUN american_scientific_journal-3571 165 3 has have VERB american_scientific_journal-3571 165 4 its its PRON american_scientific_journal-3571 165 5 stability stability NOUN american_scientific_journal-3571 165 6 margin margin NOUN american_scientific_journal-3571 165 7 is be AUX american_scientific_journal-3571 165 8 varying vary VERB american_scientific_journal-3571 165 9 between between ADP american_scientific_journal-3571 165 10 a a DET american_scientific_journal-3571 165 11 range range NOUN american_scientific_journal-3571 165 12 of of ADP american_scientific_journal-3571 165 13 values value NOUN american_scientific_journal-3571 165 14 according accord VERB american_scientific_journal-3571 165 15 to to ADP american_scientific_journal-3571 165 16 which which PRON american_scientific_journal-3571 165 17 leg leg NOUN american_scientific_journal-3571 165 18 is be AUX american_scientific_journal-3571 165 19 swing swe VERB american_scientific_journal-3571 165 20 in in ADP american_scientific_journal-3571 165 21 the the DET american_scientific_journal-3571 165 22 air air NOUN american_scientific_journal-3571 165 23 . . PUNCT american_scientific_journal-3571 166 1 after after ADP american_scientific_journal-3571 166 2 finding find VERB american_scientific_journal-3571 166 3 the the DET american_scientific_journal-3571 166 4 stability stability NOUN american_scientific_journal-3571 166 5 margin margin NOUN american_scientific_journal-3571 166 6 of of ADP american_scientific_journal-3571 166 7 each each DET american_scientific_journal-3571 166 8 gait gait NOUN american_scientific_journal-3571 166 9 , , PUNCT american_scientific_journal-3571 166 10 applying apply VERB american_scientific_journal-3571 166 11 the the DET american_scientific_journal-3571 166 12 pso pso NOUN american_scientific_journal-3571 166 13 optimization optimization NOUN american_scientific_journal-3571 166 14 algorithm algorithm NOUN american_scientific_journal-3571 166 15 to to PART american_scientific_journal-3571 166 16 achieve achieve VERB american_scientific_journal-3571 166 17 the the DET american_scientific_journal-3571 166 18 best good ADJ american_scientific_journal-3571 166 19 stability stability NOUN american_scientific_journal-3571 166 20 margin margin NOUN american_scientific_journal-3571 166 21 which which PRON american_scientific_journal-3571 166 22 gives give VERB american_scientific_journal-3571 166 23 the the DET american_scientific_journal-3571 166 24 best good ADJ american_scientific_journal-3571 166 25 stability stability NOUN american_scientific_journal-3571 166 26 that that SCONJ american_scientific_journal-3571 166 27 it it PRON american_scientific_journal-3571 166 28 used use VERB american_scientific_journal-3571 166 29 to to PART american_scientific_journal-3571 166 30 balance balance VERB american_scientific_journal-3571 166 31 the the DET american_scientific_journal-3571 166 32 quadruped quadruped NOUN american_scientific_journal-3571 166 33 robot robot NOUN american_scientific_journal-3571 166 34 at at ADP american_scientific_journal-3571 166 35 the the DET american_scientific_journal-3571 166 36 period period NOUN american_scientific_journal-3571 166 37 when when SCONJ american_scientific_journal-3571 166 38 it it PRON american_scientific_journal-3571 166 39 walks walk VERB american_scientific_journal-3571 166 40 with with ADP american_scientific_journal-3571 166 41 creeping creep VERB american_scientific_journal-3571 166 42 gait gait ADJ american_scientific_journal-3571 166 43 locomotion locomotion NOUN american_scientific_journal-3571 166 44 . . PUNCT american_scientific_journal-3571 167 1 as as SCONJ american_scientific_journal-3571 167 2 shown show VERB american_scientific_journal-3571 167 3 in in ADP american_scientific_journal-3571 167 4 the the DET american_scientific_journal-3571 167 5 following follow VERB american_scientific_journal-3571 167 6 figures figure NOUN american_scientific_journal-3571 167 7 . . PUNCT american_scientific_journal-3571 168 1 ( ( PUNCT american_scientific_journal-3571 168 2 a a X american_scientific_journal-3571 168 3 ) ) PUNCT american_scientific_journal-3571 168 4 ( ( PUNCT american_scientific_journal-3571 168 5 b b X american_scientific_journal-3571 168 6 ) ) PUNCT american_scientific_journal-3571 168 7 figure figure NOUN american_scientific_journal-3571 168 8 8 8 NUM american_scientific_journal-3571 168 9 : : PUNCT american_scientific_journal-3571 168 10 ( ( PUNCT american_scientific_journal-3571 168 11 a a X american_scientific_journal-3571 168 12 ) ) PUNCT american_scientific_journal-3571 168 13 leg leg NOUN american_scientific_journal-3571 168 14 4 4 NUM american_scientific_journal-3571 168 15 in in ADP american_scientific_journal-3571 168 16 swinging swinge VERB american_scientific_journal-3571 168 17 phase phase NOUN american_scientific_journal-3571 168 18 ( ( PUNCT american_scientific_journal-3571 168 19 b b X american_scientific_journal-3571 168 20 ) ) PUNCT american_scientific_journal-3571 168 21 the the DET american_scientific_journal-3571 168 22 stability stability NOUN american_scientific_journal-3571 168 23 margin margin NOUN american_scientific_journal-3571 168 24 𝑆𝑆𝑠𝑠1(cm 𝑆𝑆𝑠𝑠1(cm PROPN american_scientific_journal-3571 168 25 ) ) PUNCT american_scientific_journal-3571 168 26 when when SCONJ american_scientific_journal-3571 168 27 leg4 leg4 PROPN american_scientific_journal-3571 168 28 is be AUX american_scientific_journal-3571 168 29 swing swe VERB american_scientific_journal-3571 168 30 . . PUNCT american_scientific_journal-3571 169 1 50 50 NUM american_scientific_journal-3571 169 2 40 40 NUM american_scientific_journal-3571 169 3 x x SYM american_scientific_journal-3571 169 4 30 30 NUM american_scientific_journal-3571 169 5 20 20 NUM american_scientific_journal-3571 169 6 10 10 NUM american_scientific_journal-3571 169 7 0 0 NUM american_scientific_journal-3571 169 8 10 10 NUM american_scientific_journal-3571 169 9 0 0 NUM american_scientific_journal-3571 169 10 10 10 NUM american_scientific_journal-3571 169 11 20 20 NUM american_scientific_journal-3571 169 12 y y NOUN american_scientific_journal-3571 169 13 30 30 NUM american_scientific_journal-3571 169 14 40 40 NUM american_scientific_journal-3571 169 15 leg leg NOUN american_scientific_journal-3571 169 16 4 4 NUM american_scientific_journal-3571 169 17 swing swing NOUN american_scientific_journal-3571 169 18 support support NOUN american_scientific_journal-3571 169 19 triangle triangle NOUN american_scientific_journal-3571 169 20 0 0 NUM american_scientific_journal-3571 169 21 50 50 NUM american_scientific_journal-3571 169 22 100 100 NUM american_scientific_journal-3571 169 23 150 150 NUM american_scientific_journal-3571 169 24 200 200 NUM american_scientific_journal-3571 169 25 250 250 NUM american_scientific_journal-3571 169 26 300 300 NUM american_scientific_journal-3571 169 27 350 350 NUM american_scientific_journal-3571 169 28 1 1 NUM american_scientific_journal-3571 169 29 1.5 1.5 NUM american_scientific_journal-3571 169 30 2 2 NUM american_scientific_journal-3571 169 31 2.5 2.5 NUM american_scientific_journal-3571 169 32 3 3 NUM american_scientific_journal-3571 169 33 3.5 3.5 NUM american_scientific_journal-3571 169 34 4 4 NUM american_scientific_journal-3571 169 35 4.5 4.5 NUM american_scientific_journal-3571 169 36 5 5 NUM american_scientific_journal-3571 169 37 iteration iteration NOUN american_scientific_journal-3571 169 38 s s PART american_scientific_journal-3571 169 39 m m NOUN american_scientific_journal-3571 169 40 1 1 NUM american_scientific_journal-3571 169 41 ( ( PUNCT american_scientific_journal-3571 169 42 c c NOUN american_scientific_journal-3571 169 43 m m AUX american_scientific_journal-3571 169 44 ) ) PUNCT american_scientific_journal-3571 169 45 sm1 sm1 PROPN american_scientific_journal-3571 169 46 american american PROPN american_scientific_journal-3571 169 47 scientific scientific PROPN american_scientific_journal-3571 169 48 research research PROPN american_scientific_journal-3571 169 49 journal journal NOUN american_scientific_journal-3571 169 50 for for ADP american_scientific_journal-3571 169 51 engineering engineering NOUN american_scientific_journal-3571 169 52 , , PUNCT american_scientific_journal-3571 169 53 technology technology NOUN american_scientific_journal-3571 169 54 , , PUNCT american_scientific_journal-3571 169 55 and and CCONJ american_scientific_journal-3571 169 56 sciences science NOUN american_scientific_journal-3571 169 57 ( ( PUNCT american_scientific_journal-3571 169 58 asrjets asrjet NOUN american_scientific_journal-3571 169 59 ) ) PUNCT american_scientific_journal-3571 169 60 ( ( PUNCT american_scientific_journal-3571 169 61 2017 2017 NUM american_scientific_journal-3571 169 62 ) ) PUNCT american_scientific_journal-3571 169 63 volume volume NOUN american_scientific_journal-3571 169 64 38 38 NUM american_scientific_journal-3571 169 65 , , PUNCT american_scientific_journal-3571 169 66 no no DET american_scientific_journal-3571 169 67 1 1 NUM american_scientific_journal-3571 169 68 , , PUNCT american_scientific_journal-3571 169 69 pp pp ADV american_scientific_journal-3571 169 70 17 17 NUM american_scientific_journal-3571 169 71 - - SYM american_scientific_journal-3571 169 72 32 32 NUM american_scientific_journal-3571 169 73 28 28 NUM american_scientific_journal-3571 169 74 ( ( PUNCT american_scientific_journal-3571 169 75 a a NOUN american_scientific_journal-3571 169 76 ) ) PUNCT american_scientific_journal-3571 169 77 ( ( PUNCT american_scientific_journal-3571 169 78 b b X american_scientific_journal-3571 169 79 ) ) PUNCT american_scientific_journal-3571 169 80 figure figure NOUN american_scientific_journal-3571 169 81 9 9 NUM american_scientific_journal-3571 169 82 : : PUNCT american_scientific_journal-3571 169 83 ( ( PUNCT american_scientific_journal-3571 169 84 a a X american_scientific_journal-3571 169 85 ) ) PUNCT american_scientific_journal-3571 169 86 leg leg NOUN american_scientific_journal-3571 169 87 2 2 NUM american_scientific_journal-3571 169 88 in in ADP american_scientific_journal-3571 169 89 swinging swinge VERB american_scientific_journal-3571 169 90 phase phase NOUN american_scientific_journal-3571 169 91 . . PUNCT american_scientific_journal-3571 170 1 ( ( PUNCT american_scientific_journal-3571 170 2 b b X american_scientific_journal-3571 170 3 ) ) PUNCT american_scientific_journal-3571 170 4 the the DET american_scientific_journal-3571 170 5 stability stability NOUN american_scientific_journal-3571 170 6 margin margin NOUN american_scientific_journal-3571 170 7 𝑆𝑆𝑠𝑠2(cm 𝑆𝑆𝑠𝑠2(cm NOUN american_scientific_journal-3571 170 8 ) ) PUNCT american_scientific_journal-3571 170 9 when when SCONJ american_scientific_journal-3571 170 10 leg2 leg2 NOUN american_scientific_journal-3571 170 11 is be AUX american_scientific_journal-3571 170 12 swing swe VERB american_scientific_journal-3571 170 13 . . PUNCT american_scientific_journal-3571 171 1 ( ( PUNCT american_scientific_journal-3571 171 2 a a X american_scientific_journal-3571 171 3 ) ) PUNCT american_scientific_journal-3571 171 4 ( ( PUNCT american_scientific_journal-3571 171 5 b b X american_scientific_journal-3571 171 6 ) ) PUNCT american_scientific_journal-3571 171 7 figure figure NOUN american_scientific_journal-3571 171 8 10 10 NUM american_scientific_journal-3571 171 9 : : PUNCT american_scientific_journal-3571 171 10 ( ( PUNCT american_scientific_journal-3571 171 11 a a X american_scientific_journal-3571 171 12 ) ) PUNCT american_scientific_journal-3571 171 13 leg leg NOUN american_scientific_journal-3571 171 14 3 3 NUM american_scientific_journal-3571 171 15 in in ADP american_scientific_journal-3571 171 16 swinging swinge VERB american_scientific_journal-3571 171 17 phase phase NOUN american_scientific_journal-3571 171 18 . . PUNCT american_scientific_journal-3571 172 1 ( ( PUNCT american_scientific_journal-3571 172 2 b b X american_scientific_journal-3571 172 3 ) ) PUNCT american_scientific_journal-3571 172 4 the the DET american_scientific_journal-3571 172 5 stability stability NOUN american_scientific_journal-3571 172 6 margin margin NOUN american_scientific_journal-3571 172 7 𝑆𝑆𝑠𝑠3(cm 𝑆𝑆𝑠𝑠3(cm NOUN american_scientific_journal-3571 172 8 ) ) PUNCT american_scientific_journal-3571 172 9 when when SCONJ american_scientific_journal-3571 172 10 leg3 leg3 PROPN american_scientific_journal-3571 172 11 is be AUX american_scientific_journal-3571 172 12 swing swing NOUN american_scientific_journal-3571 172 13 . . PUNCT american_scientific_journal-3571 173 1 ( ( PUNCT american_scientific_journal-3571 173 2 a a X american_scientific_journal-3571 173 3 ) ) PUNCT american_scientific_journal-3571 173 4 ( ( PUNCT american_scientific_journal-3571 173 5 b b X american_scientific_journal-3571 173 6 ) ) PUNCT american_scientific_journal-3571 173 7 figure figure NOUN american_scientific_journal-3571 173 8 11 11 NUM american_scientific_journal-3571 173 9 : : PUNCT american_scientific_journal-3571 173 10 ( ( PUNCT american_scientific_journal-3571 173 11 a a X american_scientific_journal-3571 173 12 ) ) PUNCT american_scientific_journal-3571 173 13 leg leg NOUN american_scientific_journal-3571 173 14 1 1 NUM american_scientific_journal-3571 173 15 in in ADP american_scientific_journal-3571 173 16 swinging swinge VERB american_scientific_journal-3571 173 17 phase phase NOUN american_scientific_journal-3571 173 18 . . PUNCT american_scientific_journal-3571 174 1 ( ( PUNCT american_scientific_journal-3571 174 2 b b X american_scientific_journal-3571 174 3 ) ) PUNCT american_scientific_journal-3571 174 4 the the DET american_scientific_journal-3571 174 5 stability stability NOUN american_scientific_journal-3571 174 6 margin margin NOUN american_scientific_journal-3571 174 7 𝑆𝑆𝑠𝑠4(cm 𝑆𝑆𝑠𝑠4(cm NOUN american_scientific_journal-3571 174 8 ) ) PUNCT american_scientific_journal-3571 174 9 when when SCONJ american_scientific_journal-3571 174 10 leg1 leg1 NOUN american_scientific_journal-3571 174 11 is be AUX american_scientific_journal-3571 174 12 swing swing NOUN american_scientific_journal-3571 174 13 . . PUNCT american_scientific_journal-3571 175 1 from from ADP american_scientific_journal-3571 175 2 above above ADP american_scientific_journal-3571 175 3 figures figure NOUN american_scientific_journal-3571 175 4 it it PRON american_scientific_journal-3571 175 5 can can AUX american_scientific_journal-3571 175 6 be be AUX american_scientific_journal-3571 175 7 seen see VERB american_scientific_journal-3571 175 8 the the DET american_scientific_journal-3571 175 9 following following NOUN american_scientific_journal-3571 175 10 : : PUNCT american_scientific_journal-3571 176 1 1 1 X american_scientific_journal-3571 176 2 . . X american_scientific_journal-3571 176 3 in in ADP american_scientific_journal-3571 176 4 fig.(8 fig.(8 PROPN american_scientific_journal-3571 176 5 ): ): PUNCT american_scientific_journal-3571 176 6 leg4 leg4 NOUN american_scientific_journal-3571 176 7 tip tip NOUN american_scientific_journal-3571 176 8 is be AUX american_scientific_journal-3571 176 9 swinging swinge VERB american_scientific_journal-3571 176 10 and and CCONJ american_scientific_journal-3571 176 11 the the DET american_scientific_journal-3571 176 12 stability stability NOUN american_scientific_journal-3571 176 13 margin margin NOUN american_scientific_journal-3571 176 14 𝑆𝑆𝑠𝑠1(cm 𝑆𝑆𝑠𝑠1(cm NOUN american_scientific_journal-3571 176 15 ) ) PUNCT american_scientific_journal-3571 176 16 equals equal VERB american_scientific_journal-3571 176 17 to to ADP american_scientific_journal-3571 176 18 ( ( PUNCT american_scientific_journal-3571 176 19 1.71 1.71 NUM american_scientific_journal-3571 176 20 ) ) PUNCT american_scientific_journal-3571 176 21 cm cm NOUN american_scientific_journal-3571 176 22 . . PUNCT american_scientific_journal-3571 177 1 2 2 NUM american_scientific_journal-3571 177 2 . . X american_scientific_journal-3571 177 3 in in ADP american_scientific_journal-3571 177 4 fig.(9 fig.(9 PROPN american_scientific_journal-3571 177 5 ): ): PUNCT american_scientific_journal-3571 177 6 leg2 leg2 NOUN american_scientific_journal-3571 177 7 swinging swinge VERB american_scientific_journal-3571 177 8 and and CCONJ american_scientific_journal-3571 177 9 the the DET american_scientific_journal-3571 177 10 stability stability NOUN american_scientific_journal-3571 177 11 margin margin NOUN american_scientific_journal-3571 177 12 𝑆𝑆𝑠𝑠2(cm 𝑆𝑆𝑠𝑠2(cm NOUN american_scientific_journal-3571 177 13 ) ) PUNCT american_scientific_journal-3571 177 14 equals equal VERB american_scientific_journal-3571 177 15 to to ADP american_scientific_journal-3571 177 16 ( ( PUNCT american_scientific_journal-3571 177 17 1.35 1.35 NUM american_scientific_journal-3571 177 18 ) ) PUNCT american_scientific_journal-3571 177 19 cm cm NOUN american_scientific_journal-3571 177 20 . . PUNCT american_scientific_journal-3571 178 1 4 4 NUM american_scientific_journal-3571 178 2 20 20 NUM american_scientific_journal-3571 178 3 x x SYM american_scientific_journal-3571 178 4 0 0 NUM american_scientific_journal-3571 178 5 -20 -20 NUM american_scientific_journal-3571 178 6 -10 -10 SYM american_scientific_journal-3571 178 7 0 0 NUM american_scientific_journal-3571 178 8 10 10 NUM american_scientific_journal-3571 178 9 y y NOUN american_scientific_journal-3571 178 10 20 20 NUM american_scientific_journal-3571 178 11 30 30 NUM american_scientific_journal-3571 178 12 40 40 NUM american_scientific_journal-3571 178 13 support support NOUN american_scientific_journal-3571 178 14 triangle triangle NOUN american_scientific_journal-3571 178 15 leg leg NOUN american_scientific_journal-3571 178 16 2 2 NUM american_scientific_journal-3571 178 17 swing swing NOUN american_scientific_journal-3571 178 18 0 0 NUM american_scientific_journal-3571 178 19 50 50 NUM american_scientific_journal-3571 178 20 100 100 NUM american_scientific_journal-3571 178 21 150 150 NUM american_scientific_journal-3571 178 22 200 200 NUM american_scientific_journal-3571 178 23 250 250 NUM american_scientific_journal-3571 178 24 300 300 NUM american_scientific_journal-3571 178 25 1 1 NUM american_scientific_journal-3571 178 26 2 2 NUM american_scientific_journal-3571 178 27 3 3 NUM american_scientific_journal-3571 178 28 4 4 NUM american_scientific_journal-3571 178 29 5 5 NUM american_scientific_journal-3571 178 30 6 6 NUM american_scientific_journal-3571 178 31 7 7 NUM american_scientific_journal-3571 178 32 itration itration NOUN american_scientific_journal-3571 178 33 s s PART american_scientific_journal-3571 178 34 m m VERB american_scientific_journal-3571 178 35 2 2 NUM american_scientific_journal-3571 178 36 ( ( PUNCT american_scientific_journal-3571 178 37 c c NOUN american_scientific_journal-3571 178 38 m m AUX american_scientific_journal-3571 178 39 ) ) PUNCT american_scientific_journal-3571 178 40 sm2 sm2 VERB american_scientific_journal-3571 178 41 30 30 NUM american_scientific_journal-3571 178 42 x x SYM american_scientific_journal-3571 178 43 20 20 NUM american_scientific_journal-3571 178 44 10 10 NUM american_scientific_journal-3571 178 45 0 0 NUM american_scientific_journal-3571 178 46 1010 1010 NUM american_scientific_journal-3571 178 47 0 0 NUM american_scientific_journal-3571 178 48 10 10 NUM american_scientific_journal-3571 178 49 20 20 NUM american_scientific_journal-3571 178 50 y y PROPN american_scientific_journal-3571 178 51 30 30 NUM american_scientific_journal-3571 178 52 40 40 NUM american_scientific_journal-3571 178 53 leg leg NOUN american_scientific_journal-3571 178 54 3 3 NUM american_scientific_journal-3571 178 55 swing swing NOUN american_scientific_journal-3571 178 56 support support NOUN american_scientific_journal-3571 178 57 triangle triangle NOUN american_scientific_journal-3571 178 58 0 0 NUM american_scientific_journal-3571 178 59 50 50 NUM american_scientific_journal-3571 178 60 100 100 NUM american_scientific_journal-3571 178 61 150 150 NUM american_scientific_journal-3571 178 62 200 200 NUM american_scientific_journal-3571 178 63 250 250 NUM american_scientific_journal-3571 178 64 300 300 NUM american_scientific_journal-3571 178 65 350 350 NUM american_scientific_journal-3571 178 66 1 1 NUM american_scientific_journal-3571 178 67 2 2 NUM american_scientific_journal-3571 178 68 3 3 NUM american_scientific_journal-3571 178 69 4 4 NUM american_scientific_journal-3571 178 70 5 5 NUM american_scientific_journal-3571 178 71 6 6 NUM american_scientific_journal-3571 178 72 iteration iteration NOUN american_scientific_journal-3571 178 73 s s PART american_scientific_journal-3571 178 74 m m VERB american_scientific_journal-3571 178 75 3 3 NUM american_scientific_journal-3571 178 76 ( ( PUNCT american_scientific_journal-3571 178 77 cm cm PROPN american_scientific_journal-3571 178 78 ) ) PUNCT american_scientific_journal-3571 178 79 sm3 sm3 PROPN american_scientific_journal-3571 178 80 40 40 NUM american_scientific_journal-3571 179 1 20 20 NUM american_scientific_journal-3571 179 2 0 0 NUM american_scientific_journal-3571 179 3 20 20 NUM american_scientific_journal-3571 179 4 -10 -10 SYM american_scientific_journal-3571 179 5 0 0 NUM american_scientific_journal-3571 179 6 10 10 NUM american_scientific_journal-3571 179 7 20 20 NUM american_scientific_journal-3571 179 8 30 30 NUM american_scientific_journal-3571 179 9 40 40 NUM american_scientific_journal-3571 179 10 50 50 NUM american_scientific_journal-3571 179 11 30 30 NUM american_scientific_journal-3571 179 12 20 20 NUM american_scientific_journal-3571 179 13 10 10 NUM american_scientific_journal-3571 179 14 0 0 NUM american_scientific_journal-3571 179 15 z z NOUN american_scientific_journal-3571 179 16 y y SYM american_scientific_journal-3571 179 17 x x SYM american_scientific_journal-3571 179 18 leg leg NOUN american_scientific_journal-3571 179 19 1 1 NUM american_scientific_journal-3571 179 20 swing swing NOUN american_scientific_journal-3571 179 21 support support NOUN american_scientific_journal-3571 179 22 triangle triangle NOUN american_scientific_journal-3571 179 23 0 0 NUM american_scientific_journal-3571 179 24 50 50 NUM american_scientific_journal-3571 179 25 100 100 NUM american_scientific_journal-3571 179 26 150 150 NUM american_scientific_journal-3571 179 27 200 200 NUM american_scientific_journal-3571 179 28 250 250 NUM american_scientific_journal-3571 179 29 300 300 NUM american_scientific_journal-3571 179 30 350 350 NUM american_scientific_journal-3571 179 31 0 0 NUM american_scientific_journal-3571 179 32 0.5 0.5 NUM american_scientific_journal-3571 179 33 1 1 NUM american_scientific_journal-3571 179 34 1.5 1.5 NUM american_scientific_journal-3571 179 35 2 2 NUM american_scientific_journal-3571 179 36 2.5 2.5 NUM american_scientific_journal-3571 179 37 3 3 NUM american_scientific_journal-3571 179 38 3.5 3.5 NUM american_scientific_journal-3571 179 39 4 4 NUM american_scientific_journal-3571 179 40 iteration iteration NOUN american_scientific_journal-3571 179 41 sm sm PROPN american_scientific_journal-3571 179 42 4 4 NUM american_scientific_journal-3571 179 43 ( ( PUNCT american_scientific_journal-3571 179 44 cm cm NOUN american_scientific_journal-3571 179 45 ) ) PUNCT american_scientific_journal-3571 179 46 sm4 sm4 PROPN american_scientific_journal-3571 179 47 american american PROPN american_scientific_journal-3571 179 48 scientific scientific PROPN american_scientific_journal-3571 179 49 research research PROPN american_scientific_journal-3571 179 50 journal journal NOUN american_scientific_journal-3571 179 51 for for ADP american_scientific_journal-3571 179 52 engineering engineering NOUN american_scientific_journal-3571 179 53 , , PUNCT american_scientific_journal-3571 179 54 technology technology NOUN american_scientific_journal-3571 179 55 , , PUNCT american_scientific_journal-3571 179 56 and and CCONJ american_scientific_journal-3571 179 57 sciences science NOUN american_scientific_journal-3571 179 58 ( ( PUNCT american_scientific_journal-3571 179 59 asrjets asrjet NOUN american_scientific_journal-3571 179 60 ) ) PUNCT american_scientific_journal-3571 179 61 ( ( PUNCT american_scientific_journal-3571 179 62 2017 2017 NUM american_scientific_journal-3571 179 63 ) ) PUNCT american_scientific_journal-3571 179 64 volume volume NOUN american_scientific_journal-3571 179 65 37 37 NUM american_scientific_journal-3571 179 66 , , PUNCT american_scientific_journal-3571 179 67 no no DET american_scientific_journal-3571 179 68 1 1 NUM american_scientific_journal-3571 179 69 , , PUNCT american_scientific_journal-3571 179 70 pp pp ADV american_scientific_journal-3571 179 71 17 17 NUM american_scientific_journal-3571 179 72 - - SYM american_scientific_journal-3571 179 73 32 32 NUM american_scientific_journal-3571 179 74 29 29 NUM american_scientific_journal-3571 179 75 3 3 NUM american_scientific_journal-3571 179 76 . . PUNCT american_scientific_journal-3571 180 1 in in ADP american_scientific_journal-3571 180 2 fig.(10 fig.(10 PROPN american_scientific_journal-3571 180 3 ): ): PUNCT american_scientific_journal-3571 180 4 leg3 leg3 ADJ american_scientific_journal-3571 180 5 swinging swinging NOUN american_scientific_journal-3571 180 6 and and CCONJ american_scientific_journal-3571 180 7 the the DET american_scientific_journal-3571 180 8 stability stability NOUN american_scientific_journal-3571 180 9 margin margin NOUN american_scientific_journal-3571 180 10 𝑆𝑆𝑠𝑠3(cm 𝑆𝑆𝑠𝑠3(cm NOUN american_scientific_journal-3571 180 11 ) ) PUNCT american_scientific_journal-3571 180 12 equals equal VERB american_scientific_journal-3571 180 13 to to ADP american_scientific_journal-3571 180 14 ( ( PUNCT american_scientific_journal-3571 180 15 2.3 2.3 NUM american_scientific_journal-3571 180 16 ) ) PUNCT american_scientific_journal-3571 180 17 cm cm NOUN american_scientific_journal-3571 180 18 . . PUNCT american_scientific_journal-3571 181 1 4 4 NUM american_scientific_journal-3571 181 2 . . X american_scientific_journal-3571 181 3 in in ADP american_scientific_journal-3571 181 4 fig.(11 fig.(11 PROPN american_scientific_journal-3571 181 5 ): ): PUNCT american_scientific_journal-3571 181 6 leg1 leg1 NOUN american_scientific_journal-3571 181 7 swinging swinging NOUN american_scientific_journal-3571 181 8 and and CCONJ american_scientific_journal-3571 181 9 the the DET american_scientific_journal-3571 181 10 stability stability NOUN american_scientific_journal-3571 181 11 margin margin NOUN american_scientific_journal-3571 181 12 𝑆𝑆𝑠𝑠4(cm 𝑆𝑆𝑠𝑠4(cm NOUN american_scientific_journal-3571 181 13 ) ) PUNCT american_scientific_journal-3571 181 14 equals equal VERB american_scientific_journal-3571 181 15 to to ADP american_scientific_journal-3571 181 16 ( ( PUNCT american_scientific_journal-3571 181 17 1.95 1.95 NUM american_scientific_journal-3571 181 18 ) ) PUNCT american_scientific_journal-3571 181 19 cm cm NOUN american_scientific_journal-3571 181 20 . . PUNCT american_scientific_journal-3571 182 1 the the DET american_scientific_journal-3571 182 2 best good ADJ american_scientific_journal-3571 182 3 stability stability NOUN american_scientific_journal-3571 182 4 margins margin NOUN american_scientific_journal-3571 182 5 achieving achieve VERB american_scientific_journal-3571 182 6 from from ADP american_scientific_journal-3571 182 7 the the DET american_scientific_journal-3571 182 8 pso pso NOUN american_scientific_journal-3571 182 9 optimization optimization NOUN american_scientific_journal-3571 182 10 algorithm algorithm NOUN american_scientific_journal-3571 182 11 are be AUX american_scientific_journal-3571 182 12 showing show VERB american_scientific_journal-3571 182 13 in in ADP american_scientific_journal-3571 182 14 the the DET american_scientific_journal-3571 182 15 following follow VERB american_scientific_journal-3571 182 16 figures figure NOUN american_scientific_journal-3571 182 17 figure figure VERB american_scientific_journal-3571 182 18 12 12 NUM american_scientific_journal-3571 182 19 : : PUNCT american_scientific_journal-3571 182 20 best good ADJ american_scientific_journal-3571 182 21 cost cost NOUN american_scientific_journal-3571 182 22 for for ADP american_scientific_journal-3571 182 23 the the DET american_scientific_journal-3571 182 24 stability stability NOUN american_scientific_journal-3571 182 25 margin margin NOUN american_scientific_journal-3571 182 26 𝑆𝑆𝑠𝑠1 𝑆𝑆𝑠𝑠1 VERB american_scientific_journal-3571 182 27 figure figure NOUN american_scientific_journal-3571 182 28 13 13 NUM american_scientific_journal-3571 182 29 : : PUNCT american_scientific_journal-3571 182 30 best good ADJ american_scientific_journal-3571 182 31 cost cost NOUN american_scientific_journal-3571 182 32 for for ADP american_scientific_journal-3571 182 33 the the DET american_scientific_journal-3571 182 34 stability stability NOUN american_scientific_journal-3571 182 35 margin margin NOUN american_scientific_journal-3571 183 1 𝑆𝑆𝑠𝑠2 𝑆𝑆𝑠𝑠2 NOUN american_scientific_journal-3571 183 2 figure figure NOUN american_scientific_journal-3571 183 3 14 14 NUM american_scientific_journal-3571 183 4 : : PUNCT american_scientific_journal-3571 183 5 best good ADJ american_scientific_journal-3571 183 6 cost cost NOUN american_scientific_journal-3571 183 7 for for ADP american_scientific_journal-3571 183 8 the the DET american_scientific_journal-3571 183 9 stability stability NOUN american_scientific_journal-3571 183 10 margin margin NOUN american_scientific_journal-3571 183 11 𝑆𝑆𝑠𝑠3 𝑆𝑆𝑠𝑠3 NUM american_scientific_journal-3571 183 12 figure figure NOUN american_scientific_journal-3571 183 13 15 15 NUM american_scientific_journal-3571 183 14 : : PUNCT american_scientific_journal-3571 183 15 best good ADJ american_scientific_journal-3571 183 16 cost cost NOUN american_scientific_journal-3571 183 17 for for ADP american_scientific_journal-3571 183 18 the the DET american_scientific_journal-3571 183 19 stability stability NOUN american_scientific_journal-3571 183 20 margin margin NOUN american_scientific_journal-3571 183 21 𝑆𝑆𝑠𝑠4 𝑆𝑆𝑠𝑠4 PROPN american_scientific_journal-3571 183 22 the the DET american_scientific_journal-3571 183 23 following follow VERB american_scientific_journal-3571 183 24 table table NOUN american_scientific_journal-3571 183 25 ( ( PUNCT american_scientific_journal-3571 183 26 2 2 NUM american_scientific_journal-3571 183 27 ) ) PUNCT american_scientific_journal-3571 183 28 is be AUX american_scientific_journal-3571 183 29 a a DET american_scientific_journal-3571 183 30 comparison comparison NOUN american_scientific_journal-3571 183 31 between between ADP american_scientific_journal-3571 183 32 the the DET american_scientific_journal-3571 183 33 classical classical ADJ american_scientific_journal-3571 183 34 stability stability NOUN american_scientific_journal-3571 183 35 margins margin VERB american_scientific_journal-3571 183 36 analysis analysis NOUN american_scientific_journal-3571 183 37 and and CCONJ american_scientific_journal-3571 183 38 proposed propose VERB american_scientific_journal-3571 183 39 optimization optimization NOUN american_scientific_journal-3571 183 40 using use VERB american_scientific_journal-3571 183 41 pso pso NOUN american_scientific_journal-3571 183 42 algorithm algorithm NOUN american_scientific_journal-3571 183 43 method method NOUN american_scientific_journal-3571 183 44 used use VERB american_scientific_journal-3571 183 45 in in ADP american_scientific_journal-3571 183 46 this this DET american_scientific_journal-3571 183 47 paper paper NOUN american_scientific_journal-3571 183 48 . . PUNCT american_scientific_journal-3571 184 1 table table NOUN american_scientific_journal-3571 184 2 2 2 NUM american_scientific_journal-3571 184 3 : : PUNCT american_scientific_journal-3571 184 4 stability stability NOUN american_scientific_journal-3571 184 5 margins margin VERB american_scientific_journal-3571 184 6 comparison comparison NOUN american_scientific_journal-3571 184 7 between between ADP american_scientific_journal-3571 184 8 the the DET american_scientific_journal-3571 184 9 classical classical ADJ american_scientific_journal-3571 184 10 analyses analysis NOUN american_scientific_journal-3571 184 11 and and CCONJ american_scientific_journal-3571 184 12 the the DET american_scientific_journal-3571 184 13 optimized optimize VERB american_scientific_journal-3571 184 14 method method NOUN american_scientific_journal-3571 184 15 classical classical ADJ american_scientific_journal-3571 184 16 analysis analysis NOUN american_scientific_journal-3571 184 17 method method NOUN american_scientific_journal-3571 184 18 proposed propose VERB american_scientific_journal-3571 184 19 optimization optimization NOUN american_scientific_journal-3571 184 20 using use VERB american_scientific_journal-3571 184 21 pso pso NOUN american_scientific_journal-3571 184 22 algorithm algorithm NOUN american_scientific_journal-3571 184 23 1 1 NUM american_scientific_journal-3571 184 24 . . PUNCT american_scientific_journal-3571 185 1 when when SCONJ american_scientific_journal-3571 185 2 leg leg NOUN american_scientific_journal-3571 185 3 4 4 NUM american_scientific_journal-3571 185 4 is be AUX american_scientific_journal-3571 185 5 swing swe VERB american_scientific_journal-3571 185 6 the the DET american_scientific_journal-3571 185 7 stability stability NOUN american_scientific_journal-3571 185 8 margin margin NOUN american_scientific_journal-3571 185 9 𝑆𝑆𝑠𝑠1 𝑆𝑆𝑠𝑠1 NOUN american_scientific_journal-3571 185 10 ranging range VERB american_scientific_journal-3571 185 11 between between ADP american_scientific_journal-3571 185 12 ( ( PUNCT american_scientific_journal-3571 185 13 2 2 NUM american_scientific_journal-3571 185 14 – – SYM american_scientific_journal-3571 185 15 4.55 4.55 NUM american_scientific_journal-3571 185 16 ) ) PUNCT american_scientific_journal-3571 185 17 cm cm NOUN american_scientific_journal-3571 185 18 . . PUNCT american_scientific_journal-3571 186 1 1 1 NUM american_scientific_journal-3571 186 2 . . X american_scientific_journal-3571 186 3 when when SCONJ american_scientific_journal-3571 186 4 leg leg NOUN american_scientific_journal-3571 186 5 4 4 NUM american_scientific_journal-3571 186 6 is be AUX american_scientific_journal-3571 186 7 swing swe VERB american_scientific_journal-3571 186 8 the the DET american_scientific_journal-3571 186 9 best good ADJ american_scientific_journal-3571 186 10 stability stability NOUN american_scientific_journal-3571 186 11 margin margin NOUN american_scientific_journal-3571 186 12 𝑆𝑆𝑠𝑠1 𝑆𝑆𝑠𝑠1 VERB american_scientific_journal-3571 186 13 equals equal VERB american_scientific_journal-3571 186 14 to2.851 to2.851 NOUN american_scientific_journal-3571 186 15 cm cm NOUN american_scientific_journal-3571 186 16 . . PUNCT american_scientific_journal-3571 187 1 2 2 NUM american_scientific_journal-3571 187 2 . . X american_scientific_journal-3571 187 3 when when SCONJ american_scientific_journal-3571 187 4 leg leg NOUN american_scientific_journal-3571 187 5 2 2 NUM american_scientific_journal-3571 187 6 is be AUX american_scientific_journal-3571 187 7 swing swe VERB american_scientific_journal-3571 187 8 the the DET american_scientific_journal-3571 187 9 stability stability NOUN american_scientific_journal-3571 187 10 margin margin NOUN american_scientific_journal-3571 187 11 𝑆𝑆𝑠𝑠2 𝑆𝑆𝑠𝑠2 NOUN american_scientific_journal-3571 187 12 ranging ranging NOUN american_scientific_journal-3571 187 13 between between ADP american_scientific_journal-3571 187 14 ( ( PUNCT american_scientific_journal-3571 187 15 3 3 NUM american_scientific_journal-3571 187 16 – – SYM american_scientific_journal-3571 187 17 6.2 6.2 NUM american_scientific_journal-3571 187 18 ) ) PUNCT american_scientific_journal-3571 187 19 cm cm NOUN american_scientific_journal-3571 187 20 . . PUNCT american_scientific_journal-3571 188 1 2 2 NUM american_scientific_journal-3571 188 2 . . X american_scientific_journal-3571 188 3 when when SCONJ american_scientific_journal-3571 188 4 leg leg NOUN american_scientific_journal-3571 188 5 2 2 NUM american_scientific_journal-3571 188 6 is be AUX american_scientific_journal-3571 188 7 swing swe VERB american_scientific_journal-3571 188 8 the the DET american_scientific_journal-3571 188 9 best good ADJ american_scientific_journal-3571 188 10 stability stability NOUN american_scientific_journal-3571 188 11 margin margin NOUN american_scientific_journal-3571 188 12 𝑆𝑆𝑠𝑠2 𝑆𝑆𝑠𝑠2 PRON american_scientific_journal-3571 188 13 equals equal VERB american_scientific_journal-3571 188 14 to2.75 to2.75 ADJ american_scientific_journal-3571 188 15 cm cm NOUN american_scientific_journal-3571 188 16 . . PUNCT american_scientific_journal-3571 189 1 3 3 NUM american_scientific_journal-3571 189 2 . . X american_scientific_journal-3571 189 3 when when SCONJ american_scientific_journal-3571 189 4 leg leg NOUN american_scientific_journal-3571 189 5 3 3 NUM american_scientific_journal-3571 189 6 is be AUX american_scientific_journal-3571 189 7 swing swe VERB american_scientific_journal-3571 189 8 the the DET american_scientific_journal-3571 189 9 stability stability NOUN american_scientific_journal-3571 189 10 margin margin NOUN american_scientific_journal-3571 189 11 𝑆𝑆𝑠𝑠3 𝑆𝑆𝑠𝑠3 NOUN american_scientific_journal-3571 189 12 ranging range VERB american_scientific_journal-3571 189 13 between between ADP american_scientific_journal-3571 189 14 ( ( PUNCT american_scientific_journal-3571 189 15 2.7 2.7 NUM american_scientific_journal-3571 189 16 – – SYM american_scientific_journal-3571 189 17 5.3 5.3 NUM american_scientific_journal-3571 189 18 ) ) PUNCT american_scientific_journal-3571 189 19 cm cm NOUN american_scientific_journal-3571 189 20 . . PUNCT american_scientific_journal-3571 190 1 3 3 NUM american_scientific_journal-3571 190 2 . . X american_scientific_journal-3571 190 3 when when SCONJ american_scientific_journal-3571 190 4 leg leg NOUN american_scientific_journal-3571 190 5 3 3 NUM american_scientific_journal-3571 190 6 is be AUX american_scientific_journal-3571 190 7 swing swe VERB american_scientific_journal-3571 190 8 the the DET american_scientific_journal-3571 190 9 best good ADJ american_scientific_journal-3571 190 10 stability stability NOUN american_scientific_journal-3571 190 11 margin margin NOUN american_scientific_journal-3571 190 12 𝑆𝑆𝑠𝑠3 𝑆𝑆𝑠𝑠3 ADJ american_scientific_journal-3571 190 13 equals equal VERB american_scientific_journal-3571 190 14 to to ADP american_scientific_journal-3571 190 15 : : PUNCT american_scientific_journal-3571 190 16 3.667 3.667 NUM american_scientific_journal-3571 190 17 cm cm NOUN american_scientific_journal-3571 190 18 . . PUNCT american_scientific_journal-3571 191 1 4 4 NUM american_scientific_journal-3571 191 2 . . X american_scientific_journal-3571 191 3 when when SCONJ american_scientific_journal-3571 191 4 leg leg NOUN american_scientific_journal-3571 191 5 1 1 NUM american_scientific_journal-3571 191 6 is be AUX american_scientific_journal-3571 191 7 swing swe VERB american_scientific_journal-3571 191 8 the the DET american_scientific_journal-3571 191 9 stability stability NOUN american_scientific_journal-3571 191 10 margin margin NOUN american_scientific_journal-3571 191 11 𝑆𝑆𝑠𝑠4 𝑆𝑆𝑠𝑠4 NOUN american_scientific_journal-3571 191 12 ranging range VERB american_scientific_journal-3571 191 13 between between ADP american_scientific_journal-3571 191 14 ( ( PUNCT american_scientific_journal-3571 191 15 1.6 1.6 NUM american_scientific_journal-3571 191 16 – – SYM american_scientific_journal-3571 191 17 3.6 3.6 NUM american_scientific_journal-3571 191 18 ) ) PUNCT american_scientific_journal-3571 191 19 cm cm NOUN american_scientific_journal-3571 191 20 . . PUNCT american_scientific_journal-3571 192 1 4 4 NUM american_scientific_journal-3571 192 2 . . X american_scientific_journal-3571 192 3 when when SCONJ american_scientific_journal-3571 192 4 leg leg NOUN american_scientific_journal-3571 192 5 1 1 NUM american_scientific_journal-3571 192 6 is be AUX american_scientific_journal-3571 192 7 swing swe VERB american_scientific_journal-3571 192 8 the the DET american_scientific_journal-3571 192 9 best good ADJ american_scientific_journal-3571 192 10 stability stability NOUN american_scientific_journal-3571 192 11 margin margin NOUN american_scientific_journal-3571 192 12 𝑆𝑆𝑠𝑠4 𝑆𝑆𝑠𝑠4 PROPN american_scientific_journal-3571 192 13 equals equal VERB american_scientific_journal-3571 192 14 to to ADP american_scientific_journal-3571 192 15 : : PUNCT american_scientific_journal-3571 192 16 2.308 2.308 NUM american_scientific_journal-3571 192 17 cm cm NOUN american_scientific_journal-3571 192 18 . . PUNCT american_scientific_journal-3571 193 1 iteration iteration NOUN american_scientific_journal-3571 193 2 0 0 NUM american_scientific_journal-3571 193 3 100 100 NUM american_scientific_journal-3571 193 4 200 200 NUM american_scientific_journal-3571 193 5 300 300 NUM american_scientific_journal-3571 193 6 400 400 NUM american_scientific_journal-3571 193 7 500 500 NUM american_scientific_journal-3571 193 8 be be AUX american_scientific_journal-3571 193 9 st st PROPN american_scientific_journal-3571 193 10 co co NOUN american_scientific_journal-3571 193 11 sts st VERB american_scientific_journal-3571 193 12 2.84 2.84 NUM american_scientific_journal-3571 193 13 2.86 2.86 NUM american_scientific_journal-3571 193 14 2.88 2.88 NUM american_scientific_journal-3571 193 15 2.9 2.9 NUM american_scientific_journal-3571 193 16 2.92 2.92 NUM american_scientific_journal-3571 193 17 2.94 2.94 NUM american_scientific_journal-3571 193 18 2.96 2.96 NUM american_scientific_journal-3571 193 19 2.98 2.98 NUM american_scientific_journal-3571 193 20 3 3 NUM american_scientific_journal-3571 193 21 best good ADJ american_scientific_journal-3571 193 22 margin margin NOUN american_scientific_journal-3571 193 23 sm1= sm1= NOUN american_scientific_journal-3571 193 24 2.851 2.851 NUM american_scientific_journal-3571 193 25 cm cm NOUN american_scientific_journal-3571 193 26 iteration iteration NOUN american_scientific_journal-3571 193 27 0 0 NUM american_scientific_journal-3571 193 28 100 100 NUM american_scientific_journal-3571 193 29 200 200 NUM american_scientific_journal-3571 193 30 300 300 NUM american_scientific_journal-3571 193 31 400 400 NUM american_scientific_journal-3571 193 32 500 500 NUM american_scientific_journal-3571 193 33 be be AUX american_scientific_journal-3571 193 34 st st PROPN american_scientific_journal-3571 193 35 c c PROPN american_scientific_journal-3571 193 36 os os NOUN american_scientific_journal-3571 193 37 ts ts ADP american_scientific_journal-3571 193 38 4.75 4.75 NUM american_scientific_journal-3571 193 39 4.76 4.76 NUM american_scientific_journal-3571 193 40 4.77 4.77 NUM american_scientific_journal-3571 193 41 4.78 4.78 NUM american_scientific_journal-3571 193 42 4.79 4.79 NUM american_scientific_journal-3571 193 43 4.8 4.8 NUM american_scientific_journal-3571 193 44 best good ADJ american_scientific_journal-3571 193 45 margin margin NOUN american_scientific_journal-3571 194 1 sm2=4.75 sm2=4.75 PROPN american_scientific_journal-3571 194 2 cm cm NOUN american_scientific_journal-3571 194 3 iteration iteration NOUN american_scientific_journal-3571 194 4 0 0 NUM american_scientific_journal-3571 194 5 100 100 NUM american_scientific_journal-3571 194 6 200 200 NUM american_scientific_journal-3571 194 7 300 300 NUM american_scientific_journal-3571 194 8 400 400 NUM american_scientific_journal-3571 194 9 500 500 NUM american_scientific_journal-3571 194 10 be be AUX american_scientific_journal-3571 194 11 st st PROPN american_scientific_journal-3571 194 12 co co NOUN american_scientific_journal-3571 194 13 sts st VERB american_scientific_journal-3571 194 14 3.665 3.665 NUM american_scientific_journal-3571 194 15 3.67 3.67 NUM american_scientific_journal-3571 194 16 3.675 3.675 NUM american_scientific_journal-3571 194 17 3.68 3.68 NUM american_scientific_journal-3571 194 18 3.685 3.685 NUM american_scientific_journal-3571 194 19 3.69 3.69 NUM american_scientific_journal-3571 194 20 best good ADJ american_scientific_journal-3571 194 21 margin margin NOUN american_scientific_journal-3571 194 22 sm3=3.667 sm3=3.667 NOUN american_scientific_journal-3571 194 23 cm cm NOUN american_scientific_journal-3571 194 24 iteration iteration NOUN american_scientific_journal-3571 194 25 0 0 NUM american_scientific_journal-3571 194 26 100 100 NUM american_scientific_journal-3571 194 27 200 200 NUM american_scientific_journal-3571 194 28 300 300 NUM american_scientific_journal-3571 194 29 400 400 NUM american_scientific_journal-3571 194 30 500 500 NUM american_scientific_journal-3571 194 31 be be AUX american_scientific_journal-3571 194 32 st st PROPN american_scientific_journal-3571 194 33 c c PROPN american_scientific_journal-3571 194 34 os os NOUN american_scientific_journal-3571 194 35 ts ts ADP american_scientific_journal-3571 194 36 2.31 2.31 NUM american_scientific_journal-3571 194 37 2.315 2.315 NUM american_scientific_journal-3571 194 38 2.32 2.32 NUM american_scientific_journal-3571 194 39 2.325 2.325 NUM american_scientific_journal-3571 194 40 2.33 2.33 NUM american_scientific_journal-3571 194 41 2.335 2.335 NUM american_scientific_journal-3571 194 42 best good ADJ american_scientific_journal-3571 194 43 margin margin NOUN american_scientific_journal-3571 194 44 sm4=2.308 sm4=2.308 ADJ american_scientific_journal-3571 194 45 cm cm PROPN american_scientific_journal-3571 194 46 american american PROPN american_scientific_journal-3571 194 47 scientific scientific ADJ american_scientific_journal-3571 194 48 research research NOUN american_scientific_journal-3571 194 49 journal journal NOUN american_scientific_journal-3571 194 50 for for ADP american_scientific_journal-3571 194 51 engineering engineering NOUN american_scientific_journal-3571 194 52 , , PUNCT american_scientific_journal-3571 194 53 technology technology NOUN american_scientific_journal-3571 194 54 , , PUNCT american_scientific_journal-3571 194 55 and and CCONJ american_scientific_journal-3571 194 56 sciences science NOUN american_scientific_journal-3571 194 57 ( ( PUNCT american_scientific_journal-3571 194 58 asrjets asrjet NOUN american_scientific_journal-3571 194 59 ) ) PUNCT american_scientific_journal-3571 194 60 ( ( PUNCT american_scientific_journal-3571 194 61 2017 2017 NUM american_scientific_journal-3571 194 62 ) ) PUNCT american_scientific_journal-3571 194 63 volume volume NOUN american_scientific_journal-3571 194 64 37 37 NUM american_scientific_journal-3571 194 65 , , PUNCT american_scientific_journal-3571 194 66 no no DET american_scientific_journal-3571 194 67 1 1 NUM american_scientific_journal-3571 194 68 , , PUNCT american_scientific_journal-3571 194 69 pp pp ADV american_scientific_journal-3571 194 70 17 17 NUM american_scientific_journal-3571 194 71 - - SYM american_scientific_journal-3571 194 72 32 32 NUM american_scientific_journal-3571 194 73 30 30 NUM american_scientific_journal-3571 194 74 from from ADP american_scientific_journal-3571 194 75 above above ADP american_scientific_journal-3571 194 76 figures figure NOUN american_scientific_journal-3571 194 77 it it PRON american_scientific_journal-3571 194 78 can can AUX american_scientific_journal-3571 194 79 be be AUX american_scientific_journal-3571 194 80 seen see VERB american_scientific_journal-3571 194 81 that that SCONJ american_scientific_journal-3571 195 1 : : PUNCT american_scientific_journal-3571 195 2 1 1 X american_scientific_journal-3571 195 3 . . X american_scientific_journal-3571 195 4 in in ADP american_scientific_journal-3571 195 5 fig.(12 fig.(12 PROPN american_scientific_journal-3571 195 6 ): ): PUNCT american_scientific_journal-3571 195 7 the the DET american_scientific_journal-3571 195 8 best good ADJ american_scientific_journal-3571 195 9 cost cost NOUN american_scientific_journal-3571 195 10 of of ADP american_scientific_journal-3571 195 11 the the DET american_scientific_journal-3571 195 12 stability stability NOUN american_scientific_journal-3571 195 13 margin margin NOUN american_scientific_journal-3571 195 14 𝑆𝑆𝑠𝑠1equals 𝑆𝑆𝑠𝑠1equal NOUN american_scientific_journal-3571 195 15 to to ADP american_scientific_journal-3571 195 16 ( ( PUNCT american_scientific_journal-3571 195 17 1.635 1.635 NUM american_scientific_journal-3571 195 18 ) ) PUNCT american_scientific_journal-3571 195 19 cm cm NOUN american_scientific_journal-3571 195 20 . . PUNCT american_scientific_journal-3571 196 1 2 2 NUM american_scientific_journal-3571 196 2 . . X american_scientific_journal-3571 196 3 in in ADP american_scientific_journal-3571 196 4 fig.(13 fig.(13 PROPN american_scientific_journal-3571 196 5 ): ): PUNCT american_scientific_journal-3571 196 6 the the DET american_scientific_journal-3571 196 7 best good ADJ american_scientific_journal-3571 196 8 cost cost NOUN american_scientific_journal-3571 196 9 of of ADP american_scientific_journal-3571 196 10 the the DET american_scientific_journal-3571 196 11 stability stability NOUN american_scientific_journal-3571 196 12 margin margin NOUN american_scientific_journal-3571 196 13 𝑆𝑆𝑠𝑠2 𝑆𝑆𝑠𝑠2 PRON american_scientific_journal-3571 196 14 equals equal VERB american_scientific_journal-3571 196 15 to to ADP american_scientific_journal-3571 196 16 ( ( PUNCT american_scientific_journal-3571 196 17 1.25 1.25 NUM american_scientific_journal-3571 196 18 ) ) PUNCT american_scientific_journal-3571 196 19 cm cm NOUN american_scientific_journal-3571 196 20 . . PUNCT american_scientific_journal-3571 197 1 3 3 X american_scientific_journal-3571 197 2 . . X american_scientific_journal-3571 197 3 in in ADP american_scientific_journal-3571 197 4 fig.(14 fig.(14 PROPN american_scientific_journal-3571 197 5 ): ): PUNCT american_scientific_journal-3571 197 6 the the DET american_scientific_journal-3571 197 7 best good ADJ american_scientific_journal-3571 197 8 cost cost NOUN american_scientific_journal-3571 197 9 of of ADP american_scientific_journal-3571 197 10 the the DET american_scientific_journal-3571 197 11 stability stability NOUN american_scientific_journal-3571 197 12 margin margin NOUN american_scientific_journal-3571 197 13 𝑆𝑆𝑠𝑠3 𝑆𝑆𝑠𝑠3 ADJ american_scientific_journal-3571 197 14 equals equal VERB american_scientific_journal-3571 197 15 to to ADP american_scientific_journal-3571 197 16 ( ( PUNCT american_scientific_journal-3571 197 17 2.173 2.173 NUM american_scientific_journal-3571 197 18 ) ) PUNCT american_scientific_journal-3571 197 19 cm cm NOUN american_scientific_journal-3571 197 20 . . PUNCT american_scientific_journal-3571 198 1 4 4 NUM american_scientific_journal-3571 198 2 . . X american_scientific_journal-3571 198 3 in in ADP american_scientific_journal-3571 198 4 fig.(15 fig.(15 PROPN american_scientific_journal-3571 198 5 ): ): PUNCT american_scientific_journal-3571 198 6 the the DET american_scientific_journal-3571 198 7 best good ADJ american_scientific_journal-3571 198 8 cost cost NOUN american_scientific_journal-3571 198 9 of of ADP american_scientific_journal-3571 198 10 the the DET american_scientific_journal-3571 198 11 stability stability NOUN american_scientific_journal-3571 198 12 margin margin NOUN american_scientific_journal-3571 198 13 𝑆𝑆𝑠𝑠4equals 𝑆𝑆𝑠𝑠4equal NOUN american_scientific_journal-3571 198 14 to to ADP american_scientific_journal-3571 198 15 ( ( PUNCT american_scientific_journal-3571 198 16 2.309 2.309 NUM american_scientific_journal-3571 198 17 ) ) PUNCT american_scientific_journal-3571 198 18 cm cm NOUN american_scientific_journal-3571 198 19 . . PUNCT american_scientific_journal-3571 199 1 during during ADP american_scientific_journal-3571 199 2 the the DET american_scientific_journal-3571 199 3 creeping creeping ADJ american_scientific_journal-3571 199 4 gait gait NOUN american_scientific_journal-3571 199 5 sequence sequence NOUN american_scientific_journal-3571 199 6 , , PUNCT american_scientific_journal-3571 199 7 the the DET american_scientific_journal-3571 199 8 quadruped quadruped NOUN american_scientific_journal-3571 199 9 robot robot NOUN american_scientific_journal-3571 199 10 leg leg NOUN american_scientific_journal-3571 199 11 angles angle NOUN american_scientific_journal-3571 199 12 are be AUX american_scientific_journal-3571 199 13 changing change VERB american_scientific_journal-3571 199 14 . . PUNCT american_scientific_journal-3571 200 1 these these DET american_scientific_journal-3571 200 2 angles angle NOUN american_scientific_journal-3571 200 3 are be AUX american_scientific_journal-3571 200 4 ( ( PUNCT american_scientific_journal-3571 200 5 πœƒπœƒ1,πœƒπœƒ2andπœƒπœƒ3 πœƒπœƒ1,πœƒπœƒ2andπœƒπœƒ3 NOUN american_scientific_journal-3571 200 6 ) ) PUNCT american_scientific_journal-3571 200 7 of of ADP american_scientific_journal-3571 200 8 each each DET american_scientific_journal-3571 200 9 leg leg NOUN american_scientific_journal-3571 200 10 . . PUNCT american_scientific_journal-3571 201 1 this this DET american_scientific_journal-3571 201 2 changing change VERB american_scientific_journal-3571 201 3 is be AUX american_scientific_journal-3571 201 4 showing show VERB american_scientific_journal-3571 201 5 in in ADP american_scientific_journal-3571 201 6 fig.(19 fig.(19 PROPN american_scientific_journal-3571 201 7 ): ): PUNCT american_scientific_journal-3571 201 8 figure figure NOUN american_scientific_journal-3571 201 9 16 16 NUM american_scientific_journal-3571 201 10 : : PUNCT american_scientific_journal-3571 201 11 changing change VERB american_scientific_journal-3571 201 12 of of ADP american_scientific_journal-3571 201 13 coxa coxa NOUN american_scientific_journal-3571 201 14 - - PUNCT american_scientific_journal-3571 201 15 angle angle NOUN american_scientific_journal-3571 201 16 in in ADP american_scientific_journal-3571 201 17 one one NUM american_scientific_journal-3571 201 18 step step NOUN american_scientific_journal-3571 201 19 movement movement NOUN american_scientific_journal-3571 201 20 figure figure NOUN american_scientific_journal-3571 201 21 17 17 NUM american_scientific_journal-3571 201 22 : : PUNCT american_scientific_journal-3571 201 23 changing change VERB american_scientific_journal-3571 201 24 of of ADP american_scientific_journal-3571 201 25 femur femur NOUN american_scientific_journal-3571 201 26 - - PUNCT american_scientific_journal-3571 201 27 angle angle NOUN american_scientific_journal-3571 201 28 in in ADP american_scientific_journal-3571 201 29 one one NUM american_scientific_journal-3571 201 30 step step NOUN american_scientific_journal-3571 201 31 movement movement NOUN american_scientific_journal-3571 201 32 figure figure NOUN american_scientific_journal-3571 201 33 18 18 NUM american_scientific_journal-3571 201 34 : : PUNCT american_scientific_journal-3571 201 35 changing change VERB american_scientific_journal-3571 201 36 of of ADP american_scientific_journal-3571 201 37 tibia tibia NOUN american_scientific_journal-3571 201 38 - - PUNCT american_scientific_journal-3571 201 39 angle angle NOUN american_scientific_journal-3571 201 40 in in ADP american_scientific_journal-3571 201 41 one one NUM american_scientific_journal-3571 201 42 step step NOUN american_scientific_journal-3571 201 43 movement movement NOUN american_scientific_journal-3571 201 44 from from ADP american_scientific_journal-3571 201 45 above above ADJ american_scientific_journal-3571 201 46 figures figure NOUN american_scientific_journal-3571 201 47 it it PRON american_scientific_journal-3571 201 48 can can AUX american_scientific_journal-3571 201 49 be be AUX american_scientific_journal-3571 201 50 seen see VERB american_scientific_journal-3571 201 51 that that SCONJ american_scientific_journal-3571 201 52 : : PUNCT american_scientific_journal-3571 202 1 1 1 X american_scientific_journal-3571 202 2 . . X american_scientific_journal-3571 202 3 fig.(16 fig.(16 NOUN american_scientific_journal-3571 202 4 ) ) PUNCT american_scientific_journal-3571 202 5 is be AUX american_scientific_journal-3571 202 6 the the DET american_scientific_journal-3571 202 7 changing changing NOUN american_scientific_journal-3571 202 8 of of ADP american_scientific_journal-3571 202 9 coxa coxa NOUN american_scientific_journal-3571 202 10 - - PUNCT american_scientific_journal-3571 202 11 angleπœƒπœƒ1 angleπœƒπœƒ1 PROPN american_scientific_journal-3571 202 12 . . PUNCT american_scientific_journal-3571 203 1 this this DET american_scientific_journal-3571 203 2 angle angle NOUN american_scientific_journal-3571 203 3 is be AUX american_scientific_journal-3571 203 4 varying vary VERB american_scientific_journal-3571 203 5 between between ADP american_scientific_journal-3571 203 6 ( ( PUNCT american_scientific_journal-3571 203 7 90 90 NUM american_scientific_journal-3571 203 8 degree degree NOUN american_scientific_journal-3571 203 9 ) ) PUNCT american_scientific_journal-3571 203 10 to to ADP american_scientific_journal-3571 203 11 ( ( PUNCT american_scientific_journal-3571 203 12 76 76 NUM american_scientific_journal-3571 203 13 degree degree NOUN american_scientific_journal-3571 203 14 ) ) PUNCT american_scientific_journal-3571 203 15 . . PUNCT american_scientific_journal-3571 204 1 2 2 X american_scientific_journal-3571 204 2 . . X american_scientific_journal-3571 204 3 fig.(17 fig.(17 PROPN american_scientific_journal-3571 204 4 ) ) PUNCT american_scientific_journal-3571 204 5 is be AUX american_scientific_journal-3571 204 6 the the DET american_scientific_journal-3571 204 7 changing changing NOUN american_scientific_journal-3571 204 8 of of ADP american_scientific_journal-3571 204 9 femur femur NOUN american_scientific_journal-3571 204 10 - - PUNCT american_scientific_journal-3571 204 11 angle angle NOUN american_scientific_journal-3571 204 12 πœƒπœƒ2 πœƒπœƒ2 NOUN american_scientific_journal-3571 204 13 . . PUNCT american_scientific_journal-3571 205 1 this this DET american_scientific_journal-3571 205 2 angle angle NOUN american_scientific_journal-3571 205 3 is be AUX american_scientific_journal-3571 205 4 varying vary VERB american_scientific_journal-3571 205 5 between between ADP american_scientific_journal-3571 205 6 ( ( PUNCT american_scientific_journal-3571 205 7 23 23 NUM american_scientific_journal-3571 205 8 degree degree NOUN american_scientific_journal-3571 205 9 ) ) PUNCT american_scientific_journal-3571 205 10 to to ADP american_scientific_journal-3571 205 11 ( ( PUNCT american_scientific_journal-3571 205 12 60 60 NUM american_scientific_journal-3571 205 13 degree degree NOUN american_scientific_journal-3571 205 14 ) ) PUNCT american_scientific_journal-3571 205 15 . . PUNCT american_scientific_journal-3571 206 1 3 3 X american_scientific_journal-3571 206 2 . . X american_scientific_journal-3571 207 1 fig.(18 fig.(18 NOUN american_scientific_journal-3571 207 2 ) ) PUNCT american_scientific_journal-3571 207 3 is be AUX american_scientific_journal-3571 207 4 the the DET american_scientific_journal-3571 207 5 changing changing NOUN american_scientific_journal-3571 207 6 of of ADP american_scientific_journal-3571 207 7 tibia tibia NOUN american_scientific_journal-3571 207 8 - - PUNCT american_scientific_journal-3571 207 9 angle angle NOUN american_scientific_journal-3571 207 10 πœƒπœƒ3 πœƒπœƒ3 NOUN american_scientific_journal-3571 207 11 . . PUNCT american_scientific_journal-3571 208 1 this this DET american_scientific_journal-3571 208 2 angle angle NOUN american_scientific_journal-3571 208 3 is be AUX american_scientific_journal-3571 208 4 varying vary VERB american_scientific_journal-3571 208 5 between between ADP american_scientific_journal-3571 208 6 ( ( PUNCT american_scientific_journal-3571 208 7 30 30 NUM american_scientific_journal-3571 208 8 degree degree NOUN american_scientific_journal-3571 208 9 ) ) PUNCT american_scientific_journal-3571 208 10 to to ADP american_scientific_journal-3571 208 11 ( ( PUNCT american_scientific_journal-3571 208 12 49 49 NUM american_scientific_journal-3571 208 13 degree degree NOUN american_scientific_journal-3571 208 14 ) ) PUNCT american_scientific_journal-3571 208 15 . . PUNCT american_scientific_journal-3571 209 1 2 2 NUM american_scientific_journal-3571 209 2 4 4 NUM american_scientific_journal-3571 209 3 6 6 NUM american_scientific_journal-3571 209 4 8 8 NUM american_scientific_journal-3571 209 5 10 10 NUM american_scientific_journal-3571 209 6 12 12 NUM american_scientific_journal-3571 209 7 75 75 NUM american_scientific_journal-3571 209 8 80 80 NUM american_scientific_journal-3571 209 9 85 85 NUM american_scientific_journal-3571 209 10 90 90 NUM american_scientific_journal-3571 209 11 iteration iteration NOUN american_scientific_journal-3571 209 12 th th X american_scientific_journal-3571 209 13 et et NOUN american_scientific_journal-3571 209 14 a1 a1 NOUN american_scientific_journal-3571 209 15 ( ( PUNCT american_scientific_journal-3571 209 16 d d NOUN american_scientific_journal-3571 209 17 eg eg X american_scientific_journal-3571 209 18 re re NOUN american_scientific_journal-3571 209 19 e e NOUN american_scientific_journal-3571 209 20 ) ) PUNCT american_scientific_journal-3571 209 21 l1,1 l1,1 PROPN american_scientific_journal-3571 209 22 2 2 NUM american_scientific_journal-3571 209 23 4 4 NUM american_scientific_journal-3571 209 24 6 6 NUM american_scientific_journal-3571 209 25 8 8 NUM american_scientific_journal-3571 209 26 10 10 NUM american_scientific_journal-3571 209 27 12 12 NUM american_scientific_journal-3571 209 28 20 20 NUM american_scientific_journal-3571 209 29 30 30 NUM american_scientific_journal-3571 209 30 40 40 NUM american_scientific_journal-3571 209 31 50 50 NUM american_scientific_journal-3571 209 32 60 60 NUM american_scientific_journal-3571 209 33 70 70 NUM american_scientific_journal-3571 209 34 iteration iteration NOUN american_scientific_journal-3571 209 35 t t NOUN american_scientific_journal-3571 210 1 he he PRON american_scientific_journal-3571 210 2 ta ta PROPN american_scientific_journal-3571 210 3 2 2 NUM american_scientific_journal-3571 210 4 ( ( PUNCT american_scientific_journal-3571 210 5 de de X american_scientific_journal-3571 210 6 gr gr X american_scientific_journal-3571 210 7 ee ee PROPN american_scientific_journal-3571 210 8 ) ) PUNCT american_scientific_journal-3571 211 1 l1,2 l1,2 ADJ american_scientific_journal-3571 211 2 2 2 NUM american_scientific_journal-3571 211 3 4 4 NUM american_scientific_journal-3571 211 4 6 6 NUM american_scientific_journal-3571 211 5 8 8 NUM american_scientific_journal-3571 211 6 10 10 NUM american_scientific_journal-3571 211 7 12 12 NUM american_scientific_journal-3571 211 8 30 30 NUM american_scientific_journal-3571 211 9 35 35 NUM american_scientific_journal-3571 211 10 40 40 NUM american_scientific_journal-3571 211 11 45 45 NUM american_scientific_journal-3571 211 12 50 50 NUM american_scientific_journal-3571 211 13 iteration iteration NOUN american_scientific_journal-3571 211 14 th th X american_scientific_journal-3571 211 15 et et NOUN american_scientific_journal-3571 211 16 a3 a3 NOUN american_scientific_journal-3571 211 17 ( ( PUNCT american_scientific_journal-3571 211 18 d d X american_scientific_journal-3571 211 19 eg eg X american_scientific_journal-3571 211 20 re re NOUN american_scientific_journal-3571 211 21 e e NOUN american_scientific_journal-3571 211 22 ) ) PUNCT american_scientific_journal-3571 211 23 l1,3 l1,3 ADJ american_scientific_journal-3571 211 24 american american ADJ american_scientific_journal-3571 211 25 scientific scientific ADJ american_scientific_journal-3571 211 26 research research NOUN american_scientific_journal-3571 211 27 journal journal NOUN american_scientific_journal-3571 211 28 for for ADP american_scientific_journal-3571 211 29 engineering engineering NOUN american_scientific_journal-3571 211 30 , , PUNCT american_scientific_journal-3571 211 31 technology technology NOUN american_scientific_journal-3571 211 32 , , PUNCT american_scientific_journal-3571 211 33 and and CCONJ american_scientific_journal-3571 211 34 sciences science NOUN american_scientific_journal-3571 211 35 ( ( PUNCT american_scientific_journal-3571 211 36 asrjets asrjet NOUN american_scientific_journal-3571 211 37 ) ) PUNCT american_scientific_journal-3571 211 38 ( ( PUNCT american_scientific_journal-3571 211 39 2017 2017 NUM american_scientific_journal-3571 211 40 ) ) PUNCT american_scientific_journal-3571 211 41 volume volume NOUN american_scientific_journal-3571 211 42 37 37 NUM american_scientific_journal-3571 211 43 , , PUNCT american_scientific_journal-3571 211 44 no no DET american_scientific_journal-3571 211 45 1 1 NUM american_scientific_journal-3571 211 46 , , PUNCT american_scientific_journal-3571 211 47 pp pp ADV american_scientific_journal-3571 211 48 17 17 NUM american_scientific_journal-3571 211 49 - - SYM american_scientific_journal-3571 211 50 32 32 NUM american_scientific_journal-3571 211 51 31 31 NUM american_scientific_journal-3571 211 52 8 8 NUM american_scientific_journal-3571 211 53 . . PUNCT american_scientific_journal-3571 212 1 conclusion conclusion NOUN american_scientific_journal-3571 212 2 illuminating illuminate VERB american_scientific_journal-3571 212 3 the the DET american_scientific_journal-3571 212 4 basic basic ADJ american_scientific_journal-3571 212 5 points point NOUN american_scientific_journal-3571 212 6 of of ADP american_scientific_journal-3571 212 7 this this DET american_scientific_journal-3571 212 8 paper paper NOUN american_scientific_journal-3571 212 9 , , PUNCT american_scientific_journal-3571 212 10 analyze analyze NOUN american_scientific_journal-3571 212 11 of of ADP american_scientific_journal-3571 212 12 the the DET american_scientific_journal-3571 212 13 quadruped quadruped NOUN american_scientific_journal-3571 212 14 robot robot NOUN american_scientific_journal-3571 212 15 walking walking NOUN american_scientific_journal-3571 212 16 of of ADP american_scientific_journal-3571 212 17 creeping creep VERB american_scientific_journal-3571 212 18 gait gait NOUN american_scientific_journal-3571 212 19 and and CCONJ american_scientific_journal-3571 212 20 the the DET american_scientific_journal-3571 212 21 derivation derivation NOUN american_scientific_journal-3571 212 22 , , PUNCT american_scientific_journal-3571 212 23 emphasize emphasize VERB american_scientific_journal-3571 212 24 and and CCONJ american_scientific_journal-3571 212 25 showed show VERB american_scientific_journal-3571 212 26 that that SCONJ american_scientific_journal-3571 212 27 the the DET american_scientific_journal-3571 212 28 quadruped quadruped NOUN american_scientific_journal-3571 212 29 robot robot NOUN american_scientific_journal-3571 212 30 is be AUX american_scientific_journal-3571 212 31 statically statically ADV american_scientific_journal-3571 212 32 stable stable ADJ american_scientific_journal-3571 212 33 throughout throughout ADP american_scientific_journal-3571 212 34 walking walk VERB american_scientific_journal-3571 212 35 . . PUNCT american_scientific_journal-3571 213 1 to to PART american_scientific_journal-3571 213 2 access access VERB american_scientific_journal-3571 213 3 the the DET american_scientific_journal-3571 213 4 objective objective NOUN american_scientific_journal-3571 213 5 of of ADP american_scientific_journal-3571 213 6 the the DET american_scientific_journal-3571 213 7 work work NOUN american_scientific_journal-3571 213 8 , , PUNCT american_scientific_journal-3571 213 9 firstly firstly ADV american_scientific_journal-3571 213 10 , , PUNCT american_scientific_journal-3571 213 11 the the DET american_scientific_journal-3571 213 12 whole whole ADJ american_scientific_journal-3571 213 13 forward forward ADV american_scientific_journal-3571 213 14 and and CCONJ american_scientific_journal-3571 213 15 inverse inverse NOUN american_scientific_journal-3571 213 16 kinematics kinematic NOUN american_scientific_journal-3571 213 17 model model NOUN american_scientific_journal-3571 213 18 have have AUX american_scientific_journal-3571 213 19 been be AUX american_scientific_journal-3571 213 20 derived derive VERB american_scientific_journal-3571 213 21 and and CCONJ american_scientific_journal-3571 213 22 utilized utilize VERB american_scientific_journal-3571 213 23 for for ADP american_scientific_journal-3571 213 24 stability stability NOUN american_scientific_journal-3571 213 25 validation validation NOUN american_scientific_journal-3571 213 26 of of ADP american_scientific_journal-3571 213 27 walking walk VERB american_scientific_journal-3571 213 28 steps step NOUN american_scientific_journal-3571 213 29 . . PUNCT american_scientific_journal-3571 214 1 so so ADV american_scientific_journal-3571 214 2 the the DET american_scientific_journal-3571 214 3 intersection intersection NOUN american_scientific_journal-3571 214 4 between between ADP american_scientific_journal-3571 214 5 sequence sequence NOUN american_scientific_journal-3571 214 6 of of ADP american_scientific_journal-3571 214 7 robot robot NOUN american_scientific_journal-3571 214 8 creeping creep VERB american_scientific_journal-3571 214 9 gait gait NOUN american_scientific_journal-3571 214 10 and and CCONJ american_scientific_journal-3571 214 11 the the DET american_scientific_journal-3571 214 12 geometric geometric ADJ american_scientific_journal-3571 214 13 modeling modeling NOUN american_scientific_journal-3571 214 14 of of ADP american_scientific_journal-3571 214 15 robot robot NOUN american_scientific_journal-3571 214 16 legs leg NOUN american_scientific_journal-3571 214 17 - - PUNCT american_scientific_journal-3571 214 18 tip tip NOUN american_scientific_journal-3571 214 19 which which PRON american_scientific_journal-3571 214 20 are be AUX american_scientific_journal-3571 214 21 derived derive VERB american_scientific_journal-3571 214 22 to to PART american_scientific_journal-3571 214 23 find find VERB american_scientific_journal-3571 214 24 the the DET american_scientific_journal-3571 214 25 entire entire ADJ american_scientific_journal-3571 214 26 static static ADJ american_scientific_journal-3571 214 27 stability stability NOUN american_scientific_journal-3571 214 28 margins margin NOUN american_scientific_journal-3571 214 29 during during ADP american_scientific_journal-3571 214 30 walking walk VERB american_scientific_journal-3571 214 31 . . PUNCT american_scientific_journal-3571 215 1 the the DET american_scientific_journal-3571 215 2 results result NOUN american_scientific_journal-3571 215 3 certainly certainly ADV american_scientific_journal-3571 215 4 proved prove VERB american_scientific_journal-3571 215 5 the the DET american_scientific_journal-3571 215 6 best good ADJ american_scientific_journal-3571 215 7 of of ADP american_scientific_journal-3571 215 8 stability stability NOUN american_scientific_journal-3571 215 9 margins margin NOUN american_scientific_journal-3571 215 10 that that PRON american_scientific_journal-3571 215 11 own own VERB american_scientific_journal-3571 215 12 the the DET american_scientific_journal-3571 215 13 minimum minimum ADJ american_scientific_journal-3571 215 14 values value NOUN american_scientific_journal-3571 215 15 with with ADP american_scientific_journal-3571 215 16 utilizing utilize VERB american_scientific_journal-3571 215 17 pso pso NOUN american_scientific_journal-3571 215 18 algorithm algorithm NOUN american_scientific_journal-3571 215 19 to to PART american_scientific_journal-3571 215 20 guarantee guarantee VERB american_scientific_journal-3571 215 21 the the DET american_scientific_journal-3571 215 22 robot robot NOUN american_scientific_journal-3571 215 23 cog cog PROPN american_scientific_journal-3571 215 24 preservation preservation NOUN american_scientific_journal-3571 215 25 into into ADP american_scientific_journal-3571 215 26 the the DET american_scientific_journal-3571 215 27 supporting support VERB american_scientific_journal-3571 215 28 triangle triangle NOUN american_scientific_journal-3571 215 29 via via ADP american_scientific_journal-3571 215 30 the the DET american_scientific_journal-3571 215 31 swing swing NOUN american_scientific_journal-3571 215 32 phase phase NOUN american_scientific_journal-3571 215 33 for for ADP american_scientific_journal-3571 215 34 one one NUM american_scientific_journal-3571 215 35 leg leg NOUN american_scientific_journal-3571 215 36 with with ADP american_scientific_journal-3571 215 37 the the DET american_scientific_journal-3571 215 38 rest rest NOUN american_scientific_journal-3571 215 39 legs leg NOUN american_scientific_journal-3571 215 40 that that PRON american_scientific_journal-3571 215 41 on on ADP american_scientific_journal-3571 215 42 the the DET american_scientific_journal-3571 215 43 ground ground NOUN american_scientific_journal-3571 215 44 . . PUNCT american_scientific_journal-3571 216 1 furthermore furthermore ADV american_scientific_journal-3571 216 2 , , PUNCT american_scientific_journal-3571 216 3 an an DET american_scientific_journal-3571 216 4 improvement improvement NOUN american_scientific_journal-3571 216 5 for for ADP american_scientific_journal-3571 216 6 future future ADJ american_scientific_journal-3571 216 7 work work NOUN american_scientific_journal-3571 216 8 , , PUNCT american_scientific_journal-3571 216 9 it it PRON american_scientific_journal-3571 216 10 ’s ’ VERB american_scientific_journal-3571 216 11 necessary necessary ADJ american_scientific_journal-3571 216 12 to to PART american_scientific_journal-3571 216 13 analyze analyze VERB american_scientific_journal-3571 216 14 and and CCONJ american_scientific_journal-3571 216 15 enhance enhance VERB american_scientific_journal-3571 216 16 the the DET american_scientific_journal-3571 216 17 quadruped quadruped NOUN american_scientific_journal-3571 216 18 robot robot NOUN american_scientific_journal-3571 216 19 walking walk VERB american_scientific_journal-3571 216 20 on on ADP american_scientific_journal-3571 216 21 hard hard ADJ american_scientific_journal-3571 216 22 and and CCONJ american_scientific_journal-3571 216 23 rough rough ADJ american_scientific_journal-3571 216 24 terrain terrain NOUN american_scientific_journal-3571 216 25 . . PUNCT american_scientific_journal-3571 217 1 references reference NOUN american_scientific_journal-3571 217 2 [ [ X american_scientific_journal-3571 217 3 1 1 NUM american_scientific_journal-3571 217 4 ] ] X american_scientific_journal-3571 217 5 kumar kumar PROPN american_scientific_journal-3571 217 6 , , PUNCT american_scientific_journal-3571 217 7 t. t. PROPN american_scientific_journal-3571 217 8 komal komal PROPN american_scientific_journal-3571 217 9 , , PUNCT american_scientific_journal-3571 217 10 r. r. PROPN american_scientific_journal-3571 217 11 kumar kumar PROPN american_scientific_journal-3571 217 12 , , PUNCT american_scientific_journal-3571 217 13 s. s. PROPN american_scientific_journal-3571 217 14 mogily mogily PROPN american_scientific_journal-3571 217 15 , , PUNCT american_scientific_journal-3571 217 16 d. d. PROPN american_scientific_journal-3571 217 17 goel goel PROPN american_scientific_journal-3571 217 18 , , PUNCT american_scientific_journal-3571 217 19 n. n. PROPN american_scientific_journal-3571 217 20 pareekutty pareekutty PROPN american_scientific_journal-3571 217 21 , , PUNCT american_scientific_journal-3571 217 22 s. s. PROPN american_scientific_journal-3571 217 23 v. v. PROPN american_scientific_journal-3571 217 24 shah shah PROPN american_scientific_journal-3571 217 25 , , PUNCT american_scientific_journal-3571 217 26 and and CCONJ american_scientific_journal-3571 217 27 k. k. PROPN american_scientific_journal-3571 217 28 madhava madhava PROPN american_scientific_journal-3571 217 29 krishna krishna PROPN american_scientific_journal-3571 217 30 . . PUNCT american_scientific_journal-3571 218 1 " " PUNCT american_scientific_journal-3571 218 2 implementation implementation NOUN american_scientific_journal-3571 218 3 of of ADP american_scientific_journal-3571 218 4 gaits gait NOUN american_scientific_journal-3571 218 5 for for ADP american_scientific_journal-3571 218 6 achieving achieve VERB american_scientific_journal-3571 218 7 omnidirectional omnidirectional ADJ american_scientific_journal-3571 218 8 walking walking NOUN american_scientific_journal-3571 218 9 in in ADP american_scientific_journal-3571 218 10 a a DET american_scientific_journal-3571 218 11 quadruped quadruped NOUN american_scientific_journal-3571 218 12 robot robot NOUN american_scientific_journal-3571 218 13 . . PUNCT american_scientific_journal-3571 219 1 "proceedings "proceeding NOUN american_scientific_journal-3571 219 2 of of ADP american_scientific_journal-3571 219 3 the the DET american_scientific_journal-3571 219 4 2015 2015 NUM american_scientific_journal-3571 219 5 conference conference NOUN american_scientific_journal-3571 219 6 on on ADP american_scientific_journal-3571 219 7 advances advance NOUN american_scientific_journal-3571 219 8 in in ADP american_scientific_journal-3571 219 9 robotics robotic NOUN american_scientific_journal-3571 219 10 air air NOUN american_scientific_journal-3571 219 11 ' ' PUNCT american_scientific_journal-3571 219 12 15(2015 15(2015 NUM american_scientific_journal-3571 219 13 ) ) PUNCT american_scientific_journal-3571 219 14 . . PUNCT american_scientific_journal-3571 220 1 [ [ X american_scientific_journal-3571 220 2 2 2 NUM american_scientific_journal-3571 220 3 ] ] PUNCT american_scientific_journal-3571 220 4 rebula rebula NOUN american_scientific_journal-3571 220 5 , , PUNCT american_scientific_journal-3571 220 6 j. j. PROPN american_scientific_journal-3571 220 7 r. r. PROPN american_scientific_journal-3571 220 8 , , PUNCT american_scientific_journal-3571 220 9 neuhaus neuhaus PROPN american_scientific_journal-3571 220 10 , , PUNCT american_scientific_journal-3571 220 11 p. p. PROPN american_scientific_journal-3571 220 12 d. d. PROPN american_scientific_journal-3571 220 13 , , PUNCT american_scientific_journal-3571 220 14 bonnlander bonnlander PROPN american_scientific_journal-3571 220 15 , , PUNCT american_scientific_journal-3571 220 16 b. b. PROPN american_scientific_journal-3571 220 17 v,.johnson v,.johnson PROPN american_scientific_journal-3571 220 18 , , PUNCT american_scientific_journal-3571 220 19 m. m. NOUN american_scientific_journal-3571 220 20 j. j. PROPN american_scientific_journal-3571 220 21 , , PUNCT american_scientific_journal-3571 220 22 pratt pratt PROPN american_scientific_journal-3571 220 23 , , PUNCT american_scientific_journal-3571 220 24 j. j. PROPN american_scientific_journal-3571 220 25 e. e. PROPN american_scientific_journal-3571 220 26 ( ( PUNCT american_scientific_journal-3571 220 27 2007 2007 NUM american_scientific_journal-3571 220 28 ) ) PUNCT american_scientific_journal-3571 220 29 . . PUNCT american_scientific_journal-3571 221 1 β€œ " PUNCT american_scientific_journal-3571 221 2 a a DET american_scientific_journal-3571 221 3 controller controller NOUN american_scientific_journal-3571 221 4 forthelittledog forthelittledog NOUN american_scientific_journal-3571 221 5 quadruped quadruped NOUN american_scientific_journal-3571 221 6 walking walk VERB american_scientific_journal-3571 221 7 on on ADP american_scientific_journal-3571 221 8 rough rough ADJ american_scientific_journal-3571 221 9 terrain”.icra terrain”.icra ADP american_scientific_journal-3571 221 10 , , PUNCT american_scientific_journal-3571 221 11 1467 1467 NUM american_scientific_journal-3571 221 12 - - SYM american_scientific_journal-3571 221 13 1473 1473 NUM american_scientific_journal-3571 221 14 . . PUNCT american_scientific_journal-3571 222 1 [ [ X american_scientific_journal-3571 222 2 3 3 NUM american_scientific_journal-3571 222 3 ] ] X american_scientific_journal-3571 222 4 raibert raibert NOUN american_scientific_journal-3571 222 5 , , PUNCT american_scientific_journal-3571 222 6 m. m. NOUN american_scientific_journal-3571 222 7 , , PUNCT american_scientific_journal-3571 222 8 blankespoor blankespoor NOUN american_scientific_journal-3571 222 9 , , PUNCT american_scientific_journal-3571 222 10 k. k. PROPN american_scientific_journal-3571 222 11 , , PUNCT american_scientific_journal-3571 222 12 nelson nelson PROPN american_scientific_journal-3571 222 13 , , PUNCT american_scientific_journal-3571 222 14 g. g. PROPN american_scientific_journal-3571 222 15 , , PUNCT american_scientific_journal-3571 222 16 playter playter NOUN american_scientific_journal-3571 222 17 , , PUNCT american_scientific_journal-3571 222 18 r.(2008 r.(2008 NOUN american_scientific_journal-3571 222 19 ) ) PUNCT american_scientific_journal-3571 222 20 . . PUNCT american_scientific_journal-3571 223 1 bigdog bigdog PROPN american_scientific_journal-3571 223 2 , , PUNCT american_scientific_journal-3571 223 3 the the DET american_scientific_journal-3571 223 4 rough rough ADJ american_scientific_journal-3571 223 5 - - PUNCT american_scientific_journal-3571 223 6 terrain terrain NOUN american_scientific_journal-3571 223 7 quadruped quadruped NOUN american_scientific_journal-3571 223 8 robot robot NOUN american_scientific_journal-3571 223 9 . . PUNCT american_scientific_journal-3571 224 1 inproc inproc PROPN american_scientific_journal-3571 224 2 , , PUNCT american_scientific_journal-3571 224 3 of of ADP american_scientific_journal-3571 224 4 the the DET american_scientific_journal-3571 224 5 17th 17th ADJ american_scientific_journal-3571 224 6 world world PROPN american_scientific_journal-3571 224 7 congress congress PROPN american_scientific_journal-3571 224 8 , , PUNCT american_scientific_journal-3571 224 9 17(1 17(1 NUM american_scientific_journal-3571 224 10 ) ) PUNCT american_scientific_journal-3571 224 11 , , PUNCT american_scientific_journal-3571 224 12 10822 10822 NUM american_scientific_journal-3571 224 13 - - SYM american_scientific_journal-3571 224 14 10825 10825 NUM american_scientific_journal-3571 224 15 . . PUNCT american_scientific_journal-3571 225 1 [ [ X american_scientific_journal-3571 225 2 4 4 NUM american_scientific_journal-3571 225 3 ] ] X american_scientific_journal-3571 225 4 shimoyama shimoyama NOUN american_scientific_journal-3571 225 5 , , PUNCT american_scientific_journal-3571 225 6 i. i. PROPN american_scientific_journal-3571 225 7 , , PUNCT american_scientific_journal-3571 225 8 miura miura PROPN american_scientific_journal-3571 225 9 , , PUNCT american_scientific_journal-3571 225 10 h. h. PROPN american_scientific_journal-3571 225 11 , , PUNCT american_scientific_journal-3571 225 12 horita horita PROPN american_scientific_journal-3571 225 13 , , PUNCT american_scientific_journal-3571 225 14 m. m. NOUN american_scientific_journal-3571 225 15 , , PUNCT american_scientific_journal-3571 225 16 hattori hattori PROPN american_scientific_journal-3571 225 17 , , PUNCT american_scientific_journal-3571 225 18 y.(1991 y.(1991 PROPN american_scientific_journal-3571 225 19 ) ) PUNCT american_scientific_journal-3571 225 20 . . PUNCT american_scientific_journal-3571 226 1 analysis analysis NOUN american_scientific_journal-3571 226 2 of of ADP american_scientific_journal-3571 226 3 walk walk NOUN american_scientific_journal-3571 226 4 for for ADP american_scientific_journal-3571 226 5 quadruped quadruped NOUN american_scientific_journal-3571 226 6 . . PUNCT american_scientific_journal-3571 227 1 iros,15411544 iros,15411544 NOUN american_scientific_journal-3571 227 2 . . PUNCT american_scientific_journal-3571 228 1 [ [ X american_scientific_journal-3571 228 2 5 5 NUM american_scientific_journal-3571 228 3 ] ] PUNCT american_scientific_journal-3571 228 4 fukuoka fukuoka NOUN american_scientific_journal-3571 228 5 , , PUNCT american_scientific_journal-3571 228 6 y. y. NOUN american_scientific_journal-3571 228 7 , , PUNCT american_scientific_journal-3571 228 8 kimura kimura NOUN american_scientific_journal-3571 228 9 , , PUNCT american_scientific_journal-3571 228 10 h. h. PROPN american_scientific_journal-3571 228 11 , , PUNCT american_scientific_journal-3571 228 12 cohen cohen PROPN american_scientific_journal-3571 228 13 , , PUNCT american_scientific_journal-3571 228 14 a. a. PROPN american_scientific_journal-3571 228 15 h. h. PROPN american_scientific_journal-3571 229 1 ( ( PUNCT american_scientific_journal-3571 229 2 2003).adaptive 2003).adaptive NUM american_scientific_journal-3571 229 3 dynamic dynamic ADJ american_scientific_journal-3571 229 4 walking walking NOUN american_scientific_journal-3571 229 5 of of ADP american_scientific_journal-3571 229 6 a a DET american_scientific_journal-3571 229 7 quadruped quadruped NOUN american_scientific_journal-3571 229 8 robot robot NOUN american_scientific_journal-3571 229 9 onirregular onirregular ADJ american_scientific_journal-3571 229 10 terrain terrain NOUN american_scientific_journal-3571 229 11 based base VERB american_scientific_journal-3571 229 12 on on ADP american_scientific_journal-3571 229 13 biological biological ADJ american_scientific_journal-3571 229 14 concepts concept NOUN american_scientific_journal-3571 229 15 . . PUNCT american_scientific_journal-3571 230 1 the the DET american_scientific_journal-3571 230 2 int.j int.j PROPN american_scientific_journal-3571 230 3 . . PROPN american_scientific_journal-3571 230 4 of of ADP american_scientific_journal-3571 230 5 robotics robotic NOUN american_scientific_journal-3571 230 6 research research NOUN american_scientific_journal-3571 230 7 , , PUNCT american_scientific_journal-3571 230 8 22(3 22(3 NUM american_scientific_journal-3571 230 9 - - SYM american_scientific_journal-3571 230 10 4 4 NUM american_scientific_journal-3571 230 11 ) ) PUNCT american_scientific_journal-3571 230 12 , , PUNCT american_scientific_journal-3571 230 13 187 187 NUM american_scientific_journal-3571 230 14 - - SYM american_scientific_journal-3571 230 15 202 202 NUM american_scientific_journal-3571 230 16 . . PUNCT american_scientific_journal-3571 231 1 [ [ X american_scientific_journal-3571 231 2 6 6 NUM american_scientific_journal-3571 231 3 ] ] SYM american_scientific_journal-3571 231 4 ma ma PROPN american_scientific_journal-3571 231 5 , , PUNCT american_scientific_journal-3571 231 6 s. s. PROPN american_scientific_journal-3571 231 7 , , PUNCT american_scientific_journal-3571 231 8 tomiyama tomiyama PROPN american_scientific_journal-3571 231 9 , , PUNCT american_scientific_journal-3571 231 10 t. t. PROPN american_scientific_journal-3571 231 11 , , PUNCT american_scientific_journal-3571 231 12 wada wada PROPN american_scientific_journal-3571 231 13 , , PUNCT american_scientific_journal-3571 231 14 h. h. PROPN american_scientific_journal-3571 231 15 ( ( PUNCT american_scientific_journal-3571 231 16 2005).omnidirectional 2005).omnidirectional NUM american_scientific_journal-3571 231 17 static static ADJ american_scientific_journal-3571 231 18 walking walking NOUN american_scientific_journal-3571 231 19 of of ADP american_scientific_journal-3571 231 20 a a DET american_scientific_journal-3571 231 21 quadrupedrobot.transactions quadrupedrobot.transaction NOUN american_scientific_journal-3571 231 22 on on ADP american_scientific_journal-3571 231 23 robotics robotic NOUN american_scientific_journal-3571 231 24 , , PUNCT american_scientific_journal-3571 231 25 21(2 21(2 NUM american_scientific_journal-3571 231 26 ) ) PUNCT american_scientific_journal-3571 231 27 , , PUNCT american_scientific_journal-3571 231 28 152 152 NUM american_scientific_journal-3571 231 29 - - SYM american_scientific_journal-3571 231 30 161 161 NUM american_scientific_journal-3571 231 31 . . PUNCT american_scientific_journal-3571 232 1 [ [ X american_scientific_journal-3571 232 2 7 7 NUM american_scientific_journal-3571 232 3 ] ] X american_scientific_journal-3571 232 4 lee lee PROPN american_scientific_journal-3571 232 5 , , PUNCT american_scientific_journal-3571 232 6 t. t. PROPN american_scientific_journal-3571 232 7 t. t. PROPN american_scientific_journal-3571 232 8 , , PUNCT american_scientific_journal-3571 232 9 shih shih PROPN american_scientific_journal-3571 232 10 , , PUNCT american_scientific_journal-3571 232 11 c. c. PROPN american_scientific_journal-3571 232 12 l. l. PROPN american_scientific_journal-3571 232 13 ( ( PUNCT american_scientific_journal-3571 232 14 1986 1986 NUM american_scientific_journal-3571 232 15 ) ) PUNCT american_scientific_journal-3571 232 16 . . PUNCT american_scientific_journal-3571 233 1 a a DET american_scientific_journal-3571 233 2 study study NOUN american_scientific_journal-3571 233 3 of of ADP american_scientific_journal-3571 233 4 the the DET american_scientific_journal-3571 233 5 gaitcontrol gaitcontrol NOUN american_scientific_journal-3571 233 6 of of ADP american_scientific_journal-3571 233 7 a a DET american_scientific_journal-3571 233 8 quadruped quadruped NOUN american_scientific_journal-3571 233 9 walking walk VERB american_scientific_journal-3571 233 10 vehicle vehicle NOUN american_scientific_journal-3571 233 11 . . PUNCT american_scientific_journal-3571 234 1 j. j. PROPN american_scientific_journal-3571 234 2 of of ADP american_scientific_journal-3571 234 3 roboticsand roboticsand PROPN american_scientific_journal-3571 234 4 automation automation NOUN american_scientific_journal-3571 234 5 , , PUNCT american_scientific_journal-3571 234 6 2(2 2(2 NUM american_scientific_journal-3571 234 7 ) ) PUNCT american_scientific_journal-3571 234 8 , , PUNCT american_scientific_journal-3571 234 9 61 61 NUM american_scientific_journal-3571 234 10 - - SYM american_scientific_journal-3571 234 11 69 69 NUM american_scientific_journal-3571 234 12 . . PUNCT american_scientific_journal-3571 235 1 [ [ X american_scientific_journal-3571 235 2 8 8 NUM american_scientific_journal-3571 235 3 ] ] X american_scientific_journal-3571 235 4 kim kim PROPN american_scientific_journal-3571 235 5 , , PUNCT american_scientific_journal-3571 235 6 b. b. PROPN american_scientific_journal-3571 235 7 h. h. PROPN american_scientific_journal-3571 235 8 ( ( PUNCT american_scientific_journal-3571 235 9 2009 2009 NUM american_scientific_journal-3571 235 10 ) ) PUNCT american_scientific_journal-3571 235 11 . . PUNCT american_scientific_journal-3571 236 1 centroid centroid NOUN american_scientific_journal-3571 236 2 - - PUNCT american_scientific_journal-3571 236 3 based base VERB american_scientific_journal-3571 236 4 analysis analysis NOUN american_scientific_journal-3571 236 5 ofquadruped ofquadrupe VERB american_scientific_journal-3571 236 6 - - PUNCT american_scientific_journal-3571 236 7 robot robot NOUN american_scientific_journal-3571 236 8 walking walk VERB american_scientific_journal-3571 236 9 balance balance NOUN american_scientific_journal-3571 236 10 . . PUNCT american_scientific_journal-3571 237 1 int int NOUN american_scientific_journal-3571 237 2 . . PUNCT american_scientific_journal-3571 237 3 conf conf PROPN american_scientific_journal-3571 237 4 . . PUNCT american_scientific_journal-3571 238 1 onadvanced onadvance VERB american_scientific_journal-3571 238 2 robotics robotic NOUN american_scientific_journal-3571 238 3 , , PUNCT american_scientific_journal-3571 238 4 1 1 NUM american_scientific_journal-3571 238 5 - - SYM american_scientific_journal-3571 238 6 6 6 NUM american_scientific_journal-3571 238 7 . . PUNCT american_scientific_journal-3571 239 1 [ [ X american_scientific_journal-3571 239 2 9 9 NUM american_scientific_journal-3571 239 3 ] ] X american_scientific_journal-3571 239 4 firas firas PROPN american_scientific_journal-3571 239 5 a. a. PROPN american_scientific_journal-3571 239 6 raheem raheem PROPN american_scientific_journal-3571 239 7 , , PUNCT american_scientific_journal-3571 239 8 hind hind PROPN american_scientific_journal-3571 239 9 z. z. PROPN american_scientific_journal-3571 239 10 khaleel khaleel PROPN american_scientific_journal-3571 239 11 , , PUNCT american_scientific_journal-3571 239 12 " " PUNCT american_scientific_journal-3571 239 13 hexapod hexapod ADJ american_scientific_journal-3571 239 14 robot robot NOUN american_scientific_journal-3571 239 15 static static ADJ american_scientific_journal-3571 239 16 stability stability NOUN american_scientific_journal-3571 239 17 enhancement enhancement NOUN american_scientific_journal-3571 239 18 using use VERB american_scientific_journal-3571 239 19 genetic genetic ADJ american_scientific_journal-3571 239 20 algorithm algorithm NOUN american_scientific_journal-3571 239 21 al al PROPN american_scientific_journal-3571 239 22 - - PUNCT american_scientific_journal-3571 239 23 khwarizmi khwarizmi PROPN american_scientific_journal-3571 239 24 engineering engineering NOUN american_scientific_journal-3571 239 25 journal journal NOUN american_scientific_journal-3571 239 26 , , PUNCT american_scientific_journal-3571 239 27 vol vol NOUN american_scientific_journal-3571 239 28 . . PROPN american_scientific_journal-3571 239 29 11 11 NUM american_scientific_journal-3571 239 30 , , PUNCT american_scientific_journal-3571 239 31 no no INTJ american_scientific_journal-3571 239 32 . . NOUN american_scientific_journal-3571 239 33 4 4 NUM american_scientific_journal-3571 239 34 , , PUNCT american_scientific_journal-3571 239 35 p.p p.p PROPN american_scientific_journal-3571 239 36 . . PROPN american_scientific_journal-3571 239 37 44 44 NUM american_scientific_journal-3571 239 38 - - SYM american_scientific_journal-3571 239 39 59 59 NUM american_scientific_journal-3571 239 40 , , PUNCT american_scientific_journal-3571 239 41 2015 2015 NUM american_scientific_journal-3571 239 42 . . PUNCT american_scientific_journal-3571 240 1 [ [ X american_scientific_journal-3571 240 2 10 10 NUM american_scientific_journal-3571 240 3 ] ] X american_scientific_journal-3571 240 4 chen chen PROPN american_scientific_journal-3571 240 5 , , PUNCT american_scientific_journal-3571 240 6 binbin binbin PROPN american_scientific_journal-3571 240 7 , , PUNCT american_scientific_journal-3571 240 8 shaoyuan shaoyuan PROPN american_scientific_journal-3571 240 9 li li PROPN american_scientific_journal-3571 240 10 , , PUNCT american_scientific_journal-3571 240 11 and and CCONJ american_scientific_journal-3571 240 12 dan dan PROPN american_scientific_journal-3571 240 13 huang huang PROPN american_scientific_journal-3571 240 14 . . PUNCT american_scientific_journal-3571 241 1 " " PUNCT american_scientific_journal-3571 241 2 quadruped quadrupe VERB american_scientific_journal-3571 241 3 robot robot NOUN american_scientific_journal-3571 241 4 crawl crawl NOUN american_scientific_journal-3571 241 5 gait gait PROPN american_scientific_journal-3571 241 6 planning planning NOUN american_scientific_journal-3571 241 7 based base VERB american_scientific_journal-3571 241 8 on on ADP american_scientific_journal-3571 241 9 dst dst PROPN american_scientific_journal-3571 241 10 . . PUNCT american_scientific_journal-3571 241 11 " " PUNCT american_scientific_journal-3571 242 1 american american ADJ american_scientific_journal-3571 242 2 scientific scientific ADJ american_scientific_journal-3571 242 3 research research NOUN american_scientific_journal-3571 242 4 journal journal NOUN american_scientific_journal-3571 242 5 for for ADP american_scientific_journal-3571 242 6 engineering engineering NOUN american_scientific_journal-3571 242 7 , , PUNCT american_scientific_journal-3571 242 8 technology technology NOUN american_scientific_journal-3571 242 9 , , PUNCT american_scientific_journal-3571 242 10 and and CCONJ american_scientific_journal-3571 242 11 sciences science NOUN american_scientific_journal-3571 242 12 ( ( PUNCT american_scientific_journal-3571 242 13 asrjets asrjet NOUN american_scientific_journal-3571 242 14 ) ) PUNCT american_scientific_journal-3571 242 15 ( ( PUNCT american_scientific_journal-3571 242 16 2017 2017 NUM american_scientific_journal-3571 242 17 ) ) PUNCT american_scientific_journal-3571 242 18 volume volume NOUN american_scientific_journal-3571 242 19 37 37 NUM american_scientific_journal-3571 242 20 , , PUNCT american_scientific_journal-3571 242 21 no no DET american_scientific_journal-3571 242 22 1 1 NUM american_scientific_journal-3571 242 23 , , PUNCT american_scientific_journal-3571 242 24 pp pp ADV american_scientific_journal-3571 242 25 17 17 NUM american_scientific_journal-3571 242 26 - - SYM american_scientific_journal-3571 242 27 32 32 NUM american_scientific_journal-3571 242 28 32 32 NUM american_scientific_journal-3571 242 29 proceedings proceeding NOUN american_scientific_journal-3571 242 30 of of ADP american_scientific_journal-3571 242 31 the the DET american_scientific_journal-3571 242 32 33rd 33rd ADJ american_scientific_journal-3571 242 33 chinese chinese ADJ american_scientific_journal-3571 242 34 control control PROPN american_scientific_journal-3571 242 35 conference conference PROPN american_scientific_journal-3571 242 36 ( ( PUNCT american_scientific_journal-3571 242 37 2014 2014 NUM american_scientific_journal-3571 242 38 ) ) PUNCT american_scientific_journal-3571 242 39 . . PUNCT american_scientific_journal-3571 243 1 [ [ X american_scientific_journal-3571 243 2 11 11 NUM american_scientific_journal-3571 243 3 ] ] X american_scientific_journal-3571 243 4 liu liu PROPN american_scientific_journal-3571 243 5 , , PUNCT american_scientific_journal-3571 243 6 fei fei PROPN american_scientific_journal-3571 243 7 . . PUNCT american_scientific_journal-3571 243 8 research research NOUN american_scientific_journal-3571 243 9 about about ADP american_scientific_journal-3571 243 10 " " PUNCT american_scientific_journal-3571 243 11 gait gait ADJ american_scientific_journal-3571 243 12 planning planning NOUN american_scientific_journal-3571 243 13 and and CCONJ american_scientific_journal-3571 243 14 balance balance NOUN american_scientific_journal-3571 243 15 control control NOUN american_scientific_journal-3571 243 16 ofquadruped ofquadrupe VERB american_scientific_journal-3571 243 17 robot robot NOUN american_scientific_journal-3571 243 18 " " PUNCT american_scientific_journal-3571 243 19 , , PUNCT american_scientific_journal-3571 243 20 doctoral doctoral ADJ american_scientific_journal-3571 243 21 dissertation dissertation NOUN american_scientific_journal-3571 243 22 , , PUNCT american_scientific_journal-3571 243 23 university university NOUN american_scientific_journal-3571 243 24 of of ADP american_scientific_journal-3571 243 25 scienceand scienceand NOUN american_scientific_journal-3571 243 26 technology technology NOUN american_scientific_journal-3571 243 27 of of ADP american_scientific_journal-3571 243 28 china china PROPN american_scientific_journal-3571 243 29 , , PUNCT american_scientific_journal-3571 243 30 2010 2010 NUM american_scientific_journal-3571 243 31 . . PUNCT american_scientific_journal-3571 244 1 [ [ X american_scientific_journal-3571 244 2 12 12 NUM american_scientific_journal-3571 244 3 ] ] X american_scientific_journal-3571 244 4 buchli buchli NOUN american_scientific_journal-3571 244 5 , , PUNCT american_scientific_journal-3571 244 6 jonas jonas PROPN american_scientific_journal-3571 244 7 and and CCONJ american_scientific_journal-3571 244 8 kalakrishnan kalakrishnan PROPN american_scientific_journal-3571 244 9 , , PUNCT american_scientific_journal-3571 244 10 mrinal mrinal ADJ american_scientific_journal-3571 244 11 and and CCONJ american_scientific_journal-3571 244 12 mistry mistry PROPN american_scientific_journal-3571 244 13 , , PUNCT american_scientific_journal-3571 244 14 michaeland michaeland PROPN american_scientific_journal-3571 244 15 pastor pastor PROPN american_scientific_journal-3571 244 16 , , PUNCT american_scientific_journal-3571 244 17 peter peter PROPN american_scientific_journal-3571 244 18 and and CCONJ american_scientific_journal-3571 244 19 schaal schaal PROPN american_scientific_journal-3571 244 20 , , PUNCT american_scientific_journal-3571 244 21 stefan stefan PROPN american_scientific_journal-3571 244 22 , , PUNCT american_scientific_journal-3571 244 23 compliant compliant ADJ american_scientific_journal-3571 244 24 quadruped quadrupe VERB american_scientific_journal-3571 244 25 locomotion locomotion NOUN american_scientific_journal-3571 244 26 over over ADP american_scientific_journal-3571 244 27 rough rough ADJ american_scientific_journal-3571 244 28 terrain terrain NOUN american_scientific_journal-3571 244 29 , , PUNCT american_scientific_journal-3571 244 30 the the DET american_scientific_journal-3571 244 31 2009 2009 NUM american_scientific_journal-3571 244 32 ieee ieee NOUN american_scientific_journal-3571 244 33 / / SYM american_scientific_journal-3571 244 34 rsj rsj NOUN american_scientific_journal-3571 244 35 internationalconference internationalconference NOUN american_scientific_journal-3571 244 36 on on ADP american_scientific_journal-3571 244 37 intelligent intelligent ADJ american_scientific_journal-3571 244 38 robots robot NOUN american_scientific_journal-3571 244 39 and and CCONJ american_scientific_journal-3571 244 40 systems system NOUN american_scientific_journal-3571 244 41 : : PUNCT american_scientific_journal-3571 244 42 814–820 814–820 NUM american_scientific_journal-3571 244 43 , , PUNCT american_scientific_journal-3571 244 44 2009 2009 NUM american_scientific_journal-3571 244 45 . . PUNCT american_scientific_journal-3571 245 1 [ [ X american_scientific_journal-3571 245 2 13 13 NUM american_scientific_journal-3571 245 3 ] ] X american_scientific_journal-3571 245 4 liu liu PROPN american_scientific_journal-3571 245 5 , , PUNCT american_scientific_journal-3571 245 6 f. f. PROPN american_scientific_journal-3571 245 7 , , PUNCT american_scientific_journal-3571 245 8 d. d. PROPN american_scientific_journal-3571 245 9 wu wu PROPN american_scientific_journal-3571 245 10 , , PUNCT american_scientific_journal-3571 245 11 and and CCONJ american_scientific_journal-3571 245 12 k. k. PROPN american_scientific_journal-3571 245 13 chen chen PROPN american_scientific_journal-3571 245 14 . . PUNCT american_scientific_journal-3571 246 1 " " PUNCT american_scientific_journal-3571 246 2 the the DET american_scientific_journal-3571 246 3 simplest simple ADJ american_scientific_journal-3571 246 4 creeping creeping ADJ american_scientific_journal-3571 246 5 gait gait NOUN american_scientific_journal-3571 246 6 for for ADP american_scientific_journal-3571 246 7 a a DET american_scientific_journal-3571 246 8 quadruped quadruped NOUN american_scientific_journal-3571 246 9 robot robot NOUN american_scientific_journal-3571 246 10 " " PUNCT american_scientific_journal-3571 246 11 . . PUNCT american_scientific_journal-3571 247 1 proceedings proceeding NOUN american_scientific_journal-3571 247 2 of of ADP american_scientific_journal-3571 247 3 the the DET american_scientific_journal-3571 247 4 institution institution NOUN american_scientific_journal-3571 247 5 of of ADP american_scientific_journal-3571 247 6 mechanical mechanical ADJ american_scientific_journal-3571 247 7 engineers engineer NOUN american_scientific_journal-3571 247 8 , , PUNCT american_scientific_journal-3571 247 9 part part NOUN american_scientific_journal-3571 247 10 c c NOUN american_scientific_journal-3571 247 11 : : PUNCT american_scientific_journal-3571 247 12 journal journal NOUN american_scientific_journal-3571 247 13 of of ADP american_scientific_journal-3571 247 14 mechanical mechanical ADJ american_scientific_journal-3571 247 15 engineering engineering NOUN american_scientific_journal-3571 247 16 science science NOUN american_scientific_journal-3571 247 17 227.1 227.1 NUM american_scientific_journal-3571 247 18 ( ( PUNCT american_scientific_journal-3571 247 19 2012 2012 NUM american_scientific_journal-3571 247 20 ): ): PUNCT american_scientific_journal-3571 247 21 170 170 NUM american_scientific_journal-3571 247 22 - - SYM american_scientific_journal-3571 247 23 177 177 NUM american_scientific_journal-3571 247 24 . . PUNCT american_scientific_journal-3571 247 25 web web NOUN american_scientific_journal-3571 247 26 . . PUNCT american_scientific_journal-3571 248 1 [ [ X american_scientific_journal-3571 248 2 14 14 NUM american_scientific_journal-3571 248 3 ] ] X american_scientific_journal-3571 248 4 mΔƒnoiu mΔƒnoiu NOUN american_scientific_journal-3571 248 5 - - PUNCT american_scientific_journal-3571 248 6 olarusorin olarusorin NOUN american_scientific_journal-3571 248 7 , , PUNCT american_scientific_journal-3571 248 8 niΕ£ulescumircea niΕ£ulescumircea NOUN american_scientific_journal-3571 248 9 , , PUNCT american_scientific_journal-3571 248 10 β€œ " PUNCT american_scientific_journal-3571 248 11 matlabsimulator matlabsimulator NOUN american_scientific_journal-3571 248 12 for for ADP american_scientific_journal-3571 248 13 gravitational gravitational ADJ american_scientific_journal-3571 248 14 stability stability NOUN american_scientific_journal-3571 248 15 analysis analysis NOUN american_scientific_journal-3571 248 16 of of ADP american_scientific_journal-3571 248 17 a a DET american_scientific_journal-3571 248 18 hexapodrobot hexapodrobot NOUN american_scientific_journal-3571 248 19 , , PUNCT american_scientific_journal-3571 248 20 ” " PUNCT american_scientific_journal-3571 248 21 the the DET american_scientific_journal-3571 248 22 romanian romanian ADJ american_scientific_journal-3571 248 23 review review PROPN american_scientific_journal-3571 248 24 precisionmechanics precisionmechanic NOUN american_scientific_journal-3571 248 25 , , PUNCT american_scientific_journal-3571 248 26 optics optics PROPN american_scientific_journal-3571 248 27 & & CCONJ american_scientific_journal-3571 248 28 mechatronics mechatronic NOUN american_scientific_journal-3571 248 29 , , PUNCT american_scientific_journal-3571 248 30 158 158 NUM american_scientific_journal-3571 248 31 2011 2011 NUM american_scientific_journal-3571 248 32 , , PUNCT american_scientific_journal-3571 248 33 no no INTJ american_scientific_journal-3571 248 34 . . NOUN american_scientific_journal-3571 248 35 39 39 NUM american_scientific_journal-3571 248 36 mechanics mechanic NOUN american_scientific_journal-3571 248 37 , , PUNCT american_scientific_journal-3571 248 38 optics optic NOUN american_scientific_journal-3571 248 39 & & CCONJ american_scientific_journal-3571 248 40 mechatronics mechatronic NOUN american_scientific_journal-3571 248 41 , , PUNCT american_scientific_journal-3571 248 42 2011 2011 NUM american_scientific_journal-3571 248 43 . . PUNCT american_scientific_journal-3571 249 1 [ [ X american_scientific_journal-3571 249 2 15 15 NUM american_scientific_journal-3571 249 3 ] ] X american_scientific_journal-3571 249 4 freyrhardarson,"stability freyrhardarson,"stability NOUN american_scientific_journal-3571 249 5 analysis analysis NOUN american_scientific_journal-3571 249 6 and and CCONJ american_scientific_journal-3571 249 7 synthesis synthesis NOUN american_scientific_journal-3571 249 8 ofstatically ofstatically ADV american_scientific_journal-3571 249 9 balanced balance VERB american_scientific_journal-3571 249 10 walkingfor walkingfor ADP american_scientific_journal-3571 249 11 quadruped quadrupe VERB american_scientific_journal-3571 249 12 robots",doctoralthesismechatronicslabdepartment robots",doctoralthesismechatronicslabdepartment NOUN american_scientific_journal-3571 249 13 of of ADP american_scientific_journal-3571 249 14 machine machine NOUN american_scientific_journal-3571 249 15 designroyal designroyal PROPN american_scientific_journal-3571 249 16 institute institute PROPN american_scientific_journal-3571 249 17 of of ADP american_scientific_journal-3571 249 18 technology technology PROPN american_scientific_journal-3571 249 19 , , PUNCT american_scientific_journal-3571 249 20 kths-100 kths-100 PROPN american_scientific_journal-3571 249 21 44 44 NUM american_scientific_journal-3571 249 22 stockholm stockholm PROPN american_scientific_journal-3571 249 23 , , PUNCT american_scientific_journal-3571 249 24 sweden,2002 sweden,2002 NOUN american_scientific_journal-3571 249 25 . . PUNCT american_scientific_journal-3571 250 1 [ [ X american_scientific_journal-3571 250 2 16 16 NUM american_scientific_journal-3571 250 3 ] ] X american_scientific_journal-3571 250 4 f. f. PROPN american_scientific_journal-3571 250 5 moldovan moldovan PROPN american_scientific_journal-3571 250 6 , , PUNCT american_scientific_journal-3571 250 7 v. v. ADP american_scientific_journal-3571 250 8 dolga dolga ADJ american_scientific_journal-3571 250 9 , , PUNCT american_scientific_journal-3571 250 10 c. c. PROPN american_scientific_journal-3571 250 11 sticlaru sticlaru NOUN american_scientific_journal-3571 250 12 , , PUNCT american_scientific_journal-3571 250 13 " " PUNCT american_scientific_journal-3571 250 14 a a DET american_scientific_journal-3571 250 15 new new ADJ american_scientific_journal-3571 250 16 type type NOUN american_scientific_journal-3571 250 17 of of ADP american_scientific_journal-3571 250 18 walking walking NOUN american_scientific_journal-3571 250 19 robot robot NOUN american_scientific_journal-3571 250 20 based base VERB american_scientific_journal-3571 250 21 upon upon SCONJ american_scientific_journal-3571 250 22 jansen jansen PROPN american_scientific_journal-3571 250 23 mechanism mechanism NOUN american_scientific_journal-3571 250 24 " " PUNCT american_scientific_journal-3571 250 25 , , PUNCT american_scientific_journal-3571 250 26 advanced advanced ADJ american_scientific_journal-3571 250 27 materials material NOUN american_scientific_journal-3571 250 28 research research NOUN american_scientific_journal-3571 250 29 , , PUNCT american_scientific_journal-3571 250 30 vols vol NOUN american_scientific_journal-3571 250 31 . . PUNCT american_scientific_journal-3571 251 1 463 463 NUM american_scientific_journal-3571 251 2 - - SYM american_scientific_journal-3571 251 3 464 464 NUM american_scientific_journal-3571 251 4 , , PUNCT american_scientific_journal-3571 251 5 pp pp ADJ american_scientific_journal-3571 251 6 . . PUNCT american_scientific_journal-3571 252 1 997 997 NUM american_scientific_journal-3571 252 2 - - SYM american_scientific_journal-3571 252 3 1001 1001 NUM american_scientific_journal-3571 252 4 , , PUNCT american_scientific_journal-3571 252 5 2012 2012 NUM american_scientific_journal-3571 252 6 . . PUNCT