id	sid	tid	token	lemma	pos
ap-8672	1	1	acta	acta	PROPN
ap-8672	1	2	polytechnica	polytechnica	PROPN
ap-8672	1	3	https://doi.org/10.14311/ap.2023.63.0326	https://doi.org/10.14311/ap.2023.63.0326	PROPN
ap-8672	1	4	acta	acta	PROPN
ap-8672	1	5	polytechnica	polytechnica	PROPN
ap-8672	1	6	63(5):326–346	63(5):326–346	PROPN
ap-8672	1	7	,	,	PUNCT
ap-8672	1	8	2023	2023	NUM
ap-8672	1	9	©	©	ADP
ap-8672	1	10	2023	2023	NUM
ap-8672	1	11	the	the	DET
ap-8672	1	12	author(s	author(s	NOUN
ap-8672	1	13	)	)	PUNCT
ap-8672	1	14	.	.	PUNCT
ap-8672	2	1	licensed	license	VERB
ap-8672	2	2	under	under	ADP
ap-8672	2	3	a	a	DET
ap-8672	2	4	cc	cc	NOUN
ap-8672	2	5	-	-	PUNCT
ap-8672	2	6	by	by	ADP
ap-8672	2	7	4.0	4.0	NUM
ap-8672	2	8	licence	licence	NOUN
ap-8672	2	9	published	publish	VERB
ap-8672	2	10	by	by	ADP
ap-8672	2	11	the	the	DET
ap-8672	2	12	czech	czech	PROPN
ap-8672	2	13	technical	technical	PROPN
ap-8672	2	14	university	university	PROPN
ap-8672	2	15	in	in	ADP
ap-8672	2	16	prague	prague	PROPN
ap-8672	2	17	geometric	geometric	ADJ
ap-8672	2	18	approach	approach	NOUN
ap-8672	2	19	to	to	ADP
ap-8672	2	20	solving	solve	VERB
ap-8672	2	21	inverse	inverse	ADJ
ap-8672	2	22	kinematics	kinematic	NOUN
ap-8672	2	23	of	of	ADP
ap-8672	2	24	six	six	NUM
ap-8672	2	25	dof	dof	NOUN
ap-8672	2	26	robot	robot	NOUN
ap-8672	2	27	with	with	ADP
ap-8672	2	28	spherical	spherical	ADJ
ap-8672	2	29	joints	joint	NOUN
ap-8672	2	30	nacer	nacer	VERB
ap-8672	2	31	hadidia,∗	hadidia,∗	NOUN
ap-8672	2	32	,	,	PUNCT
ap-8672	2	33	mohamed	mohamed	PROPN
ap-8672	2	34	bouaziza	bouaziza	PROPN
ap-8672	2	35	,	,	PUNCT
ap-8672	2	36	chawki	chawki	NOUN
ap-8672	2	37	mahfoudib	mahfoudib	NOUN
ap-8672	2	38	,	,	PUNCT
ap-8672	2	39	mohamed	mohamed	PROPN
ap-8672	2	40	zaharuddinc	zaharuddinc	PROPN
ap-8672	2	41	a	a	DET
ap-8672	2	42	ecole	ecole	PROPN
ap-8672	2	43	nationale	nationale	PROPN
ap-8672	2	44	polytechnique	polytechnique	NOUN
ap-8672	2	45	,	,	PUNCT
ap-8672	2	46	laboratoire	laboratoire	PROPN
ap-8672	2	47	de	de	X
ap-8672	2	48	genie	genie	PROPN
ap-8672	2	49	mecanique	mecanique	PROPN
ap-8672	2	50	et	et	PROPN
ap-8672	2	51	devellopement	devellopement	PROPN
ap-8672	2	52	,	,	PUNCT
ap-8672	2	53	department	department	NOUN
ap-8672	2	54	of	of	ADP
ap-8672	2	55	mechanical	mechanical	ADJ
ap-8672	2	56	engineering	engineering	NOUN
ap-8672	2	57	,	,	PUNCT
ap-8672	2	58	10	10	NUM
ap-8672	2	59	avenue	avenue	PROPN
ap-8672	2	60	hassan	hassan	PROPN
ap-8672	2	61	badi	badi	PROPN
ap-8672	2	62	,	,	PUNCT
ap-8672	2	63	16200	16200	NUM
ap-8672	2	64	el	el	PROPN
ap-8672	2	65	harrach	harrach	PROPN
ap-8672	2	66	,	,	PUNCT
ap-8672	2	67	algeria	algeria	PROPN
ap-8672	2	68	b	b	PROPN
ap-8672	2	69	university	university	PROPN
ap-8672	2	70	larbi	larbi	PROPN
ap-8672	2	71	ben	ben	PROPN
ap-8672	2	72	mhidi	mhidi	PROPN
ap-8672	2	73	,	,	PUNCT
ap-8672	2	74	campus	campus	PROPN
ap-8672	2	75	of	of	ADP
ap-8672	2	76	ainbeida	ainbeida	PROPN
ap-8672	2	77	,	,	PUNCT
ap-8672	2	78	department	department	NOUN
ap-8672	2	79	of	of	ADP
ap-8672	2	80	mechanical	mechanical	ADJ
ap-8672	2	81	engineering	engineering	NOUN
ap-8672	2	82	,	,	PUNCT
ap-8672	2	83	route	route	PROPN
ap-8672	2	84	de	de	PROPN
ap-8672	2	85	constantine	constantine	PROPN
ap-8672	2	86	,	,	PUNCT
ap-8672	2	87	b.p	b.p	PROPN
ap-8672	2	88	.	.	PROPN
ap-8672	2	89	358	358	NUM
ap-8672	2	90	,	,	PUNCT
ap-8672	2	91	04000	04000	NUM
ap-8672	2	92	oum	oum	PROPN
ap-8672	2	93	el	el	PROPN
ap-8672	2	94	bouaghi	bouaghi	PROPN
ap-8672	2	95	,	,	PUNCT
ap-8672	2	96	algeria	algeria	PROPN
ap-8672	2	97	c	c	PROPN
ap-8672	2	98	universiti	universiti	PROPN
ap-8672	2	99	teknologi	teknologi	PROPN
ap-8672	2	100	malaysia	malaysia	PROPN
ap-8672	2	101	,	,	PUNCT
ap-8672	2	102	faculty	faculty	NOUN
ap-8672	2	103	of	of	ADP
ap-8672	2	104	electrical	electrical	ADJ
ap-8672	2	105	engineering	engineering	NOUN
ap-8672	2	106	,	,	PUNCT
ap-8672	2	107	department	department	NOUN
ap-8672	2	108	of	of	ADP
ap-8672	2	109	mechatronics	mechatronic	NOUN
ap-8672	2	110	,	,	PUNCT
ap-8672	2	111	81310	81310	NUM
ap-8672	2	112	johor	johor	PROPN
ap-8672	2	113	bahru	bahru	PROPN
ap-8672	2	114	,	,	PUNCT
ap-8672	2	115	malaysia	malaysia	PROPN
ap-8672	2	116	∗	∗	NOUN
ap-8672	2	117	corresponding	correspond	VERB
ap-8672	2	118	author	author	NOUN
ap-8672	2	119	:	:	PUNCT
ap-8672	2	120	nacer.hadidi@g.enp.edu.dz	nacer.hadidi@g.enp.edu.dz	ADJ
ap-8672	2	121	abstract	abstract	ADJ
ap-8672	2	122	.	.	PUNCT
ap-8672	3	1	inverse	inverse	NOUN
ap-8672	3	2	kinematics	kinematic	NOUN
ap-8672	3	3	is	be	AUX
ap-8672	3	4	a	a	DET
ap-8672	3	5	fundamental	fundamental	ADJ
ap-8672	3	6	concept	concept	NOUN
ap-8672	3	7	in	in	ADP
ap-8672	3	8	robotics	robotic	NOUN
ap-8672	3	9	that	that	PRON
ap-8672	3	10	plays	play	VERB
ap-8672	3	11	a	a	DET
ap-8672	3	12	crucial	crucial	ADJ
ap-8672	3	13	role	role	NOUN
ap-8672	3	14	in	in	ADP
ap-8672	3	15	a	a	DET
ap-8672	3	16	robot	robot	NOUN
ap-8672	3	17	’s	’s	PART
ap-8672	3	18	ability	ability	NOUN
ap-8672	3	19	to	to	PART
ap-8672	3	20	perform	perform	VERB
ap-8672	3	21	tasks	task	NOUN
ap-8672	3	22	.	.	PUNCT
ap-8672	4	1	in	in	ADP
ap-8672	4	2	this	this	DET
ap-8672	4	3	contribution	contribution	NOUN
ap-8672	4	4	,	,	PUNCT
ap-8672	4	5	we	we	PRON
ap-8672	4	6	propose	propose	VERB
ap-8672	4	7	a	a	DET
ap-8672	4	8	novel	novel	ADJ
ap-8672	4	9	geometric	geometric	ADJ
ap-8672	4	10	approach	approach	NOUN
ap-8672	4	11	based	base	VERB
ap-8672	4	12	on	on	ADP
ap-8672	4	13	vector	vector	NOUN
ap-8672	4	14	calculus	calculus	NOUN
ap-8672	4	15	to	to	PART
ap-8672	4	16	solve	solve	VERB
ap-8672	4	17	the	the	DET
ap-8672	4	18	inverse	inverse	NOUN
ap-8672	4	19	kinematics	kinematic	NOUN
ap-8672	4	20	problem	problem	NOUN
ap-8672	4	21	.	.	PUNCT
ap-8672	5	1	the	the	DET
ap-8672	5	2	primary	primary	ADJ
ap-8672	5	3	advantage	advantage	NOUN
ap-8672	5	4	of	of	ADP
ap-8672	5	5	this	this	DET
ap-8672	5	6	approach	approach	NOUN
ap-8672	5	7	originates	originate	NOUN
ap-8672	5	8	from	from	ADP
ap-8672	5	9	the	the	DET
ap-8672	5	10	solutions	solution	NOUN
ap-8672	5	11	,	,	PUNCT
ap-8672	5	12	which	which	PRON
ap-8672	5	13	exhibit	exhibit	VERB
ap-8672	5	14	a	a	DET
ap-8672	5	15	linear	linear	ADJ
ap-8672	5	16	form	form	NOUN
ap-8672	5	17	and	and	CCONJ
ap-8672	5	18	uncoupled	uncoupled	ADJ
ap-8672	5	19	equations	equation	NOUN
ap-8672	5	20	.	.	PUNCT
ap-8672	6	1	to	to	PART
ap-8672	6	2	validate	validate	VERB
ap-8672	6	3	the	the	DET
ap-8672	6	4	effectiveness	effectiveness	NOUN
ap-8672	6	5	and	and	CCONJ
ap-8672	6	6	correctness	correctness	NOUN
ap-8672	6	7	of	of	ADP
ap-8672	6	8	our	our	PRON
ap-8672	6	9	proposed	propose	VERB
ap-8672	6	10	method	method	NOUN
ap-8672	6	11	,	,	PUNCT
ap-8672	6	12	we	we	PRON
ap-8672	6	13	constructed	construct	VERB
ap-8672	6	14	a	a	DET
ap-8672	6	15	six	six	NUM
ap-8672	6	16	-	-	PUNCT
ap-8672	6	17	degrees	degree	NOUN
ap-8672	6	18	-	-	PUNCT
ap-8672	6	19	of	of	ADP
ap-8672	6	20	-	-	PUNCT
ap-8672	6	21	freedom	freedom	NOUN
ap-8672	6	22	robot	robot	NOUN
ap-8672	6	23	.	.	PUNCT
ap-8672	7	1	this	this	DET
ap-8672	7	2	robot	robot	NOUN
ap-8672	7	3	is	be	AUX
ap-8672	7	4	controlled	control	VERB
ap-8672	7	5	by	by	ADP
ap-8672	7	6	an	an	DET
ap-8672	7	7	arduino	arduino	NOUN
ap-8672	7	8	mega	mega	X
ap-8672	7	9	2650	2650	NUM
ap-8672	7	10	on	on	ADP
ap-8672	7	11	which	which	PRON
ap-8672	7	12	we	we	PRON
ap-8672	7	13	have	have	AUX
ap-8672	7	14	implemented	implement	VERB
ap-8672	7	15	the	the	DET
ap-8672	7	16	inverse	inverse	NOUN
ap-8672	7	17	kinematics	kinematic	NOUN
ap-8672	7	18	algorithm	algorithm	NOUN
ap-8672	7	19	.	.	PUNCT
ap-8672	8	1	the	the	DET
ap-8672	8	2	validation	validation	NOUN
ap-8672	8	3	process	process	NOUN
ap-8672	8	4	involved	involve	VERB
ap-8672	8	5	considering	consider	VERB
ap-8672	8	6	various	various	ADJ
ap-8672	8	7	desired	desire	VERB
ap-8672	8	8	trajectories	trajectory	NOUN
ap-8672	8	9	of	of	ADP
ap-8672	8	10	the	the	DET
ap-8672	8	11	end	end	NOUN
ap-8672	8	12	-	-	PUNCT
ap-8672	8	13	effector	effector	NOUN
ap-8672	8	14	,	,	PUNCT
ap-8672	8	15	which	which	PRON
ap-8672	8	16	were	be	AUX
ap-8672	8	17	simulated	simulate	VERB
ap-8672	8	18	in	in	ADP
ap-8672	8	19	matlab	matlab	PROPN
ap-8672	8	20	and	and	CCONJ
ap-8672	8	21	then	then	ADV
ap-8672	8	22	performed	perform	VERB
ap-8672	8	23	by	by	ADP
ap-8672	8	24	the	the	DET
ap-8672	8	25	physical	physical	ADJ
ap-8672	8	26	robot	robot	NOUN
ap-8672	8	27	.	.	PUNCT
ap-8672	9	1	importantly	importantly	ADV
ap-8672	9	2	,	,	PUNCT
ap-8672	9	3	our	our	PRON
ap-8672	9	4	findings	finding	NOUN
ap-8672	9	5	confirm	confirm	VERB
ap-8672	9	6	that	that	SCONJ
ap-8672	9	7	the	the	DET
ap-8672	9	8	end	end	NOUN
ap-8672	9	9	-	-	PUNCT
ap-8672	9	10	effector	effector	NOUN
ap-8672	9	11	successfully	successfully	ADV
ap-8672	9	12	tracks	track	VERB
ap-8672	9	13	the	the	DET
ap-8672	9	14	predefined	predefine	VERB
ap-8672	9	15	trajectories	trajectory	NOUN
ap-8672	9	16	.	.	PUNCT
ap-8672	10	1	furthermore	furthermore	ADV
ap-8672	10	2	,	,	PUNCT
ap-8672	10	3	we	we	PRON
ap-8672	10	4	conducted	conduct	VERB
ap-8672	10	5	a	a	DET
ap-8672	10	6	comparative	comparative	ADJ
ap-8672	10	7	analysis	analysis	NOUN
ap-8672	10	8	between	between	ADP
ap-8672	10	9	paul	paul	PROPN
ap-8672	10	10	’s	’s	PART
ap-8672	10	11	method	method	NOUN
ap-8672	10	12	and	and	CCONJ
ap-8672	10	13	the	the	DET
ap-8672	10	14	results	result	NOUN
ap-8672	10	15	obtained	obtain	VERB
ap-8672	10	16	from	from	ADP
ap-8672	10	17	joint	joint	ADJ
ap-8672	10	18	angles	angle	NOUN
ap-8672	10	19	using	use	VERB
ap-8672	10	20	our	our	PRON
ap-8672	10	21	proposed	propose	VERB
ap-8672	10	22	approach	approach	NOUN
ap-8672	10	23	.	.	PUNCT
ap-8672	11	1	interestingly	interestingly	ADV
ap-8672	11	2	,	,	PUNCT
ap-8672	11	3	our	our	PRON
ap-8672	11	4	study	study	NOUN
ap-8672	11	5	reveals	reveal	VERB
ap-8672	11	6	a	a	DET
ap-8672	11	7	significant	significant	ADJ
ap-8672	11	8	similarity	similarity	NOUN
ap-8672	11	9	between	between	ADP
ap-8672	11	10	the	the	DET
ap-8672	11	11	two	two	NUM
ap-8672	11	12	sets	set	NOUN
ap-8672	11	13	of	of	ADP
ap-8672	11	14	results	result	NOUN
ap-8672	11	15	,	,	PUNCT
ap-8672	11	16	reaffirming	reaffirm	VERB
ap-8672	11	17	the	the	DET
ap-8672	11	18	accuracy	accuracy	NOUN
ap-8672	11	19	and	and	CCONJ
ap-8672	11	20	validity	validity	NOUN
ap-8672	11	21	of	of	ADP
ap-8672	11	22	the	the	DET
ap-8672	11	23	approach	approach	NOUN
ap-8672	11	24	presented	present	VERB
ap-8672	11	25	in	in	ADP
ap-8672	11	26	this	this	DET
ap-8672	11	27	study	study	NOUN
ap-8672	11	28	.	.	PUNCT
ap-8672	12	1	keywords	keyword	NOUN
ap-8672	12	2	:	:	PUNCT
ap-8672	12	3	robotic	robotic	ADJ
ap-8672	12	4	,	,	PUNCT
ap-8672	12	5	forward	forward	ADJ
ap-8672	12	6	kinematics	kinematic	NOUN
ap-8672	12	7	,	,	PUNCT
ap-8672	12	8	inverse	inverse	NOUN
ap-8672	12	9	kinematics	kinematic	NOUN
ap-8672	12	10	,	,	PUNCT
ap-8672	12	11	geometric	geometric	ADJ
ap-8672	12	12	modelling	modelling	NOUN
ap-8672	12	13	,	,	PUNCT
ap-8672	12	14	space	space	NOUN
ap-8672	12	15	geometry	geometry	NOUN
ap-8672	12	16	.	.	PUNCT
ap-8672	13	1	1	1	X
ap-8672	13	2	.	.	X
ap-8672	13	3	introduction	introduction	NOUN
ap-8672	13	4	due	due	ADP
ap-8672	13	5	to	to	ADP
ap-8672	13	6	the	the	DET
ap-8672	13	7	interesting	interesting	ADJ
ap-8672	13	8	and	and	CCONJ
ap-8672	13	9	complex	complex	ADJ
ap-8672	13	10	nature	nature	NOUN
ap-8672	13	11	of	of	ADP
ap-8672	13	12	field	field	NOUN
ap-8672	13	13	of	of	ADP
ap-8672	13	14	robotics	robotic	NOUN
ap-8672	13	15	,	,	PUNCT
ap-8672	13	16	several	several	ADJ
ap-8672	13	17	approaches	approach	NOUN
ap-8672	13	18	to	to	ADP
ap-8672	13	19	the	the	DET
ap-8672	13	20	research	research	NOUN
ap-8672	13	21	of	of	ADP
ap-8672	13	22	robots	robot	NOUN
ap-8672	13	23	have	have	AUX
ap-8672	13	24	been	be	AUX
ap-8672	13	25	taken	take	VERB
ap-8672	13	26	.	.	PUNCT
ap-8672	14	1	one	one	NUM
ap-8672	14	2	of	of	ADP
ap-8672	14	3	the	the	DET
ap-8672	14	4	challenging	challenging	ADJ
ap-8672	14	5	tasks	task	NOUN
ap-8672	14	6	is	be	AUX
ap-8672	14	7	the	the	DET
ap-8672	14	8	kinematic	kinematic	ADJ
ap-8672	14	9	modelling	modelling	NOUN
ap-8672	14	10	(	(	PUNCT
ap-8672	14	11	forward	forward	ADV
ap-8672	14	12	and	and	CCONJ
ap-8672	14	13	inverse	inverse	NOUN
ap-8672	14	14	kinematics	kinematic	NOUN
ap-8672	14	15	)	)	PUNCT
ap-8672	14	16	.	.	PUNCT
ap-8672	15	1	research	research	NOUN
ap-8672	15	2	into	into	ADP
ap-8672	15	3	the	the	DET
ap-8672	15	4	treatment	treatment	NOUN
ap-8672	15	5	of	of	ADP
ap-8672	15	6	the	the	DET
ap-8672	15	7	robot	robot	NOUN
ap-8672	15	8	kinematics	kinematic	NOUN
ap-8672	15	9	continues	continue	VERB
ap-8672	15	10	to	to	PART
ap-8672	15	11	spread	spread	VERB
ap-8672	15	12	over	over	ADP
ap-8672	15	13	different	different	ADJ
ap-8672	15	14	types	type	NOUN
ap-8672	15	15	of	of	ADP
ap-8672	15	16	robots	robot	NOUN
ap-8672	15	17	.	.	PUNCT
ap-8672	16	1	in	in	ADP
ap-8672	16	2	the	the	DET
ap-8672	16	3	literature	literature	NOUN
ap-8672	16	4	,	,	PUNCT
ap-8672	16	5	some	some	DET
ap-8672	16	6	works	work	NOUN
ap-8672	16	7	have	have	AUX
ap-8672	16	8	focused	focus	VERB
ap-8672	16	9	on	on	ADP
ap-8672	16	10	the	the	DET
ap-8672	16	11	serial	serial	ADJ
ap-8672	16	12	manipulator	manipulator	NOUN
ap-8672	16	13	robots	robot	NOUN
ap-8672	16	14	[	[	X
ap-8672	16	15	1–5	1–5	X
ap-8672	16	16	]	]	X
ap-8672	16	17	.	.	PUNCT
ap-8672	17	1	while	while	SCONJ
ap-8672	17	2	others	other	NOUN
ap-8672	17	3	have	have	AUX
ap-8672	17	4	dealt	deal	VERB
ap-8672	17	5	with	with	ADP
ap-8672	17	6	parallel	parallel	ADJ
ap-8672	17	7	robots	robot	NOUN
ap-8672	17	8	and	and	CCONJ
ap-8672	17	9	hybrid	hybrid	NOUN
ap-8672	17	10	robots	robot	NOUN
ap-8672	17	11	’	'	PUNCT
ap-8672	17	12	structure	structure	NOUN
ap-8672	17	13	[	[	X
ap-8672	17	14	6	6	NUM
ap-8672	17	15	,	,	PUNCT
ap-8672	17	16	7	7	NUM
ap-8672	17	17	]	]	PUNCT
ap-8672	17	18	.	.	PUNCT
ap-8672	18	1	in	in	ADP
ap-8672	18	2	addition	addition	NOUN
ap-8672	18	3	,	,	PUNCT
ap-8672	18	4	some	some	DET
ap-8672	18	5	research	research	NOUN
ap-8672	18	6	has	have	AUX
ap-8672	18	7	focused	focus	VERB
ap-8672	18	8	on	on	ADP
ap-8672	18	9	specific	specific	ADJ
ap-8672	18	10	robot	robot	NOUN
ap-8672	18	11	configurations	configuration	NOUN
ap-8672	18	12	,	,	PUNCT
ap-8672	18	13	such	such	ADJ
ap-8672	18	14	as	as	ADP
ap-8672	18	15	snake	snake	NOUN
ap-8672	18	16	robots	robot	NOUN
ap-8672	18	17	[	[	X
ap-8672	18	18	8	8	NUM
ap-8672	18	19	]	]	PUNCT
ap-8672	18	20	,	,	PUNCT
ap-8672	18	21	wheeled	wheeled	ADJ
ap-8672	18	22	robots	robot	NOUN
ap-8672	18	23	,	,	PUNCT
ap-8672	18	24	and	and	CCONJ
ap-8672	18	25	quadruped	quadrupe	VERB
ap-8672	18	26	robots	robot	NOUN
ap-8672	18	27	[	[	X
ap-8672	18	28	9	9	NUM
ap-8672	18	29	,	,	PUNCT
ap-8672	18	30	10	10	NUM
ap-8672	18	31	]	]	PUNCT
ap-8672	18	32	.	.	PUNCT
ap-8672	19	1	forward	forward	ADJ
ap-8672	19	2	kinematics	kinematic	NOUN
ap-8672	19	3	(	(	PUNCT
ap-8672	19	4	fk	fk	INTJ
ap-8672	19	5	)	)	PUNCT
ap-8672	19	6	does	do	AUX
ap-8672	19	7	not	not	PART
ap-8672	19	8	pose	pose	VERB
ap-8672	19	9	significant	significant	ADJ
ap-8672	19	10	difficulties	difficulty	NOUN
ap-8672	19	11	because	because	SCONJ
ap-8672	19	12	it	it	PRON
ap-8672	19	13	involves	involve	VERB
ap-8672	19	14	a	a	DET
ap-8672	19	15	mathematically	mathematically	ADV
ap-8672	19	16	straightforward	straightforward	ADJ
ap-8672	19	17	multiplication	multiplication	NOUN
ap-8672	19	18	of	of	ADP
ap-8672	19	19	successive	successive	ADJ
ap-8672	19	20	homogeneous	homogeneous	ADJ
ap-8672	19	21	matrices	matrix	NOUN
ap-8672	19	22	that	that	PRON
ap-8672	19	23	lead	lead	VERB
ap-8672	19	24	the	the	DET
ap-8672	19	25	end	end	NOUN
ap-8672	19	26	-	-	PUNCT
ap-8672	19	27	effector	effector	NOUN
ap-8672	19	28	to	to	ADP
ap-8672	19	29	a	a	DET
ap-8672	19	30	corresponding	correspond	VERB
ap-8672	19	31	position	position	NOUN
ap-8672	19	32	and	and	CCONJ
ap-8672	19	33	orientation	orientation	NOUN
ap-8672	19	34	[	[	X
ap-8672	19	35	11–13	11–13	NUM
ap-8672	19	36	]	]	X
ap-8672	19	37	.	.	PUNCT
ap-8672	20	1	however	however	ADV
ap-8672	20	2	,	,	PUNCT
ap-8672	20	3	inverse	inverse	ADJ
ap-8672	20	4	kinematics	kinematic	NOUN
ap-8672	20	5	(	(	PUNCT
ap-8672	20	6	ik	ik	X
ap-8672	20	7	)	)	PUNCT
ap-8672	20	8	entails	entail	VERB
ap-8672	20	9	specifying	specify	VERB
ap-8672	20	10	a	a	DET
ap-8672	20	11	precise	precise	ADJ
ap-8672	20	12	pose	pose	NOUN
ap-8672	20	13	for	for	ADP
ap-8672	20	14	the	the	DET
ap-8672	20	15	robot	robot	NOUN
ap-8672	20	16	’s	’s	PART
ap-8672	20	17	end	end	NOUN
ap-8672	20	18	-	-	PUNCT
ap-8672	20	19	effector	effector	NOUN
ap-8672	20	20	within	within	ADP
ap-8672	20	21	its	its	PRON
ap-8672	20	22	workspace	workspace	NOUN
ap-8672	20	23	,	,	PUNCT
ap-8672	20	24	defined	define	VERB
ap-8672	20	25	by	by	ADP
ap-8672	20	26	its	its	PRON
ap-8672	20	27	position	position	NOUN
ap-8672	20	28	and	and	CCONJ
ap-8672	20	29	orientation	orientation	NOUN
ap-8672	20	30	in	in	ADP
ap-8672	20	31	euclidean	euclidean	ADJ
ap-8672	20	32	space	space	NOUN
ap-8672	20	33	r3	r3	PROPN
ap-8672	20	34	.	.	PUNCT
ap-8672	21	1	in	in	ADP
ap-8672	21	2	this	this	DET
ap-8672	21	3	context	context	NOUN
ap-8672	21	4	,	,	PUNCT
ap-8672	21	5	finding	find	VERB
ap-8672	21	6	a	a	DET
ap-8672	21	7	suitable	suitable	ADJ
ap-8672	21	8	set	set	NOUN
ap-8672	21	9	of	of	ADP
ap-8672	21	10	joint	joint	ADJ
ap-8672	21	11	configurations	configuration	NOUN
ap-8672	21	12	that	that	PRON
ap-8672	21	13	enables	enable	VERB
ap-8672	21	14	the	the	DET
ap-8672	21	15	end	end	NOUN
ap-8672	21	16	-	-	PUNCT
ap-8672	21	17	effector	effector	NOUN
ap-8672	21	18	to	to	PART
ap-8672	21	19	reach	reach	VERB
ap-8672	21	20	the	the	DET
ap-8672	21	21	desired	desire	VERB
ap-8672	21	22	positions	position	NOUN
ap-8672	21	23	is	be	AUX
ap-8672	21	24	the	the	DET
ap-8672	21	25	main	main	ADJ
ap-8672	21	26	challenge	challenge	NOUN
ap-8672	21	27	.	.	PUNCT
ap-8672	22	1	in	in	ADP
ap-8672	22	2	the	the	DET
ap-8672	22	3	literature	literature	NOUN
ap-8672	22	4	,	,	PUNCT
ap-8672	22	5	inverse	inverse	NOUN
ap-8672	22	6	kinematics	kinematic	NOUN
ap-8672	22	7	(	(	PUNCT
ap-8672	22	8	ik	ik	ADJ
ap-8672	22	9	)	)	PUNCT
ap-8672	22	10	problem	problem	NOUN
ap-8672	22	11	has	have	AUX
ap-8672	22	12	been	be	AUX
ap-8672	22	13	addressed	address	VERB
ap-8672	22	14	by	by	ADP
ap-8672	22	15	several	several	ADJ
ap-8672	22	16	authors	author	NOUN
ap-8672	22	17	using	use	VERB
ap-8672	22	18	different	different	ADJ
ap-8672	22	19	approaches	approach	NOUN
ap-8672	22	20	.	.	PUNCT
ap-8672	23	1	basically	basically	ADV
ap-8672	23	2	,	,	PUNCT
ap-8672	23	3	these	these	DET
ap-8672	23	4	approaches	approach	NOUN
ap-8672	23	5	can	can	AUX
ap-8672	23	6	be	be	AUX
ap-8672	23	7	categorised	categorise	VERB
ap-8672	23	8	into	into	ADP
ap-8672	23	9	analytical	analytical	ADJ
ap-8672	23	10	approaches	approach	NOUN
ap-8672	23	11	,	,	PUNCT
ap-8672	23	12	numerical	numerical	ADJ
ap-8672	23	13	approaches	approach	NOUN
ap-8672	23	14	,	,	PUNCT
ap-8672	23	15	and	and	CCONJ
ap-8672	23	16	hybrid	hybrid	ADJ
ap-8672	23	17	approaches	approach	NOUN
ap-8672	23	18	,	,	PUNCT
ap-8672	23	19	using	use	VERB
ap-8672	23	20	different	different	ADJ
ap-8672	23	21	methods	method	NOUN
ap-8672	23	22	in	in	ADP
ap-8672	23	23	order	order	NOUN
ap-8672	23	24	to	to	PART
ap-8672	23	25	achieve	achieve	VERB
ap-8672	23	26	a	a	DET
ap-8672	23	27	smooth	smooth	ADJ
ap-8672	23	28	solution	solution	NOUN
ap-8672	23	29	.	.	PUNCT
ap-8672	24	1	where	where	SCONJ
ap-8672	24	2	the	the	DET
ap-8672	24	3	primary	primary	ADJ
ap-8672	24	4	aim	aim	NOUN
ap-8672	24	5	of	of	ADP
ap-8672	24	6	these	these	DET
ap-8672	24	7	methods	method	NOUN
ap-8672	24	8	is	be	AUX
ap-8672	24	9	to	to	PART
ap-8672	24	10	provide	provide	VERB
ap-8672	24	11	flexible	flexible	ADJ
ap-8672	24	12	mobility	mobility	NOUN
ap-8672	24	13	for	for	ADP
ap-8672	24	14	the	the	DET
ap-8672	24	15	robot	robot	NOUN
ap-8672	24	16	,	,	PUNCT
ap-8672	24	17	which	which	PRON
ap-8672	24	18	is	be	AUX
ap-8672	24	19	dependent	dependent	ADJ
ap-8672	24	20	on	on	ADP
ap-8672	24	21	the	the	DET
ap-8672	24	22	robot	robot	NOUN
ap-8672	24	23	’s	’s	PART
ap-8672	24	24	geometric	geometric	ADJ
ap-8672	24	25	structure	structure	NOUN
ap-8672	24	26	and	and	CCONJ
ap-8672	24	27	the	the	DET
ap-8672	24	28	number	number	NOUN
ap-8672	24	29	of	of	ADP
ap-8672	24	30	degrees	degree	NOUN
ap-8672	24	31	of	of	ADP
ap-8672	24	32	freedom	freedom	NOUN
ap-8672	24	33	(	(	PUNCT
ap-8672	24	34	dof	dof	NOUN
ap-8672	24	35	)	)	PUNCT
ap-8672	25	1	[	[	X
ap-8672	25	2	14	14	NUM
ap-8672	25	3	,	,	PUNCT
ap-8672	25	4	15	15	NUM
ap-8672	25	5	]	]	PUNCT
ap-8672	25	6	.	.	PUNCT
ap-8672	26	1	in	in	ADP
ap-8672	26	2	euclidian	euclidian	ADJ
ap-8672	26	3	space	space	NOUN
ap-8672	26	4	r3	r3	PROPN
ap-8672	26	5	,	,	PUNCT
ap-8672	26	6	analytical	analytical	ADJ
ap-8672	26	7	methods	method	NOUN
ap-8672	26	8	provide	provide	VERB
ap-8672	26	9	closed	closed	ADJ
ap-8672	26	10	-	-	PUNCT
ap-8672	26	11	form	form	NOUN
ap-8672	26	12	solutions	solution	NOUN
ap-8672	26	13	for	for	ADP
ap-8672	26	14	the	the	DET
ap-8672	26	15	inverse	inverse	NOUN
ap-8672	26	16	kinematics	kinematic	NOUN
ap-8672	26	17	under	under	ADP
ap-8672	26	18	certain	certain	ADJ
ap-8672	26	19	conditions	condition	NOUN
ap-8672	26	20	:	:	PUNCT
ap-8672	26	21	(	(	PUNCT
ap-8672	26	22	1	1	X
ap-8672	26	23	.	.	PUNCT
ap-8672	26	24	)	)	PUNCT
ap-8672	27	1	when	when	SCONJ
ap-8672	27	2	three	three	NUM
ap-8672	27	3	successive	successive	ADJ
ap-8672	27	4	revolute	revolute	ADJ
ap-8672	27	5	joint	joint	ADJ
ap-8672	27	6	axes	axis	NOUN
ap-8672	27	7	intersect	intersect	ADJ
ap-8672	27	8	at	at	ADP
ap-8672	27	9	the	the	DET
ap-8672	27	10	same	same	ADJ
ap-8672	27	11	point	point	NOUN
ap-8672	27	12	;	;	PUNCT
ap-8672	27	13	(	(	PUNCT
ap-8672	27	14	2	2	NUM
ap-8672	27	15	.	.	PUNCT
ap-8672	27	16	)	)	PUNCT
ap-8672	28	1	when	when	SCONJ
ap-8672	28	2	three	three	NUM
ap-8672	28	3	consecutive	consecutive	ADJ
ap-8672	28	4	revolute	revolute	ADJ
ap-8672	28	5	joint	joint	ADJ
ap-8672	28	6	axes	axis	NOUN
ap-8672	28	7	are	be	AUX
ap-8672	28	8	parallel	parallel	ADJ
ap-8672	28	9	.	.	PUNCT
ap-8672	29	1	mathematically	mathematically	ADV
ap-8672	29	2	,	,	PUNCT
ap-8672	29	3	analytical	analytical	ADJ
ap-8672	29	4	methods	method	NOUN
ap-8672	29	5	are	be	AUX
ap-8672	29	6	represented	represent	VERB
ap-8672	29	7	by	by	ADP
ap-8672	29	8	the	the	DET
ap-8672	29	9	following	follow	VERB
ap-8672	29	10	general	general	ADJ
ap-8672	29	11	matrix	matrix	NOUN
ap-8672	29	12	equation	equation	NOUN
ap-8672	29	13	[	[	X
ap-8672	29	14	16–19	16–19	NUM
ap-8672	29	15	]	]	PUNCT
ap-8672	29	16	:	:	PUNCT
ap-8672	29	17	0t1	0t1	NUM
ap-8672	30	1	1t2	1t2	NUM
ap-8672	30	2	2t3	2t3	NUM
ap-8672	30	3	3t4	3t4	NUM
ap-8672	30	4	4t5	4t5	NUM
ap-8672	30	5	5t6	5t6	NUM
ap-8672	30	6	=	=	SYM
ap-8672	30	7	t	t	PROPN
ap-8672	30	8	,	,	PUNCT
ap-8672	30	9	(	(	PUNCT
ap-8672	30	10	1	1	X
ap-8672	30	11	)	)	PUNCT
ap-8672	30	12	326	326	NUM
ap-8672	30	13	https://doi.org/10.14311/ap.2023.63.0326	https://doi.org/10.14311/ap.2023.63.0326	NOUN
ap-8672	30	14	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-8672	30	15	https://www.cvut.cz/en	https://www.cvut.cz/en	NUM
ap-8672	30	16	vol	vol	NOUN
ap-8672	30	17	.	.	PROPN
ap-8672	31	1	63	63	NUM
ap-8672	31	2	no	no	NOUN
ap-8672	31	3	.	.	PUNCT
ap-8672	32	1	5/2023	5/2023	NUM
ap-8672	32	2	geometric	geometric	ADJ
ap-8672	32	3	approach	approach	NOUN
ap-8672	32	4	to	to	ADP
ap-8672	32	5	solving	solve	VERB
ap-8672	32	6	inverse	inverse	ADJ
ap-8672	32	7	kinematics	kinematic	NOUN
ap-8672	32	8	of	of	ADP
ap-8672	32	9	six	six	NUM
ap-8672	32	10	dof	dof	NOUN
ap-8672	32	11	robot	robot	NOUN
ap-8672	32	12	where	where	SCONJ
ap-8672	32	13	j−1tj	j−1tj	NOUN
ap-8672	32	14	represents	represent	VERB
ap-8672	32	15	the	the	DET
ap-8672	32	16	homogeneous	homogeneous	ADJ
ap-8672	32	17	matrix	matrix	NOUN
ap-8672	32	18	between	between	ADP
ap-8672	32	19	frames	frame	NOUN
ap-8672	32	20	j	j	PROPN
ap-8672	32	21	and	and	CCONJ
ap-8672	32	22	j	j	PROPN
ap-8672	32	23	−	−	PROPN
ap-8672	32	24	1	1	NUM
ap-8672	32	25	,	,	PUNCT
ap-8672	32	26	and	and	CCONJ
ap-8672	32	27	t	t	PROPN
ap-8672	32	28	is	be	AUX
ap-8672	32	29	the	the	DET
ap-8672	32	30	matrix	matrix	NOUN
ap-8672	32	31	representing	represent	VERB
ap-8672	32	32	the	the	DET
ap-8672	32	33	desired	desire	VERB
ap-8672	32	34	position	position	NOUN
ap-8672	32	35	of	of	ADP
ap-8672	32	36	the	the	DET
ap-8672	32	37	end	end	NOUN
ap-8672	32	38	-	-	PUNCT
ap-8672	32	39	effector	effector	NOUN
ap-8672	32	40	.	.	PUNCT
ap-8672	33	1	however	however	ADV
ap-8672	33	2	,	,	PUNCT
ap-8672	33	3	solutions	solution	NOUN
ap-8672	33	4	to	to	ADP
ap-8672	33	5	these	these	DET
ap-8672	33	6	problems	problem	NOUN
ap-8672	33	7	are	be	AUX
ap-8672	33	8	typically	typically	ADV
ap-8672	33	9	derived	derive	VERB
ap-8672	33	10	through	through	ADP
ap-8672	33	11	nonlinear	nonlinear	ADJ
ap-8672	33	12	and	and	CCONJ
ap-8672	33	13	coupled	couple	VERB
ap-8672	33	14	equations	equation	NOUN
ap-8672	33	15	that	that	PRON
ap-8672	33	16	often	often	ADV
ap-8672	33	17	involve	involve	VERB
ap-8672	33	18	matrix	matrix	NOUN
ap-8672	33	19	calculations	calculation	NOUN
ap-8672	33	20	.	.	PUNCT
ap-8672	34	1	several	several	ADJ
ap-8672	34	2	methods	method	NOUN
ap-8672	34	3	have	have	AUX
ap-8672	34	4	been	be	AUX
ap-8672	34	5	developed	develop	VERB
ap-8672	34	6	in	in	ADP
ap-8672	34	7	the	the	DET
ap-8672	34	8	literature	literature	NOUN
ap-8672	34	9	to	to	PART
ap-8672	34	10	address	address	VERB
ap-8672	34	11	these	these	DET
ap-8672	34	12	challenges	challenge	NOUN
ap-8672	34	13	.	.	PUNCT
ap-8672	35	1	notable	notable	ADJ
ap-8672	35	2	approaches	approach	NOUN
ap-8672	35	3	include	include	VERB
ap-8672	35	4	pieper	pieper	NOUN
ap-8672	35	5	’s	’s	PART
ap-8672	35	6	method	method	NOUN
ap-8672	35	7	[	[	X
ap-8672	35	8	16	16	NUM
ap-8672	35	9	]	]	X
ap-8672	35	10	,	,	PUNCT
ap-8672	35	11	which	which	PRON
ap-8672	35	12	is	be	AUX
ap-8672	35	13	applicable	applicable	ADJ
ap-8672	35	14	to	to	ADP
ap-8672	35	15	robots	robot	NOUN
ap-8672	35	16	with	with	ADP
ap-8672	35	17	three	three	NUM
ap-8672	35	18	articulatory	articulatory	ADJ
ap-8672	35	19	joints	joint	NOUN
ap-8672	35	20	featuring	feature	VERB
ap-8672	35	21	concurrent	concurrent	ADJ
ap-8672	35	22	axes	axis	NOUN
ap-8672	35	23	or	or	CCONJ
ap-8672	35	24	three	three	NUM
ap-8672	35	25	prismatic	prismatic	ADJ
ap-8672	35	26	joints	joint	NOUN
ap-8672	35	27	.	.	PUNCT
ap-8672	36	1	raghavan	raghavan	PROPN
ap-8672	36	2	and	and	CCONJ
ap-8672	36	3	roth	roth	PROPN
ap-8672	36	4	[	[	X
ap-8672	36	5	17	17	NUM
ap-8672	36	6	]	]	PUNCT
ap-8672	36	7	have	have	AUX
ap-8672	36	8	formulated	formulate	VERB
ap-8672	36	9	a	a	DET
ap-8672	36	10	system	system	NOUN
ap-8672	36	11	of	of	ADP
ap-8672	36	12	16	16	NUM
ap-8672	36	13	multivariate	multivariate	NOUN
ap-8672	36	14	polynomials	polynomial	NOUN
ap-8672	36	15	for	for	ADP
ap-8672	36	16	closed	closed	ADJ
ap-8672	36	17	-	-	PUNCT
ap-8672	36	18	loop	loop	NOUN
ap-8672	36	19	solutions	solution	NOUN
ap-8672	36	20	,	,	PUNCT
ap-8672	36	21	suitable	suitable	ADJ
ap-8672	36	22	for	for	ADP
ap-8672	36	23	6	6	NUM
ap-8672	36	24	-	-	PUNCT
ap-8672	36	25	revolute	revolute	NOUN
ap-8672	36	26	manipulators	manipulator	NOUN
ap-8672	36	27	(	(	PUNCT
ap-8672	36	28	6r	6r	NUM
ap-8672	36	29	)	)	PUNCT
ap-8672	36	30	.	.	PUNCT
ap-8672	37	1	their	their	PRON
ap-8672	37	2	solutions	solution	NOUN
ap-8672	37	3	are	be	AUX
ap-8672	37	4	based	base	VERB
ap-8672	37	5	on	on	ADP
ap-8672	37	6	successive	successive	ADJ
ap-8672	37	7	elimination	elimination	NOUN
ap-8672	37	8	techniques	technique	NOUN
ap-8672	37	9	.	.	PUNCT
ap-8672	38	1	paul	paul	PROPN
ap-8672	38	2	’s	’s	PART
ap-8672	38	3	method	method	NOUN
ap-8672	38	4	[	[	X
ap-8672	38	5	18	18	NUM
ap-8672	38	6	]	]	PUNCT
ap-8672	38	7	involves	involve	VERB
ap-8672	38	8	isolating	isolate	VERB
ap-8672	38	9	and	and	CCONJ
ap-8672	38	10	solving	solve	VERB
ap-8672	38	11	variables	variable	NOUN
ap-8672	38	12	one	one	NUM
ap-8672	38	13	by	by	ADP
ap-8672	38	14	one	one	NUM
ap-8672	38	15	,	,	PUNCT
ap-8672	38	16	making	make	VERB
ap-8672	38	17	it	it	PRON
ap-8672	38	18	suitable	suitable	ADJ
ap-8672	38	19	for	for	ADP
ap-8672	38	20	most	most	ADJ
ap-8672	38	21	industrial	industrial	ADJ
ap-8672	38	22	manipulator	manipulator	NOUN
ap-8672	38	23	robots	robot	NOUN
ap-8672	38	24	.	.	PUNCT
ap-8672	39	1	gan	gan	VERB
ap-8672	39	2	et	et	PROPN
ap-8672	39	3	al	al	PROPN
ap-8672	39	4	.	.	PUNCT
ap-8672	40	1	[	[	X
ap-8672	40	2	19	19	NUM
ap-8672	40	3	]	]	PUNCT
ap-8672	40	4	have	have	AUX
ap-8672	40	5	derived	derive	VERB
ap-8672	40	6	an	an	DET
ap-8672	40	7	inverse	inverse	NOUN
ap-8672	40	8	kinematics	kinematic	NOUN
ap-8672	40	9	(	(	PUNCT
ap-8672	40	10	ik	ik	ADJ
ap-8672	40	11	)	)	PUNCT
ap-8672	40	12	solution	solution	NOUN
ap-8672	40	13	for	for	ADP
ap-8672	40	14	a	a	DET
ap-8672	40	15	5	5	NUM
ap-8672	40	16	-	-	PUNCT
ap-8672	40	17	dof	dof	ADJ
ap-8672	40	18	robotic	robotic	ADJ
ap-8672	40	19	arm	arm	NOUN
ap-8672	40	20	(	(	PUNCT
ap-8672	40	21	pioneer	pioneer	NOUN
ap-8672	40	22	2	2	NUM
ap-8672	40	23	)	)	PUNCT
ap-8672	40	24	,	,	PUNCT
ap-8672	40	25	which	which	PRON
ap-8672	40	26	has	have	VERB
ap-8672	40	27	similarities	similarity	NOUN
ap-8672	40	28	to	to	ADP
ap-8672	40	29	paul	paul	PROPN
ap-8672	40	30	’s	’s	PART
ap-8672	40	31	method	method	NOUN
ap-8672	40	32	.	.	PUNCT
ap-8672	41	1	other	other	ADJ
ap-8672	41	2	studies	study	NOUN
ap-8672	41	3	have	have	AUX
ap-8672	41	4	investigated	investigate	VERB
ap-8672	41	5	the	the	DET
ap-8672	41	6	ik	ik	PROPN
ap-8672	41	7	problem	problem	NOUN
ap-8672	41	8	of	of	ADP
ap-8672	41	9	robots	robot	NOUN
ap-8672	41	10	with	with	ADP
ap-8672	41	11	redundancy	redundancy	NOUN
ap-8672	41	12	,	,	PUNCT
ap-8672	41	13	providing	provide	VERB
ap-8672	41	14	analytical	analytical	ADJ
ap-8672	41	15	solutions	solution	NOUN
ap-8672	41	16	based	base	VERB
ap-8672	41	17	on	on	ADP
ap-8672	41	18	various	various	ADJ
ap-8672	41	19	assumptions	assumption	NOUN
ap-8672	41	20	related	relate	VERB
ap-8672	41	21	to	to	ADP
ap-8672	41	22	the	the	DET
ap-8672	41	23	redundancy	redundancy	NOUN
ap-8672	41	24	settings	setting	NOUN
ap-8672	41	25	[	[	X
ap-8672	41	26	20–22	20–22	NUM
ap-8672	41	27	]	]	SYM
ap-8672	41	28	.	.	PUNCT
ap-8672	42	1	numerous	numerous	ADJ
ap-8672	42	2	works	work	NOUN
ap-8672	42	3	have	have	AUX
ap-8672	42	4	addressed	address	VERB
ap-8672	42	5	the	the	DET
ap-8672	42	6	numerical	numerical	ADJ
ap-8672	42	7	approach	approach	NOUN
ap-8672	42	8	to	to	PART
ap-8672	42	9	solve	solve	VERB
ap-8672	42	10	the	the	DET
ap-8672	42	11	inverse	inverse	NOUN
ap-8672	42	12	kinematics	kinematic	NOUN
ap-8672	42	13	(	(	PUNCT
ap-8672	42	14	ik	ik	PROPN
ap-8672	42	15	)	)	PUNCT
ap-8672	42	16	problem	problem	NOUN
ap-8672	42	17	[	[	X
ap-8672	42	18	1	1	NUM
ap-8672	42	19	–	–	PUNCT
ap-8672	42	20	3	3	NUM
ap-8672	42	21	,	,	PUNCT
ap-8672	42	22	23–27	23–27	NUM
ap-8672	42	23	]	]	PUNCT
ap-8672	42	24	.	.	PUNCT
ap-8672	43	1	the	the	DET
ap-8672	43	2	majority	majority	NOUN
ap-8672	43	3	of	of	ADP
ap-8672	43	4	these	these	DET
ap-8672	43	5	solutions	solution	NOUN
ap-8672	43	6	have	have	AUX
ap-8672	43	7	been	be	AUX
ap-8672	43	8	derived	derive	VERB
ap-8672	43	9	using	use	VERB
ap-8672	43	10	different	different	ADJ
ap-8672	43	11	methods	method	NOUN
ap-8672	43	12	,	,	PUNCT
ap-8672	43	13	including	include	VERB
ap-8672	43	14	numerical	numerical	ADJ
ap-8672	43	15	algorithms	algorithm	NOUN
ap-8672	43	16	[	[	X
ap-8672	43	17	2	2	NUM
ap-8672	43	18	]	]	PUNCT
ap-8672	43	19	,	,	PUNCT
ap-8672	43	20	neural	neural	ADJ
ap-8672	43	21	networks	network	NOUN
ap-8672	43	22	[	[	X
ap-8672	43	23	24	24	NUM
ap-8672	43	24	,	,	PUNCT
ap-8672	43	25	28	28	NUM
ap-8672	43	26	]	]	PUNCT
ap-8672	43	27	,	,	PUNCT
ap-8672	43	28	genetic	genetic	ADJ
ap-8672	43	29	algorithms	algorithm	NOUN
ap-8672	43	30	[	[	X
ap-8672	43	31	29	29	NUM
ap-8672	43	32	]	]	PUNCT
ap-8672	43	33	,	,	PUNCT
ap-8672	43	34	fuzzy	fuzzy	ADJ
ap-8672	43	35	logic	logic	NOUN
ap-8672	43	36	,	,	PUNCT
ap-8672	43	37	and	and	CCONJ
ap-8672	43	38	others	other	NOUN
ap-8672	43	39	.	.	PUNCT
ap-8672	44	1	within	within	ADP
ap-8672	44	2	this	this	DET
ap-8672	44	3	context	context	NOUN
ap-8672	44	4	,	,	PUNCT
ap-8672	44	5	numerical	numerical	ADJ
ap-8672	44	6	algorithms	algorithm	NOUN
ap-8672	44	7	have	have	AUX
ap-8672	44	8	been	be	AUX
ap-8672	44	9	used	use	VERB
ap-8672	44	10	to	to	PART
ap-8672	44	11	ensure	ensure	VERB
ap-8672	44	12	convergence	convergence	NOUN
ap-8672	44	13	and	and	CCONJ
ap-8672	44	14	accuracy	accuracy	NOUN
ap-8672	44	15	.	.	PUNCT
ap-8672	45	1	however	however	ADV
ap-8672	45	2	,	,	PUNCT
ap-8672	45	3	it	it	PRON
ap-8672	45	4	’s	’	VERB
ap-8672	45	5	important	important	ADJ
ap-8672	45	6	to	to	PART
ap-8672	45	7	note	note	VERB
ap-8672	45	8	that	that	SCONJ
ap-8672	45	9	many	many	ADJ
ap-8672	45	10	of	of	ADP
ap-8672	45	11	the	the	DET
ap-8672	45	12	currently	currently	ADV
ap-8672	45	13	available	available	ADJ
ap-8672	45	14	methods	method	NOUN
ap-8672	45	15	are	be	AUX
ap-8672	45	16	plagued	plague	VERB
ap-8672	45	17	by	by	ADP
ap-8672	45	18	high	high	ADJ
ap-8672	45	19	computational	computational	ADJ
ap-8672	45	20	costs	cost	NOUN
ap-8672	45	21	and	and	CCONJ
ap-8672	45	22	the	the	DET
ap-8672	45	23	generation	generation	NOUN
ap-8672	45	24	of	of	ADP
ap-8672	45	25	unrealistic	unrealistic	ADJ
ap-8672	45	26	poses	pose	NOUN
ap-8672	45	27	[	[	X
ap-8672	45	28	14	14	NUM
ap-8672	45	29	]	]	PUNCT
ap-8672	45	30	.	.	PUNCT
ap-8672	46	1	in	in	ADP
ap-8672	46	2	addition	addition	NOUN
ap-8672	46	3	,	,	PUNCT
ap-8672	46	4	some	some	DET
ap-8672	46	5	robots	robot	NOUN
ap-8672	46	6	with	with	ADP
ap-8672	46	7	7	7	NUM
ap-8672	46	8	degrees	degree	NOUN
ap-8672	46	9	of	of	ADP
ap-8672	46	10	freedom	freedom	NOUN
ap-8672	46	11	(	(	PUNCT
ap-8672	46	12	7	7	NUM
ap-8672	46	13	-	-	PUNCT
ap-8672	46	14	dof	dof	NOUN
ap-8672	46	15	)	)	PUNCT
ap-8672	46	16	have	have	AUX
ap-8672	46	17	been	be	AUX
ap-8672	46	18	addressed	address	VERB
ap-8672	46	19	using	use	VERB
ap-8672	46	20	numerical	numerical	ADJ
ap-8672	46	21	approaches	approach	NOUN
ap-8672	46	22	,	,	PUNCT
ap-8672	46	23	aiming	aim	VERB
ap-8672	46	24	to	to	PART
ap-8672	46	25	resolve	resolve	VERB
ap-8672	46	26	redundancy	redundancy	NOUN
ap-8672	46	27	issues	issue	NOUN
ap-8672	46	28	in	in	ADP
ap-8672	46	29	the	the	DET
ap-8672	46	30	inverse	inverse	NOUN
ap-8672	46	31	kinematics	kinematic	NOUN
ap-8672	46	32	(	(	PUNCT
ap-8672	46	33	ik	ik	ADJ
ap-8672	46	34	)	)	PUNCT
ap-8672	46	35	solutions	solution	NOUN
ap-8672	46	36	.	.	PUNCT
ap-8672	47	1	among	among	ADP
ap-8672	47	2	these	these	PRON
ap-8672	47	3	,	,	PUNCT
ap-8672	47	4	y.	y.	PROPN
ap-8672	47	5	wenbin	wenbin	PROPN
ap-8672	47	6	and	and	CCONJ
ap-8672	47	7	s.	s.	PROPN
ap-8672	47	8	lei	lei	PROPN
ap-8672	47	9	[	[	X
ap-8672	47	10	30	30	NUM
ap-8672	47	11	]	]	PUNCT
ap-8672	47	12	have	have	AUX
ap-8672	47	13	studied	study	VERB
ap-8672	47	14	an	an	DET
ap-8672	47	15	iterative	iterative	NOUN
ap-8672	47	16	approach	approach	NOUN
ap-8672	47	17	combining	combine	VERB
ap-8672	47	18	two	two	NUM
ap-8672	47	19	techniques	technique	NOUN
ap-8672	47	20	:	:	PUNCT
ap-8672	47	21	(	(	PUNCT
ap-8672	47	22	a	a	X
ap-8672	47	23	)	)	PUNCT
ap-8672	47	24	a	a	DET
ap-8672	47	25	technique	technique	NOUN
ap-8672	47	26	based	base	VERB
ap-8672	47	27	on	on	ADP
ap-8672	47	28	“	"	PUNCT
ap-8672	47	29	fixed	fix	VERB
ap-8672	47	30	joint	joint	ADJ
ap-8672	47	31	angles	angle	NOUN
ap-8672	47	32	”	"	PUNCT
ap-8672	47	33	,	,	PUNCT
ap-8672	47	34	(	(	PUNCT
ap-8672	47	35	b	b	X
ap-8672	47	36	)	)	PUNCT
ap-8672	47	37	a	a	DET
ap-8672	47	38	technique	technique	NOUN
ap-8672	47	39	involving	involve	VERB
ap-8672	47	40	a	a	DET
ap-8672	47	41	“	"	PUNCT
ap-8672	47	42	two	two	NUM
ap-8672	47	43	-	-	PUNCT
ap-8672	47	44	phase	phase	NOUN
ap-8672	47	45	computational	computational	ADJ
ap-8672	47	46	optimisation	optimisation	NOUN
ap-8672	47	47	algorithm	algorithm	NOUN
ap-8672	47	48	using	use	VERB
ap-8672	47	49	weighted	weight	VERB
ap-8672	47	50	least	least	ADJ
ap-8672	47	51	-	-	PUNCT
ap-8672	47	52	norm	norm	NOUN
ap-8672	47	53	”	"	PUNCT
ap-8672	47	54	.	.	PUNCT
ap-8672	48	1	in	in	ADP
ap-8672	48	2	addition	addition	NOUN
ap-8672	48	3	,	,	PUNCT
ap-8672	48	4	b.	b.	PROPN
ap-8672	48	5	ma	ma	PROPN
ap-8672	48	6	et	et	PROPN
ap-8672	48	7	al	al	PROPN
ap-8672	48	8	.	.	PUNCT
ap-8672	49	1	[	[	X
ap-8672	49	2	31	31	NUM
ap-8672	49	3	]	]	PUNCT
ap-8672	49	4	have	have	AUX
ap-8672	49	5	presented	present	VERB
ap-8672	49	6	a	a	DET
ap-8672	49	7	hybrid	hybrid	ADJ
ap-8672	49	8	ik	ik	ADJ
ap-8672	49	9	solution	solution	NOUN
ap-8672	49	10	for	for	ADP
ap-8672	49	11	7	7	NUM
ap-8672	49	12	-	-	PUNCT
ap-8672	49	13	dof	dof	NOUN
ap-8672	49	14	robots	robot	NOUN
ap-8672	49	15	,	,	PUNCT
ap-8672	49	16	based	base	VERB
ap-8672	49	17	on	on	ADP
ap-8672	49	18	two	two	NUM
ap-8672	49	19	analytical	analytical	ADJ
ap-8672	49	20	techniques	technique	NOUN
ap-8672	49	21	that	that	PRON
ap-8672	49	22	consider	consider	VERB
ap-8672	49	23	redundant	redundant	ADJ
ap-8672	49	24	parameters	parameter	NOUN
ap-8672	49	25	to	to	PART
ap-8672	49	26	produce	produce	VERB
ap-8672	49	27	approximate	approximate	ADJ
ap-8672	49	28	solutions	solution	NOUN
ap-8672	49	29	,	,	PUNCT
ap-8672	49	30	followed	follow	VERB
ap-8672	49	31	by	by	ADP
ap-8672	49	32	a	a	DET
ap-8672	49	33	numerical	numerical	ADJ
ap-8672	49	34	algorithm	algorithm	NOUN
ap-8672	49	35	that	that	SCONJ
ap-8672	49	36	minimises	minimise	NOUN
ap-8672	49	37	errors	error	NOUN
ap-8672	49	38	to	to	PART
ap-8672	49	39	achieve	achieve	VERB
ap-8672	49	40	convergence	convergence	NOUN
ap-8672	49	41	of	of	ADP
ap-8672	49	42	the	the	DET
ap-8672	49	43	solution	solution	NOUN
ap-8672	49	44	.	.	PUNCT
ap-8672	50	1	this	this	DET
ap-8672	50	2	paper	paper	NOUN
ap-8672	50	3	introduces	introduce	VERB
ap-8672	50	4	a	a	DET
ap-8672	50	5	novel	novel	ADJ
ap-8672	50	6	approach	approach	NOUN
ap-8672	50	7	based	base	VERB
ap-8672	50	8	on	on	ADP
ap-8672	50	9	the	the	DET
ap-8672	50	10	geometric	geometric	ADJ
ap-8672	50	11	description	description	NOUN
ap-8672	50	12	of	of	ADP
ap-8672	50	13	a	a	DET
ap-8672	50	14	robot	robot	NOUN
ap-8672	50	15	to	to	PART
ap-8672	50	16	solve	solve	VERB
ap-8672	50	17	the	the	DET
ap-8672	50	18	inverse	inverse	NOUN
ap-8672	50	19	kinematics	kinematic	NOUN
ap-8672	50	20	(	(	PUNCT
ap-8672	50	21	ik	ik	ADJ
ap-8672	50	22	)	)	PUNCT
ap-8672	50	23	problem	problem	NOUN
ap-8672	50	24	.	.	PUNCT
ap-8672	51	1	the	the	DET
ap-8672	51	2	approach	approach	NOUN
ap-8672	51	3	is	be	AUX
ap-8672	51	4	based	base	VERB
ap-8672	51	5	on	on	ADP
ap-8672	51	6	vector	vector	NOUN
ap-8672	51	7	calculus	calculus	NOUN
ap-8672	51	8	and	and	CCONJ
ap-8672	51	9	trigonometric	trigonometric	ADJ
ap-8672	51	10	relations	relation	NOUN
ap-8672	51	11	and	and	CCONJ
ap-8672	51	12	offers	offer	VERB
ap-8672	51	13	a	a	DET
ap-8672	51	14	significant	significant	ADJ
ap-8672	51	15	advantage	advantage	NOUN
ap-8672	51	16	by	by	ADP
ap-8672	51	17	providing	provide	VERB
ap-8672	51	18	solutions	solution	NOUN
ap-8672	51	19	through	through	ADP
ap-8672	51	20	simple	simple	ADJ
ap-8672	51	21	and	and	CCONJ
ap-8672	51	22	decoupled	decouple	VERB
ap-8672	51	23	linear	linear	ADJ
ap-8672	51	24	equations	equation	NOUN
ap-8672	51	25	.	.	PUNCT
ap-8672	52	1	this	this	PRON
ap-8672	52	2	eliminates	eliminate	VERB
ap-8672	52	3	the	the	DET
ap-8672	52	4	need	need	NOUN
ap-8672	52	5	to	to	PART
ap-8672	52	6	solve	solve	VERB
ap-8672	52	7	the	the	DET
ap-8672	52	8	complex	complex	ADJ
ap-8672	52	9	ik	ik	PROPN
ap-8672	52	10	problem	problem	NOUN
ap-8672	52	11	using	use	VERB
ap-8672	52	12	matrices	matrix	NOUN
ap-8672	52	13	and	and	CCONJ
ap-8672	52	14	numerical	numerical	ADJ
ap-8672	52	15	methods	method	NOUN
ap-8672	52	16	.	.	PUNCT
ap-8672	53	1	to	to	PART
ap-8672	53	2	assess	assess	VERB
ap-8672	53	3	the	the	DET
ap-8672	53	4	feasibility	feasibility	NOUN
ap-8672	53	5	and	and	CCONJ
ap-8672	53	6	accuracy	accuracy	NOUN
ap-8672	53	7	of	of	ADP
ap-8672	53	8	this	this	DET
ap-8672	53	9	approach	approach	NOUN
ap-8672	53	10	,	,	PUNCT
ap-8672	53	11	we	we	PRON
ap-8672	53	12	conducted	conduct	VERB
ap-8672	53	13	matlab	matlab	PROPN
ap-8672	53	14	simulations	simulation	NOUN
ap-8672	53	15	and	and	CCONJ
ap-8672	53	16	an	an	DET
ap-8672	53	17	experimental	experimental	ADJ
ap-8672	53	18	study	study	NOUN
ap-8672	53	19	involving	involve	VERB
ap-8672	53	20	the	the	DET
ap-8672	53	21	design	design	NOUN
ap-8672	53	22	and	and	CCONJ
ap-8672	53	23	construction	construction	NOUN
ap-8672	53	24	of	of	ADP
ap-8672	53	25	a	a	DET
ap-8672	53	26	6	6	NUM
ap-8672	53	27	-	-	PUNCT
ap-8672	53	28	degree	degree	NOUN
ap-8672	53	29	-	-	PUNCT
ap-8672	53	30	of	of	ADP
ap-8672	53	31	-	-	PUNCT
ap-8672	53	32	freedom	freedom	NOUN
ap-8672	53	33	(	(	PUNCT
ap-8672	53	34	6	6	NUM
ap-8672	53	35	-	-	PUNCT
ap-8672	53	36	dof	dof	ADJ
ap-8672	53	37	)	)	PUNCT
ap-8672	53	38	robot	robot	NOUN
ap-8672	53	39	.	.	PUNCT
ap-8672	54	1	by	by	ADP
ap-8672	54	2	instructing	instruct	VERB
ap-8672	54	3	the	the	DET
ap-8672	54	4	robot	robot	NOUN
ap-8672	54	5	’s	’s	PART
ap-8672	54	6	end	end	NOUN
ap-8672	54	7	-	-	PUNCT
ap-8672	54	8	effector	effector	NOUN
ap-8672	54	9	to	to	PART
ap-8672	54	10	follow	follow	VERB
ap-8672	54	11	predefined	predefined	ADJ
ap-8672	54	12	trajectories	trajectory	NOUN
ap-8672	54	13	,	,	PUNCT
ap-8672	54	14	our	our	PRON
ap-8672	54	15	approach	approach	NOUN
ap-8672	54	16	successfully	successfully	ADV
ap-8672	54	17	converted	convert	VERB
ap-8672	54	18	cartesian	cartesian	ADJ
ap-8672	54	19	coordinates	coordinate	NOUN
ap-8672	54	20	into	into	ADP
ap-8672	54	21	joint	joint	ADJ
ap-8672	54	22	angle	angle	NOUN
ap-8672	54	23	coordinates	coordinate	NOUN
ap-8672	54	24	in	in	ADP
ap-8672	54	25	both	both	CCONJ
ap-8672	54	26	the	the	DET
ap-8672	54	27	simulation	simulation	NOUN
ap-8672	54	28	and	and	CCONJ
ap-8672	54	29	the	the	DET
ap-8672	54	30	experiment	experiment	NOUN
ap-8672	54	31	.	.	PUNCT
ap-8672	55	1	as	as	ADP
ap-8672	55	2	a	a	DET
ap-8672	55	3	result	result	NOUN
ap-8672	55	4	,	,	PUNCT
ap-8672	55	5	the	the	DET
ap-8672	55	6	robot	robot	NOUN
ap-8672	55	7	was	be	AUX
ap-8672	55	8	able	able	ADJ
ap-8672	55	9	to	to	PART
ap-8672	55	10	accurately	accurately	ADV
ap-8672	55	11	track	track	VERB
ap-8672	55	12	the	the	DET
ap-8672	55	13	predefined	predefine	VERB
ap-8672	55	14	trajectories	trajectory	NOUN
ap-8672	55	15	.	.	PUNCT
ap-8672	56	1	we	we	PRON
ap-8672	56	2	also	also	ADV
ap-8672	56	3	performed	perform	VERB
ap-8672	56	4	a	a	DET
ap-8672	56	5	comparative	comparative	ADJ
ap-8672	56	6	analysis	analysis	NOUN
ap-8672	56	7	between	between	ADP
ap-8672	56	8	our	our	PRON
ap-8672	56	9	approach	approach	NOUN
ap-8672	56	10	and	and	CCONJ
ap-8672	56	11	paul	paul	PROPN
ap-8672	56	12	’s	’s	PART
ap-8672	56	13	method	method	NOUN
ap-8672	56	14	for	for	ADP
ap-8672	56	15	a	a	DET
ap-8672	56	16	similar	similar	ADJ
ap-8672	56	17	robot	robot	NOUN
ap-8672	56	18	arm	arm	NOUN
ap-8672	56	19	,	,	PUNCT
ap-8672	56	20	as	as	SCONJ
ap-8672	56	21	presented	present	VERB
ap-8672	56	22	in	in	ADP
ap-8672	56	23	reference	reference	NOUN
ap-8672	56	24	[	[	X
ap-8672	56	25	32	32	NUM
ap-8672	56	26	]	]	PUNCT
ap-8672	56	27	.	.	PUNCT
ap-8672	57	1	this	this	DET
ap-8672	57	2	comparison	comparison	NOUN
ap-8672	57	3	revealed	reveal	VERB
ap-8672	57	4	significant	significant	ADJ
ap-8672	57	5	consistency	consistency	NOUN
ap-8672	57	6	and	and	CCONJ
ap-8672	57	7	similarity	similarity	NOUN
ap-8672	57	8	in	in	ADP
ap-8672	57	9	the	the	DET
ap-8672	57	10	results	result	NOUN
ap-8672	57	11	,	,	PUNCT
ap-8672	57	12	confirming	confirm	VERB
ap-8672	57	13	the	the	DET
ap-8672	57	14	validity	validity	NOUN
ap-8672	57	15	and	and	CCONJ
ap-8672	57	16	reliability	reliability	NOUN
ap-8672	57	17	of	of	ADP
ap-8672	57	18	our	our	PRON
ap-8672	57	19	proposed	propose	VERB
ap-8672	57	20	approach	approach	NOUN
ap-8672	57	21	.	.	PUNCT
ap-8672	58	1	2	2	X
ap-8672	58	2	.	.	X
ap-8672	58	3	principle	principle	NOUN
ap-8672	58	4	of	of	ADP
ap-8672	58	5	the	the	DET
ap-8672	58	6	approach	approach	NOUN
ap-8672	58	7	for	for	ADP
ap-8672	58	8	inverse	inverse	NOUN
ap-8672	58	9	kinematics	kinematic	NOUN
ap-8672	58	10	an	an	DET
ap-8672	58	11	angle	angle	NOUN
ap-8672	58	12	between	between	ADP
ap-8672	58	13	two	two	NUM
ap-8672	58	14	given	give	VERB
ap-8672	58	15	vectors	vector	NOUN
ap-8672	58	16	−→	−→	NOUN
ap-8672	58	17	u	u	NOUN
ap-8672	58	18	and	and	CCONJ
ap-8672	58	19	−→	−→	ADJ
ap-8672	58	20	v	v	NOUN
ap-8672	58	21	in	in	ADP
ap-8672	58	22	r3	r3	PROPN
ap-8672	58	23	is	be	AUX
ap-8672	58	24	defined	define	VERB
ap-8672	58	25	by	by	ADP
ap-8672	58	26	its	its	PRON
ap-8672	58	27	magnitude	magnitude	NOUN
ap-8672	58	28	and	and	CCONJ
ap-8672	58	29	its	its	PRON
ap-8672	58	30	conventional	conventional	ADJ
ap-8672	58	31	orientation	orientation	NOUN
ap-8672	58	32	(	(	PUNCT
ap-8672	58	33	rotation	rotation	NOUN
ap-8672	58	34	sense	sense	NOUN
ap-8672	58	35	)	)	PUNCT
ap-8672	58	36	.	.	PUNCT
ap-8672	59	1	mathematically	mathematically	ADV
ap-8672	59	2	,	,	PUNCT
ap-8672	59	3	the	the	DET
ap-8672	59	4	magnitude	magnitude	NOUN
ap-8672	59	5	is	be	AUX
ap-8672	59	6	given	give	VERB
ap-8672	59	7	by	by	ADP
ap-8672	59	8	the	the	DET
ap-8672	59	9	cosine	cosine	NOUN
ap-8672	59	10	law	law	NOUN
ap-8672	59	11	.	.	PUNCT
ap-8672	60	1	−→	−→	ADJ
ap-8672	60	2	u	u	NOUN
ap-8672	60	3	.	.	PUNCT
ap-8672	61	1	−→	−→	NOUN
ap-8672	61	2	v	v	X
ap-8672	61	3	=	=	SYM
ap-8672	61	4	u.v	u.v	PROPN
ap-8672	61	5	cos(−→u	cos(−→u	INTJ
ap-8672	61	6	,	,	PUNCT
ap-8672	61	7	−→	−→	NOUN
ap-8672	61	8	v	v	NOUN
ap-8672	61	9	)	)	PUNCT
ap-8672	61	10	,	,	PUNCT
ap-8672	61	11	(	(	PUNCT
ap-8672	61	12	2	2	X
ap-8672	61	13	)	)	PUNCT
ap-8672	61	14	where	where	SCONJ
ap-8672	61	15	u	u	NOUN
ap-8672	61	16	and	and	CCONJ
ap-8672	61	17	v	v	PROPN
ap-8672	61	18	represent	represent	VERB
ap-8672	61	19	the	the	DET
ap-8672	61	20	magnitude	magnitude	NOUN
ap-8672	61	21	of	of	ADP
ap-8672	61	22	the	the	DET
ap-8672	61	23	vectors	vector	NOUN
ap-8672	61	24	−→	−→	NOUN
ap-8672	61	25	u	u	NOUN
ap-8672	61	26	and	and	CCONJ
ap-8672	61	27	−→	−→	NOUN
ap-8672	61	28	v	v	NOUN
ap-8672	61	29	,	,	PUNCT
ap-8672	61	30	respectively	respectively	ADV
ap-8672	61	31	.	.	PUNCT
ap-8672	62	1	the	the	DET
ap-8672	62	2	rotation	rotation	NOUN
ap-8672	62	3	sense	sense	NOUN
ap-8672	62	4	of	of	ADP
ap-8672	62	5	the	the	DET
ap-8672	62	6	angle	angle	NOUN
ap-8672	62	7	is	be	AUX
ap-8672	62	8	described	describe	VERB
ap-8672	62	9	by	by	ADP
ap-8672	62	10	applying	apply	VERB
ap-8672	62	11	the	the	DET
ap-8672	62	12	right	right	ADJ
ap-8672	62	13	hand	hand	NOUN
ap-8672	62	14	rule	rule	NOUN
ap-8672	62	15	between	between	ADP
ap-8672	62	16	three	three	NUM
ap-8672	62	17	vectors	vector	NOUN
ap-8672	62	18	:	:	PUNCT
ap-8672	62	19	−→	−→	NOUN
ap-8672	62	20	u	u	NOUN
ap-8672	62	21	and	and	CCONJ
ap-8672	62	22	−→	−→	NOUN
ap-8672	62	23	v	v	NOUN
ap-8672	62	24	and	and	CCONJ
ap-8672	62	25	−→	−→	NOUN
ap-8672	62	26	w	w	NOUN
ap-8672	62	27	.	.	PUNCT
ap-8672	63	1	where	where	SCONJ
ap-8672	63	2	−→	−→	NOUN
ap-8672	63	3	w	w	NOUN
ap-8672	63	4	is	be	AUX
ap-8672	63	5	the	the	DET
ap-8672	63	6	cross	cross	NOUN
ap-8672	63	7	product	product	NOUN
ap-8672	63	8	of	of	ADP
ap-8672	63	9	−→	−→	NOUN
ap-8672	63	10	u	u	NOUN
ap-8672	63	11	and	and	CCONJ
ap-8672	63	12	−→	−→	NOUN
ap-8672	63	13	v	v	NOUN
ap-8672	63	14	or	or	CCONJ
ap-8672	63	15	any	any	DET
ap-8672	63	16	other	other	ADJ
ap-8672	63	17	orthonormal	orthonormal	ADJ
ap-8672	63	18	vector	vector	NOUN
ap-8672	63	19	to	to	ADP
ap-8672	63	20	the	the	DET
ap-8672	63	21	plane	plane	NOUN
ap-8672	63	22	formed	form	VERB
ap-8672	63	23	by	by	ADP
ap-8672	63	24	−→	−→	NOUN
ap-8672	63	25	u	u	NOUN
ap-8672	63	26	and	and	CCONJ
ap-8672	63	27	−→	−→	ADJ
ap-8672	63	28	v	v	NOUN
ap-8672	63	29	(	(	PUNCT
ap-8672	63	30	plane	plane	NOUN
ap-8672	63	31	-	-	PUNCT
ap-8672	63	32	uv	uv	NOUN
ap-8672	63	33	)	)	PUNCT
ap-8672	63	34	,	,	PUNCT
ap-8672	63	35	as	as	SCONJ
ap-8672	63	36	illustrated	illustrate	VERB
ap-8672	63	37	in	in	ADP
ap-8672	63	38	figure	figure	NOUN
ap-8672	63	39	1	1	NUM
ap-8672	63	40	.	.	PUNCT
ap-8672	64	1	a	a	DET
ap-8672	64	2	helpful	helpful	ADJ
ap-8672	64	3	relation	relation	NOUN
ap-8672	64	4	between	between	ADP
ap-8672	64	5	the	the	DET
ap-8672	64	6	cross	cross	NOUN
ap-8672	64	7	product	product	NOUN
ap-8672	64	8	and	and	CCONJ
ap-8672	64	9	the	the	DET
ap-8672	64	10	determinant	determinant	ADJ
ap-8672	64	11	can	can	AUX
ap-8672	64	12	be	be	AUX
ap-8672	64	13	defined	define	VERB
ap-8672	64	14	as	as	SCONJ
ap-8672	64	15	follows	follow	VERB
ap-8672	64	16	:	:	PUNCT
ap-8672	64	17	−→	−→	NOUN
ap-8672	64	18	u	u	NOUN
ap-8672	64	19	∧	∧	PROPN
ap-8672	64	20	−→	−→	NOUN
ap-8672	64	21	v	v	NOUN
ap-8672	64	22	=	=	SYM
ap-8672	64	23	u.v	u.v	PROPN
ap-8672	64	24	sin(−→u	sin(−→u	INTJ
ap-8672	64	25	,	,	PUNCT
ap-8672	64	26	−→	−→	NOUN
ap-8672	64	27	v	v	NOUN
ap-8672	64	28	)	)	PUNCT
ap-8672	64	29	−→nw	−→nw	PROPN
ap-8672	64	30	.	.	PUNCT
ap-8672	65	1	(	(	PUNCT
ap-8672	65	2	3	3	X
ap-8672	65	3	)	)	PUNCT
ap-8672	65	4	by	by	ADP
ap-8672	65	5	multiplying	multiply	VERB
ap-8672	65	6	both	both	DET
ap-8672	65	7	sides	side	NOUN
ap-8672	65	8	of	of	ADP
ap-8672	65	9	equation	equation	NOUN
ap-8672	65	10	(	(	PUNCT
ap-8672	65	11	3	3	NUM
ap-8672	65	12	)	)	PUNCT
ap-8672	65	13	by	by	ADP
ap-8672	65	14	the	the	DET
ap-8672	65	15	same	same	ADJ
ap-8672	65	16	vector	vector	NOUN
ap-8672	65	17	−→nw	−→nw	PROPN
ap-8672	65	18	and	and	CCONJ
ap-8672	65	19	dividing	divide	VERB
ap-8672	65	20	by	by	ADP
ap-8672	65	21	the	the	DET
ap-8672	65	22	scalar	scalar	ADJ
ap-8672	65	23	uv	uv	NOUN
ap-8672	65	24	,	,	PUNCT
ap-8672	65	25	we	we	PRON
ap-8672	65	26	obtain	obtain	VERB
ap-8672	65	27	a	a	DET
ap-8672	65	28	new	new	ADJ
ap-8672	65	29	equality	equality	NOUN
ap-8672	65	30	in	in	ADP
ap-8672	65	31	equation	equation	NOUN
ap-8672	65	32	(	(	PUNCT
ap-8672	65	33	4	4	NUM
ap-8672	65	34	):	):	SYM
ap-8672	65	35	1	1	NUM
ap-8672	65	36	uv	uv	NOUN
ap-8672	65	37	(	(	PUNCT
ap-8672	65	38	−→u	−→u	PUNCT
ap-8672	65	39	∧	∧	PROPN
ap-8672	65	40	−→	−→	NOUN
ap-8672	65	41	v	v	NOUN
ap-8672	65	42	)	)	PUNCT
ap-8672	65	43	.−→nw	.−→nw	PUNCT
ap-8672	66	1	=	=	PUNCT
ap-8672	66	2	sin(−→u	sin(−→u	INTJ
ap-8672	66	3	,	,	PUNCT
ap-8672	66	4	−→	−→	NOUN
ap-8672	66	5	v	v	NOUN
ap-8672	66	6	)	)	PUNCT
ap-8672	66	7	.(−→nw	.(−→nw	PUNCT
ap-8672	66	8	)	)	PUNCT
ap-8672	66	9	2	2	X
ap-8672	66	10	.	.	PUNCT
ap-8672	67	1	(	(	PUNCT
ap-8672	67	2	4	4	X
ap-8672	67	3	)	)	PUNCT
ap-8672	67	4	327	327	NUM
ap-8672	67	5	n.	n.	NOUN
ap-8672	67	6	hadidi	hadidi	PROPN
ap-8672	67	7	,	,	PUNCT
ap-8672	67	8	m.	m.	NOUN
ap-8672	67	9	bouaziz	bouaziz	PROPN
ap-8672	67	10	,	,	PUNCT
ap-8672	67	11	c.	c.	PROPN
ap-8672	67	12	mahfoudi	mahfoudi	PROPN
ap-8672	67	13	,	,	PUNCT
ap-8672	67	14	m.	m.	NOUN
ap-8672	67	15	zaharuddin	zaharuddin	PROPN
ap-8672	67	16	acta	acta	PROPN
ap-8672	67	17	polytechnica	polytechnica	PROPN
ap-8672	67	18	figure	figure	NOUN
ap-8672	67	19	1	1	NUM
ap-8672	67	20	.	.	PUNCT
ap-8672	68	1	right	right	ADJ
ap-8672	68	2	hand	hand	NOUN
ap-8672	68	3	rule	rule	NOUN
ap-8672	68	4	and	and	CCONJ
ap-8672	68	5	vector	vector	NOUN
ap-8672	68	6	order	order	NOUN
ap-8672	68	7	.	.	PUNCT
ap-8672	69	1	equation	equation	NOUN
ap-8672	69	2	(	(	PUNCT
ap-8672	69	3	4	4	X
ap-8672	69	4	)	)	PUNCT
ap-8672	69	5	leads	lead	VERB
ap-8672	69	6	to	to	ADP
ap-8672	69	7	the	the	DET
ap-8672	69	8	equality	equality	NOUN
ap-8672	69	9	below	below	ADV
ap-8672	69	10	:	:	PUNCT
ap-8672	69	11	sin(−→u	sin(−→u	VERB
ap-8672	69	12	,	,	PUNCT
ap-8672	69	13	−→	−→	NOUN
ap-8672	69	14	v	v	NOUN
ap-8672	69	15	)	)	PUNCT
ap-8672	69	16	=	=	SYM
ap-8672	69	17	(	(	PUNCT
ap-8672	69	18	−→nu	−→nu	NUM
ap-8672	69	19	∧	∧	PROPN
ap-8672	69	20	−→nv	−→nv	NUM
ap-8672	69	21	.−→nw	.−→nw	PUNCT
ap-8672	69	22	)	)	PUNCT
ap-8672	70	1	=	=	PUNCT
ap-8672	71	1	det(−→nu	det(−→nu	PUNCT
ap-8672	71	2	,	,	PUNCT
ap-8672	71	3	−→nv	−→nv	NUM
ap-8672	71	4	,	,	PUNCT
ap-8672	71	5	−→nw	−→nw	PROPN
ap-8672	71	6	)	)	PUNCT
ap-8672	71	7	,	,	PUNCT
ap-8672	71	8	(	(	PUNCT
ap-8672	71	9	5	5	X
ap-8672	71	10	)	)	PUNCT
ap-8672	72	1	where	where	SCONJ
ap-8672	72	2	:	:	PUNCT
ap-8672	72	3	•	•	NUM
ap-8672	72	4	−→nu	−→nu	NOUN
ap-8672	72	5	=	=	PUNCT
ap-8672	72	6	−→	−→	NOUN
ap-8672	72	7	u	u	X
ap-8672	72	8	u	u	NOUN
ap-8672	72	9	and	and	CCONJ
ap-8672	72	10	−→nv	−→nv	NUM
ap-8672	72	11	=	=	PUNCT
ap-8672	73	1	−→	−→	NOUN
ap-8672	73	2	v	v	NUM
ap-8672	73	3	v	v	NOUN
ap-8672	73	4	are	be	AUX
ap-8672	73	5	two	two	NUM
ap-8672	73	6	unit	unit	NOUN
ap-8672	73	7	vectors	vector	NOUN
ap-8672	73	8	of	of	ADP
ap-8672	73	9	−→	−→	NOUN
ap-8672	73	10	u	u	NOUN
ap-8672	73	11	and	and	CCONJ
ap-8672	73	12	−→	−→	NOUN
ap-8672	73	13	v	v	NOUN
ap-8672	73	14	,	,	PUNCT
ap-8672	73	15	respectively	respectively	ADV
ap-8672	73	16	,	,	PUNCT
ap-8672	73	17	and	and	CCONJ
ap-8672	73	18	(	(	PUNCT
ap-8672	73	19	−→nw	−→nw	NOUN
ap-8672	73	20	)	)	PUNCT
ap-8672	73	21	2	2	NUM
ap-8672	73	22	=	=	SYM
ap-8672	73	23	1	1	NUM
ap-8672	73	24	,	,	PUNCT
ap-8672	73	25	•	•	NUM
ap-8672	73	26	det(−→nu	det(−→nu	PUNCT
ap-8672	73	27	,	,	PUNCT
ap-8672	73	28	−→nv	−→nv	NUM
ap-8672	73	29	,	,	PUNCT
ap-8672	73	30	−→nw	−→nw	NUM
ap-8672	73	31	)	)	PUNCT
ap-8672	74	1	=	=	PUNCT
ap-8672	74	2	(	(	PUNCT
ap-8672	74	3	−→nu	−→nu	NUM
ap-8672	74	4	∧	∧	PROPN
ap-8672	74	5	−→nv	−→nv	NUM
ap-8672	74	6	)	)	PUNCT
ap-8672	74	7	.−→nw	.−→nw	PUNCT
ap-8672	75	1	=	=	PUNCT
ap-8672	75	2	nwx	nwx	PROPN
ap-8672	75	3	nwy	nwy	PROPN
ap-8672	75	4	nwz	nwz	PROPN
ap-8672	75	5	nux	nux	PROPN
ap-8672	75	6	nuy	nuy	PROPN
ap-8672	75	7	nuz	nuz	PROPN
ap-8672	75	8	nvx	nvx	PROPN
ap-8672	75	9	nvy	nvy	PROPN
ap-8672	75	10	nvz	nvz	PROPN
ap-8672	75	11			PROPN
ap-8672	75	12	is	be	AUX
ap-8672	75	13	the	the	DET
ap-8672	75	14	determinant	determinant	NOUN
ap-8672	75	15	of	of	ADP
ap-8672	75	16	the	the	DET
ap-8672	75	17	three	three	NUM
ap-8672	75	18	vector	vector	NOUN
ap-8672	75	19	(	(	PUNCT
ap-8672	75	20	or	or	CCONJ
ap-8672	75	21	mixed	mixed	ADJ
ap-8672	75	22	product	product	NOUN
ap-8672	75	23	)	)	PUNCT
ap-8672	75	24	,	,	PUNCT
ap-8672	75	25	which	which	PRON
ap-8672	75	26	can	can	AUX
ap-8672	75	27	also	also	ADV
ap-8672	75	28	be	be	AUX
ap-8672	75	29	developed	develop	VERB
ap-8672	75	30	as	as	ADP
ap-8672	75	31	folows	folow	NOUN
ap-8672	75	32	:	:	PUNCT
ap-8672	75	33	det(−→nu	det(−→nu	X
ap-8672	75	34	,	,	PUNCT
ap-8672	75	35	−→nv	−→nv	NUM
ap-8672	75	36	,	,	PUNCT
ap-8672	75	37	−→nw	−→nw	NUM
ap-8672	75	38	)	)	PUNCT
ap-8672	75	39	=	=	PUNCT
ap-8672	76	1	nwx(nuy.nvz	nwx(nuy.nvz	PRON
ap-8672	76	2	−	−	ADP
ap-8672	76	3	nvy.nuz)−	nvy.nuz)−	PUNCT
ap-8672	76	4	nwy(nux.nvz	nwy(nux.nvz	PROPN
ap-8672	76	5	−	−	PROPN
ap-8672	76	6	nvx.nuz)+	nvx.nuz)+	PROPN
ap-8672	76	7	nwz(nux.nvy	nwz(nux.nvy	VERB
ap-8672	76	8	−	−	NOUN
ap-8672	76	9	nvx.nuy	nvx.nuy	NUM
ap-8672	76	10	)	)	PUNCT
ap-8672	76	11	.	.	PUNCT
ap-8672	77	1	an	an	DET
ap-8672	77	2	important	important	ADJ
ap-8672	77	3	property	property	NOUN
ap-8672	77	4	of	of	ADP
ap-8672	77	5	the	the	DET
ap-8672	77	6	determinant	determinant	NOUN
ap-8672	77	7	regarding	regard	VERB
ap-8672	77	8	its	its	PRON
ap-8672	77	9	sign	sign	NOUN
ap-8672	77	10	is	be	AUX
ap-8672	77	11	obtained	obtain	VERB
ap-8672	77	12	by	by	ADP
ap-8672	77	13	swapping	swap	VERB
ap-8672	77	14	two	two	NUM
ap-8672	77	15	columns	column	NOUN
ap-8672	77	16	[	[	X
ap-8672	77	17	33	33	NUM
ap-8672	77	18	]	]	PUNCT
ap-8672	77	19	.	.	PUNCT
ap-8672	78	1	det(−→w	det(−→w	NOUN
ap-8672	78	2	,	,	PUNCT
ap-8672	78	3	−→	−→	NOUN
ap-8672	78	4	u	u	NOUN
ap-8672	78	5	,	,	PUNCT
ap-8672	78	6	−→	−→	NOUN
ap-8672	78	7	v	v	NOUN
ap-8672	78	8	)	)	PUNCT
ap-8672	78	9	=	=	SYM
ap-8672	78	10	(	(	PUNCT
ap-8672	78	11	−1	−1	NOUN
ap-8672	78	12	)	)	PUNCT
ap-8672	79	1	det(−→w	det(−→w	NOUN
ap-8672	79	2	,	,	PUNCT
ap-8672	79	3	−→	−→	NOUN
ap-8672	79	4	v	v	NOUN
ap-8672	79	5	,	,	PUNCT
ap-8672	79	6	−→	−→	NOUN
ap-8672	79	7	u	u	NOUN
ap-8672	79	8	)	)	PUNCT
ap-8672	79	9	.	.	PUNCT
ap-8672	80	1	this	this	PRON
ap-8672	80	2	implies	imply	VERB
ap-8672	80	3	that	that	SCONJ
ap-8672	80	4	the	the	DET
ap-8672	80	5	sign	sign	NOUN
ap-8672	80	6	of	of	ADP
ap-8672	80	7	the	the	DET
ap-8672	80	8	determinant	determinant	ADJ
ap-8672	80	9	changes	change	NOUN
ap-8672	80	10	with	with	ADP
ap-8672	80	11	variations	variation	NOUN
ap-8672	80	12	in	in	ADP
ap-8672	80	13	angular	angular	ADJ
ap-8672	80	14	orientation	orientation	NOUN
ap-8672	80	15	.	.	PUNCT
ap-8672	81	1	the	the	DET
ap-8672	81	2	magnitude	magnitude	NOUN
ap-8672	81	3	and	and	CCONJ
ap-8672	81	4	direction	direction	NOUN
ap-8672	81	5	sense	sense	NOUN
ap-8672	81	6	of	of	ADP
ap-8672	81	7	each	each	DET
ap-8672	81	8	joint	joint	ADJ
ap-8672	81	9	angle	angle	NOUN
ap-8672	81	10	can	can	AUX
ap-8672	81	11	be	be	AUX
ap-8672	81	12	determined	determine	VERB
ap-8672	81	13	by	by	ADP
ap-8672	81	14	substituting	substitute	VERB
ap-8672	81	15	these	these	DET
ap-8672	81	16	two	two	NUM
ap-8672	81	17	previous	previous	ADJ
ap-8672	81	18	parameters	parameter	NOUN
ap-8672	81	19	of	of	ADP
ap-8672	81	20	equation	equation	NOUN
ap-8672	81	21	(	(	PUNCT
ap-8672	81	22	2	2	NUM
ap-8672	81	23	)	)	PUNCT
ap-8672	81	24	and	and	CCONJ
ap-8672	81	25	equation	equation	NOUN
ap-8672	81	26	(	(	PUNCT
ap-8672	81	27	5	5	NUM
ap-8672	81	28	)	)	PUNCT
ap-8672	81	29	as	as	ADP
ap-8672	81	30	arguments	argument	NOUN
ap-8672	81	31	into	into	ADP
ap-8672	81	32	the	the	DET
ap-8672	81	33	mathematical	mathematical	ADJ
ap-8672	81	34	function	function	NOUN
ap-8672	81	35	atan2(x	atan2(x	PROPN
ap-8672	81	36	,	,	PUNCT
ap-8672	81	37	y	y	PROPN
ap-8672	81	38	)	)	PUNCT
ap-8672	81	39	,	,	PUNCT
ap-8672	81	40	see	see	VERB
ap-8672	81	41	appendix	appendix	NOUN
ap-8672	81	42	a.1	a.1	PRON
ap-8672	81	43	.	.	PUNCT
ap-8672	82	1	β	β	X
ap-8672	82	2	=	=	SYM
ap-8672	82	3	atan2(det(−→nu	atan2(det(−→nu	PROPN
ap-8672	82	4	,	,	PUNCT
ap-8672	82	5	−→nv	−→nv	PROPN
ap-8672	82	6	,	,	PUNCT
ap-8672	82	7	−→nw	−→nw	PROPN
ap-8672	82	8	)	)	PUNCT
ap-8672	82	9	,	,	PUNCT
ap-8672	82	10	cos(−→u	cos(−→u	INTJ
ap-8672	82	11	,	,	PUNCT
ap-8672	82	12	−→	−→	NOUN
ap-8672	82	13	v	v	NOUN
ap-8672	82	14	)	)	PUNCT
ap-8672	82	15	)	)	PUNCT
ap-8672	82	16	.	.	PUNCT
ap-8672	83	1	(	(	PUNCT
ap-8672	83	2	6	6	NUM
ap-8672	83	3	)	)	SYM
ap-8672	83	4	3	3	NUM
ap-8672	83	5	.	.	PUNCT
ap-8672	83	6	robot	robot	NOUN
ap-8672	83	7	structure	structure	NOUN
ap-8672	83	8	and	and	CCONJ
ap-8672	83	9	geometry	geometry	NOUN
ap-8672	83	10	figure	figure	NOUN
ap-8672	83	11	2	2	NUM
ap-8672	83	12	shows	show	VERB
ap-8672	83	13	a	a	DET
ap-8672	83	14	right	right	ADJ
ap-8672	83	15	upper	upper	ADJ
ap-8672	83	16	limb	limb	NOUN
ap-8672	83	17	with	with	ADP
ap-8672	83	18	6	6	NUM
ap-8672	83	19	-	-	PUNCT
ap-8672	83	20	dof	dof	NOUN
ap-8672	83	21	of	of	ADP
ap-8672	83	22	a	a	DET
ap-8672	83	23	biped	biped	ADJ
ap-8672	83	24	robot	robot	NOUN
ap-8672	83	25	distributed	distribute	VERB
ap-8672	83	26	as	as	SCONJ
ap-8672	83	27	follows	follow	VERB
ap-8672	83	28	:	:	PUNCT
ap-8672	83	29	3	3	NUM
ap-8672	83	30	-	-	PUNCT
ap-8672	83	31	dof	dof	NOUN
ap-8672	83	32	at	at	ADP
ap-8672	83	33	the	the	DET
ap-8672	83	34	shoulder	shoulder	NOUN
ap-8672	83	35	,	,	PUNCT
ap-8672	83	36	1	1	NUM
ap-8672	83	37	-	-	PUNCT
ap-8672	83	38	dof	dof	NOUN
ap-8672	83	39	at	at	ADP
ap-8672	83	40	the	the	DET
ap-8672	83	41	elbow	elbow	NOUN
ap-8672	83	42	,	,	PUNCT
ap-8672	83	43	and	and	CCONJ
ap-8672	83	44	2	2	NUM
ap-8672	83	45	-	-	PUNCT
ap-8672	83	46	dof	dof	NOUN
ap-8672	83	47	at	at	ADP
ap-8672	83	48	the	the	DET
ap-8672	83	49	wrist	wrist	NOUN
ap-8672	83	50	.	.	PUNCT
ap-8672	84	1	these	these	DET
ap-8672	84	2	components	component	NOUN
ap-8672	84	3	are	be	AUX
ap-8672	84	4	interconnected	interconnect	VERB
ap-8672	84	5	by	by	ADP
ap-8672	84	6	three	three	NUM
ap-8672	84	7	geometric	geometric	ADJ
ap-8672	84	8	links	link	NOUN
ap-8672	84	9	:	:	PUNCT
ap-8672	84	10	the	the	DET
ap-8672	84	11	arm	arm	NOUN
ap-8672	84	12	(	(	PUNCT
ap-8672	84	13	la	la	PROPN
ap-8672	84	14	)	)	PUNCT
ap-8672	84	15	,	,	PUNCT
ap-8672	84	16	the	the	DET
ap-8672	84	17	forearm	forearm	NOUN
ap-8672	84	18	(	(	PUNCT
ap-8672	84	19	lf	lf	NOUN
ap-8672	84	20	)	)	PUNCT
ap-8672	84	21	,	,	PUNCT
ap-8672	84	22	and	and	CCONJ
ap-8672	84	23	the	the	DET
ap-8672	84	24	hand	hand	NOUN
ap-8672	84	25	(	(	PUNCT
ap-8672	84	26	lh	lh	PROPN
ap-8672	84	27	)	)	PUNCT
ap-8672	84	28	.	.	PUNCT
ap-8672	85	1	their	their	PRON
ap-8672	85	2	lengths	length	NOUN
ap-8672	85	3	are	be	AUX
ap-8672	85	4	summarised	summarise	VERB
ap-8672	85	5	in	in	ADP
ap-8672	85	6	table	table	NOUN
ap-8672	85	7	1	1	NUM
ap-8672	85	8	.	.	PUNCT
ap-8672	86	1	links	link	NOUN
ap-8672	86	2	symbol	symbol	NOUN
ap-8672	86	3	value	value	NOUN
ap-8672	87	1	[	[	X
ap-8672	87	2	m	m	X
ap-8672	87	3	]	]	X
ap-8672	87	4	arm	arm	NOUN
ap-8672	87	5	la	la	NOUN
ap-8672	87	6	0.32	0.32	NUM
ap-8672	87	7	forearm	forearm	NOUN
ap-8672	87	8	lf	lf	ADP
ap-8672	87	9	0.25	0.25	NUM
ap-8672	87	10	hand	hand	NOUN
ap-8672	87	11	lh	lh	NOUN
ap-8672	87	12	0.12	0.12	NUM
ap-8672	87	13	table	table	NOUN
ap-8672	87	14	1	1	NUM
ap-8672	87	15	.	.	PUNCT
ap-8672	87	16	robot	robot	NOUN
ap-8672	87	17	link	link	NOUN
ap-8672	87	18	lengths	length	NOUN
ap-8672	87	19	.	.	PUNCT
ap-8672	88	1	328	328	NUM
ap-8672	88	2	vol	vol	NOUN
ap-8672	88	3	.	.	PUNCT
ap-8672	88	4	63	63	NUM
ap-8672	88	5	no	no	NOUN
ap-8672	88	6	.	.	PUNCT
ap-8672	89	1	5/2023	5/2023	NUM
ap-8672	89	2	geometric	geometric	ADJ
ap-8672	89	3	approach	approach	NOUN
ap-8672	89	4	to	to	ADP
ap-8672	89	5	solving	solve	VERB
ap-8672	89	6	inverse	inverse	ADJ
ap-8672	89	7	kinematics	kinematic	NOUN
ap-8672	89	8	of	of	ADP
ap-8672	89	9	six	six	NUM
ap-8672	89	10	dof	dof	NOUN
ap-8672	89	11	robot	robot	NOUN
ap-8672	89	12	(	(	PUNCT
ap-8672	89	13	a	a	NOUN
ap-8672	89	14	)	)	PUNCT
ap-8672	89	15	.	.	PUNCT
ap-8672	90	1	image	image	NOUN
ap-8672	90	2	of	of	ADP
ap-8672	90	3	manufactured	manufacture	VERB
ap-8672	90	4	robot	robot	NOUN
ap-8672	90	5	.	.	PUNCT
ap-8672	91	1	z0	z0	PROPN
ap-8672	91	2	y0	y0	PROPN
ap-8672	91	3	x0	x0	PROPN
ap-8672	91	4	y1	y1	NOUN
ap-8672	92	1	x1	x1	PROPN
ap-8672	92	2	z1	z1	NUM
ap-8672	92	3	x2	x2	PROPN
ap-8672	92	4	z2	z2	ADJ
ap-8672	92	5	y2	y2	NOUN
ap-8672	92	6	y3	y3	NOUN
ap-8672	92	7	x3	x3	ADJ
ap-8672	92	8	z3	z3	PROPN
ap-8672	92	9	z4	z4	PROPN
ap-8672	92	10	y4	y4	PROPN
ap-8672	92	11	x4	x4	PROPN
ap-8672	92	12	y5	y5	PROPN
ap-8672	92	13	x5	x5	PROPN
ap-8672	92	14	z5	z5	PROPN
ap-8672	92	15	z6	z6	PROPN
ap-8672	92	16	y6	y6	PROPN
ap-8672	92	17	x6	x6	PROPN
ap-8672	92	18	z7	z7	PROPN
ap-8672	92	19	y7	y7	PROPN
ap-8672	93	1	x7	x7	NOUN
ap-8672	93	2	la	la	INTJ
ap-8672	93	3	lf	lf	ADP
ap-8672	93	4	lh	lh	PROPN
ap-8672	93	5	(	(	PUNCT
ap-8672	93	6	b	b	NOUN
ap-8672	93	7	)	)	PUNCT
ap-8672	93	8	.	.	PUNCT
ap-8672	94	1	robot	robot	NOUN
ap-8672	94	2	’s	’s	PART
ap-8672	94	3	kinematic	kinematic	ADJ
ap-8672	94	4	chain	chain	NOUN
ap-8672	94	5	.	.	PUNCT
ap-8672	95	1	figure	figure	NOUN
ap-8672	95	2	2	2	NUM
ap-8672	95	3	.	.	PUNCT
ap-8672	96	1	right	right	ADJ
ap-8672	96	2	upper	upper	ADJ
ap-8672	96	3	limb	limb	NOUN
ap-8672	96	4	of	of	ADP
ap-8672	96	5	a	a	DET
ap-8672	96	6	biped	biped	ADJ
ap-8672	96	7	robot	robot	NOUN
ap-8672	96	8	and	and	CCONJ
ap-8672	96	9	frame	frame	NOUN
ap-8672	96	10	assignment	assignment	NOUN
ap-8672	96	11	according	accord	VERB
ap-8672	96	12	to	to	ADP
ap-8672	96	13	dh	dh	PROPN
ap-8672	96	14	.	.	PROPN
ap-8672	97	1	4	4	X
ap-8672	97	2	.	.	X
ap-8672	97	3	mathematical	mathematical	ADJ
ap-8672	97	4	modelling	modelling	NOUN
ap-8672	97	5	of	of	ADP
ap-8672	97	6	the	the	DET
ap-8672	97	7	robot	robot	NOUN
ap-8672	97	8	this	this	DET
ap-8672	97	9	section	section	NOUN
ap-8672	97	10	is	be	AUX
ap-8672	97	11	primarily	primarily	ADV
ap-8672	97	12	dedicated	dedicated	ADJ
ap-8672	97	13	to	to	ADP
ap-8672	97	14	developing	develop	VERB
ap-8672	97	15	the	the	DET
ap-8672	97	16	mathematical	mathematical	ADJ
ap-8672	97	17	model	model	NOUN
ap-8672	97	18	that	that	PRON
ap-8672	97	19	describes	describe	VERB
ap-8672	97	20	the	the	DET
ap-8672	97	21	inverse	inverse	NOUN
ap-8672	97	22	kinematics	kinematic	NOUN
ap-8672	97	23	(	(	PUNCT
ap-8672	97	24	ik	ik	ADJ
ap-8672	97	25	)	)	PUNCT
ap-8672	97	26	solutions	solution	NOUN
ap-8672	97	27	.	.	PUNCT
ap-8672	98	1	the	the	DET
ap-8672	98	2	approach	approach	NOUN
ap-8672	98	3	outlined	outline	VERB
ap-8672	98	4	below	below	ADV
ap-8672	98	5	provides	provide	VERB
ap-8672	98	6	the	the	DET
ap-8672	98	7	corresponding	correspond	VERB
ap-8672	98	8	actuator	actuator	NOUN
ap-8672	98	9	rotations	rotation	NOUN
ap-8672	98	10	for	for	ADP
ap-8672	98	11	each	each	DET
ap-8672	98	12	state	state	NOUN
ap-8672	98	13	of	of	ADP
ap-8672	98	14	the	the	DET
ap-8672	98	15	end	end	NOUN
ap-8672	98	16	-	-	PUNCT
ap-8672	98	17	effector	effector	NOUN
ap-8672	98	18	.	.	PUNCT
ap-8672	99	1	the	the	DET
ap-8672	99	2	following	follow	VERB
ap-8672	99	3	assumptions	assumption	NOUN
ap-8672	99	4	have	have	AUX
ap-8672	99	5	been	be	AUX
ap-8672	99	6	used	use	VERB
ap-8672	99	7	in	in	ADP
ap-8672	99	8	this	this	DET
ap-8672	99	9	work	work	NOUN
ap-8672	99	10	:	:	PUNCT
ap-8672	99	11	•	•	ADP
ap-8672	99	12	the	the	DET
ap-8672	99	13	shoulder	shoulder	NOUN
ap-8672	99	14	,	,	PUNCT
ap-8672	99	15	with	with	ADP
ap-8672	99	16	its	its	PRON
ap-8672	99	17	3	3	NUM
ap-8672	99	18	degrees	degree	NOUN
ap-8672	99	19	of	of	ADP
ap-8672	99	20	freedom	freedom	NOUN
ap-8672	99	21	(	(	PUNCT
ap-8672	99	22	3	3	NUM
ap-8672	99	23	dof	dof	NOUN
ap-8672	99	24	)	)	PUNCT
ap-8672	99	25	,	,	PUNCT
ap-8672	99	26	has	have	VERB
ap-8672	99	27	its	its	PRON
ap-8672	99	28	axes	axis	NOUN
ap-8672	99	29	of	of	ADP
ap-8672	99	30	rotation	rotation	NOUN
ap-8672	99	31	intersecting	intersect	VERB
ap-8672	99	32	at	at	ADP
ap-8672	99	33	the	the	DET
ap-8672	99	34	same	same	ADJ
ap-8672	99	35	point	point	NOUN
ap-8672	99	36	.	.	PUNCT
ap-8672	100	1	consequently	consequently	ADV
ap-8672	100	2	,	,	PUNCT
ap-8672	100	3	the	the	DET
ap-8672	100	4	shoulder	shoulder	NOUN
ap-8672	100	5	’s	’s	PART
ap-8672	100	6	rotational	rotational	ADJ
ap-8672	100	7	movement	movement	NOUN
ap-8672	100	8	can	can	AUX
ap-8672	100	9	be	be	AUX
ap-8672	100	10	treated	treat	VERB
ap-8672	100	11	as	as	ADP
ap-8672	100	12	a	a	DET
ap-8672	100	13	single	single	ADJ
ap-8672	100	14	geometric	geometric	ADJ
ap-8672	100	15	point	point	NOUN
ap-8672	100	16	.	.	PUNCT
ap-8672	101	1	•	•	NOUN
ap-8672	101	2	similarly	similarly	ADV
ap-8672	101	3	,	,	PUNCT
ap-8672	101	4	the	the	DET
ap-8672	101	5	same	same	ADJ
ap-8672	101	6	assumption	assumption	NOUN
ap-8672	101	7	has	have	AUX
ap-8672	101	8	been	be	AUX
ap-8672	101	9	applied	apply	VERB
ap-8672	101	10	to	to	ADP
ap-8672	101	11	the	the	DET
ap-8672	101	12	wrist	wrist	NOUN
ap-8672	101	13	,	,	PUNCT
ap-8672	101	14	which	which	PRON
ap-8672	101	15	has	have	VERB
ap-8672	101	16	2	2	NUM
ap-8672	101	17	dof	dof	NOUN
ap-8672	101	18	.	.	PUNCT
ap-8672	102	1	consequently	consequently	ADV
ap-8672	102	2	,	,	PUNCT
ap-8672	102	3	the	the	DET
ap-8672	102	4	wrist	wrist	NOUN
ap-8672	102	5	is	be	AUX
ap-8672	102	6	also	also	ADV
ap-8672	102	7	treated	treat	VERB
ap-8672	102	8	as	as	ADP
ap-8672	102	9	a	a	DET
ap-8672	102	10	single	single	ADJ
ap-8672	102	11	geometric	geometric	ADJ
ap-8672	102	12	point	point	NOUN
ap-8672	102	13	.	.	PUNCT
ap-8672	103	1	4.1	4.1	NUM
ap-8672	103	2	.	.	PUNCT
ap-8672	104	1	forward	forward	PROPN
ap-8672	104	2	kinematics	kinematic	NOUN
ap-8672	104	3	the	the	DET
ap-8672	104	4	matrix	matrix	NOUN
ap-8672	104	5	representing	represent	VERB
ap-8672	104	6	the	the	DET
ap-8672	104	7	desired	desire	VERB
ap-8672	104	8	position	position	NOUN
ap-8672	104	9	and	and	CCONJ
ap-8672	104	10	orientation	orientation	NOUN
ap-8672	104	11	,	,	PUNCT
ap-8672	104	12	denoted	denote	VERB
ap-8672	104	13	as	as	ADP
ap-8672	104	14	t	t	NOUN
ap-8672	104	15	=	=	PUNCT
ap-8672	105	1	[	[	X
ap-8672	105	2	s	s	X
ap-8672	105	3	n	n	PRON
ap-8672	105	4	a	a	DET
ap-8672	105	5	p	p	X
ap-8672	105	6	]	]	X
ap-8672	105	7	,	,	PUNCT
ap-8672	105	8	of	of	ADP
ap-8672	105	9	the	the	DET
ap-8672	105	10	end	end	NOUN
ap-8672	105	11	-	-	PUNCT
ap-8672	105	12	effector	effector	NOUN
ap-8672	105	13	,	,	PUNCT
ap-8672	105	14	given	give	VERB
ap-8672	105	15	in	in	ADP
ap-8672	105	16	equation	equation	NOUN
ap-8672	105	17	(	(	PUNCT
ap-8672	105	18	1	1	NUM
ap-8672	105	19	)	)	PUNCT
ap-8672	105	20	and	and	CCONJ
ap-8672	105	21	obtained	obtain	VERB
ap-8672	105	22	through	through	ADP
ap-8672	105	23	successive	successive	ADJ
ap-8672	105	24	multiplications	multiplication	NOUN
ap-8672	105	25	of	of	ADP
ap-8672	105	26	homogeneous	homogeneous	ADJ
ap-8672	105	27	transformation	transformation	NOUN
ap-8672	105	28	matrices	matrix	NOUN
ap-8672	105	29	,	,	PUNCT
ap-8672	105	30	can	can	AUX
ap-8672	105	31	be	be	AUX
ap-8672	105	32	rewritten	rewrite	VERB
ap-8672	105	33	as	as	ADP
ap-8672	105	34	equation	equation	NOUN
ap-8672	105	35	(	(	PUNCT
ap-8672	105	36	7	7	NUM
ap-8672	105	37	)	)	PUNCT
ap-8672	105	38	.	.	PUNCT
ap-8672	106	1	[	[	X
ap-8672	106	2	s	s	X
ap-8672	106	3	n	n	PRON
ap-8672	106	4	a	a	DET
ap-8672	106	5	p	p	X
ap-8672	106	6	]	]	X
ap-8672	106	7	=	=	SYM
ap-8672	106	8	0t1	0t1	NUM
ap-8672	107	1	1t2	1t2	NUM
ap-8672	107	2	2t3	2t3	NUM
ap-8672	107	3	3t4	3t4	NUM
ap-8672	107	4	4t5	4t5	NUM
ap-8672	107	5	5t6	5t6	NUM
ap-8672	107	6	6t7	6t7	NUM
ap-8672	107	7	=	=	SYM
ap-8672	107	8			NOUN
ap-8672	107	9	sx	sx	NOUN
ap-8672	107	10	nx	nx	PROPN
ap-8672	107	11	ax	ax	NOUN
ap-8672	107	12	pdx	pdx	PROPN
ap-8672	107	13	sy	sy	PROPN
ap-8672	107	14	ny	ny	PROPN
ap-8672	108	1	ay	ay	PROPN
ap-8672	108	2	pdy	pdy	INTJ
ap-8672	108	3	sz	sz	PROPN
ap-8672	108	4	nz	nz	PROPN
ap-8672	108	5	az	az	PROPN
ap-8672	108	6	pdz	pdz	NOUN
ap-8672	108	7	0	0	NUM
ap-8672	108	8	0	0	NUM
ap-8672	108	9	0	0	NUM
ap-8672	108	10	1	1	NUM
ap-8672	108	11			NOUN
ap-8672	108	12	,	,	PUNCT
ap-8672	108	13	(	(	PUNCT
ap-8672	108	14	7	7	NUM
ap-8672	108	15	)	)	PUNCT
ap-8672	108	16	where	where	SCONJ
ap-8672	108	17	:	:	PUNCT
ap-8672	108	18	s	s	AUX
ap-8672	108	19	=	=	PUNCT
ap-8672	108	20	(	(	PUNCT
ap-8672	108	21	sx	sx	PROPN
ap-8672	108	22	,	,	PUNCT
ap-8672	108	23	sy	sy	PROPN
ap-8672	108	24	,	,	PUNCT
ap-8672	108	25	sz)t	sz)t	PROPN
ap-8672	108	26	,	,	PUNCT
ap-8672	108	27	n	n	PROPN
ap-8672	108	28	=	=	SYM
ap-8672	108	29	(	(	PUNCT
ap-8672	108	30	nx	nx	PROPN
ap-8672	108	31	,	,	PUNCT
ap-8672	108	32	ny	ny	PROPN
ap-8672	108	33	,	,	PUNCT
ap-8672	108	34	nz)t	nz)t	PROPN
ap-8672	108	35	,	,	PUNCT
ap-8672	108	36	a	a	PRON
ap-8672	108	37	=	=	X
ap-8672	108	38	(	(	PUNCT
ap-8672	108	39	ax	ax	NOUN
ap-8672	108	40	,	,	PUNCT
ap-8672	108	41	ay	ay	INTJ
ap-8672	108	42	,	,	PUNCT
ap-8672	108	43	az)t	az)t	PROPN
ap-8672	108	44	are	be	AUX
ap-8672	108	45	the	the	DET
ap-8672	108	46	cosine	cosine	ADJ
ap-8672	108	47	directions	direction	NOUN
ap-8672	108	48	of	of	ADP
ap-8672	108	49	the	the	DET
ap-8672	108	50	frame	frame	NOUN
ap-8672	108	51	f7(x7	f7(x7	NOUN
ap-8672	108	52	,	,	PUNCT
ap-8672	108	53	y7	y7	PROPN
ap-8672	108	54	,	,	PUNCT
ap-8672	108	55	z7	z7	PROPN
ap-8672	108	56	)	)	PUNCT
ap-8672	108	57	(	(	PUNCT
ap-8672	108	58	orientation	orientation	NOUN
ap-8672	108	59	of	of	ADP
ap-8672	108	60	the	the	DET
ap-8672	108	61	end	end	NOUN
ap-8672	108	62	-	-	PUNCT
ap-8672	108	63	effector	effector	NOUN
ap-8672	108	64	)	)	PUNCT
ap-8672	108	65	.	.	PUNCT
ap-8672	109	1	p	p	NOUN
ap-8672	109	2	=	=	PRON
ap-8672	109	3	(	(	PUNCT
ap-8672	109	4	pdx	pdx	PROPN
ap-8672	109	5	,	,	PUNCT
ap-8672	109	6	pdy	pdy	PROPN
ap-8672	109	7	,	,	PUNCT
ap-8672	109	8	pdz)t	pdz)t	PROPN
ap-8672	109	9	is	be	AUX
ap-8672	109	10	the	the	DET
ap-8672	109	11	coordinate	coordinate	NOUN
ap-8672	109	12	of	of	ADP
ap-8672	109	13	the	the	DET
ap-8672	109	14	desired	desire	VERB
ap-8672	109	15	position	position	NOUN
ap-8672	109	16	of	of	ADP
ap-8672	109	17	the	the	DET
ap-8672	109	18	end	end	NOUN
ap-8672	109	19	-	-	PUNCT
ap-8672	109	20	effector	effector	NOUN
ap-8672	109	21	and	and	CCONJ
ap-8672	109	22	i−1ti	i−1ti	NOUN
ap-8672	109	23	is	be	AUX
ap-8672	109	24	the	the	DET
ap-8672	109	25	homogeneous	homogeneous	ADJ
ap-8672	109	26	transformation	transformation	NOUN
ap-8672	109	27	between	between	ADP
ap-8672	109	28	two	two	NUM
ap-8672	109	29	successive	successive	ADJ
ap-8672	109	30	frames	frame	NOUN
ap-8672	109	31	(	(	PUNCT
ap-8672	109	32	i	i	NOUN
ap-8672	109	33	=	=	NOUN
ap-8672	109	34	1	1	NUM
ap-8672	109	35	,	,	PUNCT
ap-8672	109	36	.	.	PUNCT
ap-8672	109	37	.	.	PUNCT
ap-8672	110	1	.	.	PUNCT
ap-8672	111	1	,	,	PUNCT
ap-8672	111	2	7	7	NUM
ap-8672	111	3	)	)	PUNCT
ap-8672	111	4	.	.	PUNCT
ap-8672	112	1	table	table	NOUN
ap-8672	112	2	2	2	NUM
ap-8672	112	3	shows	show	VERB
ap-8672	112	4	parameters	parameter	NOUN
ap-8672	112	5	obtained	obtain	VERB
ap-8672	112	6	using	use	VERB
ap-8672	112	7	the	the	DET
ap-8672	112	8	dh	dh	PROPN
ap-8672	112	9	convention	convention	NOUN
ap-8672	112	10	where	where	SCONJ
ap-8672	112	11	αi	αi	PRON
ap-8672	112	12	is	be	AUX
ap-8672	112	13	the	the	DET
ap-8672	112	14	rotational	rotational	ADJ
ap-8672	112	15	angle	angle	NOUN
ap-8672	112	16	between	between	ADP
ap-8672	112	17	zi	zi	NOUN
ap-8672	112	18	axis	axis	NOUN
ap-8672	112	19	and	and	CCONJ
ap-8672	112	20	zi−1	zi−1	PROPN
ap-8672	112	21	axis	axis	NOUN
ap-8672	112	22	around	around	ADV
ap-8672	112	23	xi	xi	ADP
ap-8672	112	24	axis	axis	NOUN
ap-8672	112	25	,	,	PUNCT
ap-8672	112	26	qi	qi	PROPN
ap-8672	112	27	=	=	PUNCT
ap-8672	112	28	θi	θi	PROPN
ap-8672	113	1	+	+	CCONJ
ap-8672	113	2	q0i	q0i	ADV
ap-8672	113	3	is	be	AUX
ap-8672	113	4	the	the	DET
ap-8672	113	5	rotational	rotational	ADJ
ap-8672	113	6	angle	angle	NOUN
ap-8672	113	7	between	between	ADP
ap-8672	113	8	xi	xi	X
ap-8672	113	9	axis	axis	NOUN
ap-8672	113	10	and	and	CCONJ
ap-8672	113	11	xi−1	xi−1	PROPN
ap-8672	113	12	axis	axis	NOUN
ap-8672	113	13	around	around	ADP
ap-8672	113	14	zi	zi	NOUN
ap-8672	113	15	axis	axis	NOUN
ap-8672	113	16	where	where	SCONJ
ap-8672	113	17	θi	θi	PROPN
ap-8672	113	18	represents	represent	VERB
ap-8672	113	19	the	the	DET
ap-8672	113	20	effective	effective	ADJ
ap-8672	113	21	rotation	rotation	NOUN
ap-8672	113	22	and	and	CCONJ
ap-8672	113	23	q0i	q0i	PROPN
ap-8672	113	24	represents	represent	VERB
ap-8672	113	25	the	the	DET
ap-8672	113	26	initial	initial	ADJ
ap-8672	113	27	frame	frame	NOUN
ap-8672	113	28	rotation	rotation	NOUN
ap-8672	113	29	corresponding	correspond	VERB
ap-8672	113	30	to	to	ADP
ap-8672	113	31	the	the	DET
ap-8672	113	32	home	home	NOUN
ap-8672	113	33	position	position	NOUN
ap-8672	113	34	.	.	PUNCT
ap-8672	114	1	hence	hence	ADV
ap-8672	114	2	,	,	PUNCT
ap-8672	114	3	the	the	DET
ap-8672	114	4	homogeneous	homogeneous	ADJ
ap-8672	114	5	transformation	transformation	NOUN
ap-8672	114	6	matrix	matrix	NOUN
ap-8672	114	7	between	between	ADP
ap-8672	114	8	two	two	NUM
ap-8672	114	9	successive	successive	ADJ
ap-8672	114	10	frames	frame	NOUN
ap-8672	114	11	can	can	AUX
ap-8672	114	12	be	be	AUX
ap-8672	114	13	obtained	obtain	VERB
ap-8672	114	14	through	through	ADP
ap-8672	114	15	equation	equation	NOUN
ap-8672	114	16	(	(	PUNCT
ap-8672	114	17	8)	8)	NUM
ap-8672	114	18	:	:	PUNCT
ap-8672	114	19	329	329	NUM
ap-8672	114	20	n.	n.	NOUN
ap-8672	114	21	hadidi	hadidi	PROPN
ap-8672	114	22	,	,	PUNCT
ap-8672	114	23	m.	m.	NOUN
ap-8672	114	24	bouaziz	bouaziz	PROPN
ap-8672	114	25	,	,	PUNCT
ap-8672	114	26	c.	c.	PROPN
ap-8672	114	27	mahfoudi	mahfoudi	PROPN
ap-8672	114	28	,	,	PUNCT
ap-8672	114	29	m.	m.	NOUN
ap-8672	114	30	zaharuddin	zaharuddin	PROPN
ap-8672	114	31	acta	acta	PROPN
ap-8672	114	32	polytechnica	polytechnica	PROPN
ap-8672	114	33	frame	frame	PROPN
ap-8672	114	34	αi	αi	PROPN
ap-8672	114	35	li	li	PROPN
ap-8672	114	36	qi	qi	PROPN
ap-8672	114	37	di	di	PROPN
ap-8672	114	38	joint	joint	ADJ
ap-8672	114	39	range	range	NOUN
ap-8672	114	40	f0	f0	PROPN
ap-8672	114	41	–	–	PUNCT
ap-8672	114	42	–	–	PUNCT
ap-8672	114	43	–	–	PUNCT
ap-8672	114	44	–	–	PUNCT
ap-8672	114	45	–	–	PUNCT
ap-8672	114	46	f1	f1	NOUN
ap-8672	114	47	0	0	NUM
ap-8672	114	48	0	0	NUM
ap-8672	115	1	π	π	SYM
ap-8672	115	2	2	2	NUM
ap-8672	115	3	+	+	CCONJ
ap-8672	115	4	θ1	θ1	NOUN
ap-8672	115	5	0	0	PUNCT
ap-8672	115	6	[	[	PUNCT
ap-8672	115	7	−	−	PROPN
ap-8672	115	8	π	π	PROPN
ap-8672	115	9	2	2	NUM
ap-8672	115	10	,	,	PUNCT
ap-8672	115	11	π	π	X
ap-8672	115	12	]	]	PUNCT
ap-8672	115	13	f2	f2	PROPN
ap-8672	115	14	π	π	PROPN
ap-8672	115	15	2	2	NUM
ap-8672	115	16	0	0	NUM
ap-8672	115	17	π	π	SYM
ap-8672	115	18	2	2	NUM
ap-8672	115	19	+	+	CCONJ
ap-8672	115	20	θ2	θ2	PROPN
ap-8672	115	21	0	0	PUNCT
ap-8672	116	1	[	[	PUNCT
ap-8672	116	2	−	−	PROPN
ap-8672	116	3	π	π	PROPN
ap-8672	116	4	2	2	NUM
ap-8672	116	5	,	,	PUNCT
ap-8672	116	6	−π	−π	ADV
ap-8672	116	7	]	]	PUNCT
ap-8672	116	8	f3	f3	PROPN
ap-8672	116	9	−	−	PROPN
ap-8672	116	10	π	π	PROPN
ap-8672	116	11	2	2	NUM
ap-8672	116	12	0	0	NUM
ap-8672	116	13	−	−	PROPN
ap-8672	116	14	π	π	PROPN
ap-8672	116	15	2	2	NUM
ap-8672	116	16	+	+	CCONJ
ap-8672	116	17	θ3	θ3	PROPN
ap-8672	116	18	la	la	PROPN
ap-8672	117	1	[	[	X
ap-8672	117	2	−π	−π	X
ap-8672	117	3	,	,	PUNCT
ap-8672	117	4	π	π	X
ap-8672	117	5	]	]	X
ap-8672	117	6	f4	f4	ADJ
ap-8672	117	7	−	−	PROPN
ap-8672	117	8	π	π	NOUN
ap-8672	117	9	2	2	NUM
ap-8672	117	10	0	0	NUM
ap-8672	117	11	θ4	θ4	NOUN
ap-8672	117	12	0	0	PUNCT
ap-8672	118	1	[	[	PUNCT
ap-8672	118	2	0	0	NUM
ap-8672	118	3	,	,	PUNCT
ap-8672	118	4	3π	3π	NUM
ap-8672	118	5	4	4	NUM
ap-8672	118	6	]	]	PUNCT
ap-8672	118	7	f5	f5	PROPN
ap-8672	118	8	π	π	SYM
ap-8672	118	9	2	2	NUM
ap-8672	118	10	0	0	NUM
ap-8672	118	11	θ5	θ5	NOUN
ap-8672	118	12	lf	lf	ADP
ap-8672	119	1	[	[	X
ap-8672	119	2	0	0	NUM
ap-8672	119	3	,	,	PUNCT
ap-8672	119	4	2π	2π	NOUN
ap-8672	119	5	]	]	X
ap-8672	120	1	f6	f6	PROPN
ap-8672	120	2	−	−	PROPN
ap-8672	120	3	π	π	PROPN
ap-8672	120	4	2	2	NUM
ap-8672	120	5	0	0	NUM
ap-8672	121	1	−	−	PROPN
ap-8672	121	2	π	π	NOUN
ap-8672	121	3	2	2	NUM
ap-8672	121	4	+	+	CCONJ
ap-8672	121	5	θ6	θ6	X
ap-8672	121	6	0	0	PUNCT
ap-8672	122	1	[	[	PUNCT
ap-8672	122	2	−	−	NUM
ap-8672	122	3	3π	3π	NUM
ap-8672	122	4	4	4	NUM
ap-8672	122	5	,	,	PUNCT
ap-8672	122	6	3π	3π	NUM
ap-8672	122	7	4	4	NUM
ap-8672	122	8	]	]	PUNCT
ap-8672	122	9	f7	f7	PROPN
ap-8672	122	10	0	0	PUNCT
ap-8672	123	1	lh	lh	NOUN
ap-8672	123	2	0	0	NUM
ap-8672	123	3	0	0	NUM
ap-8672	123	4	–	–	PUNCT
ap-8672	123	5	table	table	NOUN
ap-8672	123	6	2	2	NUM
ap-8672	123	7	.	.	PUNCT
ap-8672	123	8	dh	dh	NOUN
ap-8672	123	9	parameters	parameter	NOUN
ap-8672	123	10	.	.	PUNCT
ap-8672	124	1	i−1ti	i−1ti	NOUN
ap-8672	124	2	=	=	SYM
ap-8672	124	3			NOUN
ap-8672	124	4	cos(qi	cos(qi	X
ap-8672	124	5	)	)	PUNCT
ap-8672	124	6	−	−	NOUN
ap-8672	124	7	sin(qi	sin(qi	SYM
ap-8672	124	8	)	)	PUNCT
ap-8672	124	9	0	0	NUM
ap-8672	124	10	li	li	PROPN
ap-8672	124	11	cos(αi	cos(αi	NOUN
ap-8672	124	12	)	)	PUNCT
ap-8672	124	13	sin(qi	sin(qi	PROPN
ap-8672	124	14	)	)	PUNCT
ap-8672	124	15	cos(αi	cos(αi	NOUN
ap-8672	124	16	)	)	PUNCT
ap-8672	124	17	cos(qi	cos(qi	PROPN
ap-8672	124	18	)	)	PUNCT
ap-8672	125	1	−	−	PRON
ap-8672	125	2	sin(αi	sin(αi	NOUN
ap-8672	125	3	)	)	PUNCT
ap-8672	125	4	−di	−di	NOUN
ap-8672	125	5	sin(αi	sin(αi	NOUN
ap-8672	125	6	)	)	PUNCT
ap-8672	125	7	sin(αi	sin(αi	NOUN
ap-8672	125	8	)	)	PUNCT
ap-8672	125	9	sin(qi	sin(qi	X
ap-8672	125	10	)	)	PUNCT
ap-8672	125	11	sin(αi	sin(αi	NOUN
ap-8672	125	12	)	)	PUNCT
ap-8672	125	13	cos(qi	cos(qi	PROPN
ap-8672	125	14	)	)	PUNCT
ap-8672	125	15	cos(αi	cos(αi	NOUN
ap-8672	125	16	)	)	PUNCT
ap-8672	125	17	di	di	NOUN
ap-8672	125	18	cos(αi	cos(αi	NOUN
ap-8672	125	19	)	)	PUNCT
ap-8672	125	20	0	0	NUM
ap-8672	125	21	0	0	NUM
ap-8672	125	22	0	0	NUM
ap-8672	125	23	1	1	NUM
ap-8672	125	24			NOUN
ap-8672	125	25	.	.	PUNCT
ap-8672	126	1	(	(	PUNCT
ap-8672	126	2	8)	8)	NUM
ap-8672	126	3	4.2	4.2	NUM
ap-8672	126	4	.	.	PUNCT
ap-8672	127	1	inverse	inverse	NOUN
ap-8672	127	2	kinematics	kinematic	NOUN
ap-8672	127	3	solutions	solution	NOUN
ap-8672	127	4	solving	solve	VERB
ap-8672	127	5	the	the	DET
ap-8672	127	6	inverse	inverse	NOUN
ap-8672	127	7	kinematics	kinematic	NOUN
ap-8672	127	8	involves	involve	VERB
ap-8672	127	9	determining	determine	VERB
ap-8672	127	10	the	the	DET
ap-8672	127	11	appropriate	appropriate	ADJ
ap-8672	127	12	rotations	rotation	NOUN
ap-8672	127	13	of	of	ADP
ap-8672	127	14	each	each	DET
ap-8672	127	15	robot	robot	NOUN
ap-8672	127	16	’s	’s	PART
ap-8672	127	17	articulation	articulation	NOUN
ap-8672	127	18	to	to	PART
ap-8672	127	19	bring	bring	VERB
ap-8672	127	20	the	the	DET
ap-8672	127	21	end	end	NOUN
ap-8672	127	22	-	-	PUNCT
ap-8672	127	23	effector	effector	NOUN
ap-8672	127	24	to	to	ADP
ap-8672	127	25	the	the	DET
ap-8672	127	26	desired	desire	VERB
ap-8672	127	27	situation	situation	NOUN
ap-8672	127	28	(	(	PUNCT
ap-8672	127	29	position	position	NOUN
ap-8672	127	30	and	and	CCONJ
ap-8672	127	31	orientation	orientation	NOUN
ap-8672	127	32	)	)	PUNCT
ap-8672	127	33	.	.	PUNCT
ap-8672	128	1	figure	figure	NOUN
ap-8672	128	2	3	3	NUM
ap-8672	128	3	represents	represent	VERB
ap-8672	128	4	a	a	DET
ap-8672	128	5	geometric	geometric	ADJ
ap-8672	128	6	parameterisation	parameterisation	NOUN
ap-8672	128	7	of	of	ADP
ap-8672	128	8	the	the	DET
ap-8672	128	9	robot	robot	NOUN
ap-8672	128	10	(	(	PUNCT
ap-8672	128	11	geometric	geometric	ADJ
ap-8672	128	12	entities	entity	NOUN
ap-8672	128	13	)	)	PUNCT
ap-8672	128	14	,	,	PUNCT
ap-8672	128	15	which	which	PRON
ap-8672	128	16	will	will	AUX
ap-8672	128	17	be	be	AUX
ap-8672	128	18	utilised	utilise	VERB
ap-8672	128	19	in	in	ADP
ap-8672	128	20	the	the	DET
ap-8672	128	21	inverse	inverse	NOUN
ap-8672	128	22	kinematics	kinematic	NOUN
ap-8672	128	23	problem	problem	NOUN
ap-8672	128	24	solving	solving	NOUN
ap-8672	128	25	process	process	NOUN
ap-8672	128	26	.	.	PUNCT
ap-8672	129	1	y0	y0	NOUN
ap-8672	129	2	x0	x0	PROPN
ap-8672	129	3	z0	z0	PROPN
ap-8672	129	4	o	o	PROPN
ap-8672	129	5	f6	f6	PROPN
ap-8672	129	6	f7	f7	PROPN
ap-8672	129	7	z7	z7	PROPN
ap-8672	129	8	x7	x7	VERB
ap-8672	129	9	x6	x6	PROPN
ap-8672	129	10	y7	y7	ADJ
ap-8672	129	11	z6	z6	PROPN
ap-8672	129	12	y6	y6	NOUN
ap-8672	129	13	(	(	PUNCT
ap-8672	129	14	a	a	NOUN
ap-8672	129	15	)	)	PUNCT
ap-8672	129	16	.	.	PUNCT
ap-8672	130	1	robot	robot	NOUN
ap-8672	130	2	configuration	configuration	NOUN
ap-8672	130	3	with	with	ADP
ap-8672	130	4	assignment	assignment	NOUN
ap-8672	130	5	of	of	ADP
ap-8672	130	6	main	main	ADJ
ap-8672	130	7	frames	frame	NOUN
ap-8672	130	8	.	.	PUNCT
ap-8672	131	1	ௗܲ	ௗܲ	PROPN
ap-8672	131	2	0x	0x	NOUN
ap-8672	131	3	0z	0z	NUM
ap-8672	131	4	0y	0y	NOUN
ap-8672	131	5	௘ܲ	௘ܲ	ADJ
ap-8672	131	6	௛ܲ	௛ܲ	PROPN
ap-8672	131	7	௙ܮ	௙ܮ	X
ap-8672	131	8	௦ܲ	௦ܲ	PROPN
ap-8672	131	9	௪ܲ	௪ܲ	PROPN
ap-8672	131	10	௔ܮ	௔ܮ	NUM
ap-8672	131	11	௛ܮ	௛ܮ	NOUN
ap-8672	131	12	ܪ	ܪ	PRON
ap-8672	131	13	௛௪ܮ	௛௪ܮ	NOUN
ap-8672	131	14	ݎ	ݎ	NOUN
ap-8672	131	15	௛௘ܮ	௛௘ܮ	NOUN
ap-8672	131	16	଺ݖ	଺ݖ	NOUN
ap-8672	131	17	ଵߙ	ଵߙ	VERB
ap-8672	131	18	ଶߙ	ଶߙ	PROPN
ap-8672	131	19	q	q	NOUN
ap-8672	131	20	plane	plane	NOUN
ap-8672	131	21	circle	circle	NOUN
ap-8672	131	22	of	of	ADP
ap-8672	131	23	la	la	PROPN
ap-8672	131	24	radius	radius	PROPN
ap-8672	131	25	(	(	PUNCT
ap-8672	131	26	b	b	NOUN
ap-8672	131	27	)	)	PUNCT
ap-8672	131	28	.	.	PUNCT
ap-8672	132	1	geometric	geometric	ADJ
ap-8672	132	2	entities	entity	NOUN
ap-8672	132	3	.	.	PUNCT
ap-8672	133	1	figure	figure	VERB
ap-8672	133	2	3	3	NUM
ap-8672	133	3	.	.	PUNCT
ap-8672	134	1	geometric	geometric	ADJ
ap-8672	134	2	parameterisation	parameterisation	NOUN
ap-8672	134	3	of	of	ADP
ap-8672	134	4	a	a	DET
ap-8672	134	5	right	right	ADJ
ap-8672	134	6	upper	upper	ADJ
ap-8672	134	7	limb	limb	NOUN
ap-8672	134	8	biped	biped	ADJ
ap-8672	134	9	robot	robot	NOUN
ap-8672	134	10	.	.	PUNCT
ap-8672	135	1	in	in	ADP
ap-8672	135	2	this	this	DET
ap-8672	135	3	study	study	NOUN
ap-8672	135	4	,	,	PUNCT
ap-8672	135	5	the	the	DET
ap-8672	135	6	strategy	strategy	NOUN
ap-8672	135	7	for	for	ADP
ap-8672	135	8	solving	solve	VERB
ap-8672	135	9	the	the	DET
ap-8672	135	10	inverse	inverse	NOUN
ap-8672	135	11	kinematics	kinematic	NOUN
ap-8672	135	12	problem	problem	NOUN
ap-8672	135	13	is	be	AUX
ap-8672	135	14	divided	divide	VERB
ap-8672	135	15	into	into	ADP
ap-8672	135	16	two	two	NUM
ap-8672	135	17	phases	phase	NOUN
ap-8672	135	18	:	:	PUNCT
ap-8672	135	19	the	the	DET
ap-8672	135	20	first	first	ADJ
ap-8672	135	21	phase	phase	NOUN
ap-8672	135	22	consists	consist	VERB
ap-8672	135	23	of	of	ADP
ap-8672	135	24	determining	determine	VERB
ap-8672	135	25	the	the	DET
ap-8672	135	26	geometric	geometric	ADJ
ap-8672	135	27	entities	entity	NOUN
ap-8672	135	28	that	that	PRON
ap-8672	135	29	allow	allow	VERB
ap-8672	135	30	the	the	DET
ap-8672	135	31	determination	determination	NOUN
ap-8672	135	32	of	of	ADP
ap-8672	135	33	the	the	DET
ap-8672	135	34	vectors	vector	NOUN
ap-8672	135	35	defining	define	VERB
ap-8672	135	36	each	each	DET
ap-8672	135	37	joint	joint	NOUN
ap-8672	135	38	.	.	PUNCT
ap-8672	136	1	the	the	DET
ap-8672	136	2	second	second	ADJ
ap-8672	136	3	phase	phase	NOUN
ap-8672	136	4	focuses	focus	VERB
ap-8672	136	5	on	on	ADP
ap-8672	136	6	determining	determine	VERB
ap-8672	136	7	the	the	DET
ap-8672	136	8	angles	angle	NOUN
ap-8672	136	9	of	of	ADP
ap-8672	136	10	each	each	DET
ap-8672	136	11	joint	joint	NOUN
ap-8672	136	12	,	,	PUNCT
ap-8672	136	13	which	which	PRON
ap-8672	136	14	are	be	AUX
ap-8672	136	15	based	base	VERB
ap-8672	136	16	on	on	ADP
ap-8672	136	17	the	the	DET
ap-8672	136	18	results	result	NOUN
ap-8672	136	19	obtained	obtain	VERB
ap-8672	136	20	in	in	ADP
ap-8672	136	21	the	the	DET
ap-8672	136	22	first	first	ADJ
ap-8672	136	23	phase	phase	NOUN
ap-8672	136	24	.	.	PUNCT
ap-8672	137	1	330	330	NUM
ap-8672	137	2	vol	vol	NOUN
ap-8672	137	3	.	.	PUNCT
ap-8672	137	4	63	63	NUM
ap-8672	137	5	no	no	NOUN
ap-8672	137	6	.	.	PUNCT
ap-8672	138	1	5/2023	5/2023	NUM
ap-8672	138	2	geometric	geometric	ADJ
ap-8672	138	3	approach	approach	NOUN
ap-8672	138	4	to	to	ADP
ap-8672	138	5	solving	solve	VERB
ap-8672	138	6	inverse	inverse	ADJ
ap-8672	138	7	kinematics	kinematic	NOUN
ap-8672	138	8	of	of	ADP
ap-8672	138	9	six	six	NUM
ap-8672	138	10	dof	dof	NOUN
ap-8672	138	11	robot	robot	NOUN
ap-8672	138	12	4.2.1	4.2.1	NOUN
ap-8672	138	13	.	.	PUNCT
ap-8672	138	14	calculate	calculate	VERB
ap-8672	138	15	the	the	DET
ap-8672	138	16	geometric	geometric	ADJ
ap-8672	138	17	entities	entity	NOUN
ap-8672	138	18	of	of	ADP
ap-8672	138	19	the	the	DET
ap-8672	138	20	robot	robot	NOUN
ap-8672	138	21	initially	initially	ADV
ap-8672	138	22	,	,	PUNCT
ap-8672	138	23	certain	certain	ADJ
ap-8672	138	24	geometric	geometric	ADJ
ap-8672	138	25	entities	entity	NOUN
ap-8672	138	26	,	,	PUNCT
ap-8672	138	27	including	include	VERB
ap-8672	138	28	points	point	NOUN
ap-8672	138	29	,	,	PUNCT
ap-8672	138	30	vectors	vector	NOUN
ap-8672	138	31	,	,	PUNCT
ap-8672	138	32	and	and	CCONJ
ap-8672	138	33	planes	plane	NOUN
ap-8672	138	34	,	,	PUNCT
ap-8672	138	35	must	must	AUX
ap-8672	138	36	be	be	AUX
ap-8672	138	37	determined	determine	VERB
ap-8672	138	38	.	.	PUNCT
ap-8672	139	1	to	to	PART
ap-8672	139	2	achieve	achieve	VERB
ap-8672	139	3	this	this	PRON
ap-8672	139	4	,	,	PUNCT
ap-8672	139	5	the	the	DET
ap-8672	139	6	following	follow	VERB
ap-8672	139	7	strategy	strategy	NOUN
ap-8672	139	8	is	be	AUX
ap-8672	139	9	adopted	adopt	VERB
ap-8672	139	10	:	:	PUNCT
ap-8672	139	11	•	•	NUM
ap-8672	139	12	determine	determine	VERB
ap-8672	139	13	the	the	DET
ap-8672	139	14	wrist	wrist	NOUN
ap-8672	139	15	position	position	NOUN
ap-8672	139	16	.	.	PUNCT
ap-8672	140	1	•	•	NUM
ap-8672	140	2	determine	determine	VERB
ap-8672	140	3	the	the	DET
ap-8672	140	4	elbow	elbow	NOUN
ap-8672	140	5	position	position	NOUN
ap-8672	140	6	by	by	ADP
ap-8672	140	7	the	the	DET
ap-8672	140	8	following	follow	VERB
ap-8672	140	9	procedure	procedure	NOUN
ap-8672	140	10	:	:	PUNCT
ap-8672	140	11	▷	▷	ADJ
ap-8672	140	12	determine	determine	VERB
ap-8672	140	13	the	the	DET
ap-8672	140	14	q	q	ADJ
ap-8672	140	15	-	-	PUNCT
ap-8672	140	16	plane	plane	NOUN
ap-8672	140	17	equation	equation	NOUN
ap-8672	140	18	through	through	ADP
ap-8672	140	19	the	the	DET
ap-8672	140	20	normal	normal	ADJ
ap-8672	140	21	vector	vector	NOUN
ap-8672	140	22	at	at	ADP
ap-8672	140	23	the	the	DET
ap-8672	140	24	rotational	rotational	ADJ
ap-8672	140	25	joint	joint	ADJ
ap-8672	140	26	q6	q6	NOUN
ap-8672	140	27	(	(	PUNCT
ap-8672	140	28	z6	z6	NOUN
ap-8672	140	29	-	-	PUNCT
ap-8672	140	30	axis	axis	NOUN
ap-8672	140	31	)	)	PUNCT
ap-8672	140	32	.	.	PUNCT
ap-8672	141	1	geometrically	geometrically	ADV
ap-8672	141	2	,	,	PUNCT
ap-8672	141	3	the	the	DET
ap-8672	141	4	forearm	forearm	NOUN
ap-8672	141	5	link	link	NOUN
ap-8672	141	6	has	have	VERB
ap-8672	141	7	to	to	PART
ap-8672	141	8	belong	belong	VERB
ap-8672	141	9	to	to	ADP
ap-8672	141	10	the	the	DET
ap-8672	141	11	q	q	NOUN
ap-8672	141	12	-	-	NOUN
ap-8672	141	13	plane	plane	NOUN
ap-8672	141	14	because	because	SCONJ
ap-8672	141	15	for	for	ADP
ap-8672	141	16	any	any	DET
ap-8672	141	17	position	position	NOUN
ap-8672	141	18	and	and	CCONJ
ap-8672	141	19	orientation	orientation	NOUN
ap-8672	141	20	of	of	ADP
ap-8672	141	21	the	the	DET
ap-8672	141	22	end	end	NOUN
ap-8672	141	23	-	-	PUNCT
ap-8672	141	24	effector	effector	NOUN
ap-8672	141	25	,	,	PUNCT
ap-8672	141	26	the	the	DET
ap-8672	141	27	z6	z6	NOUN
ap-8672	141	28	-	-	PUNCT
ap-8672	141	29	axis	axis	NOUN
ap-8672	141	30	remains	remain	VERB
ap-8672	141	31	perpendicular	perpendicular	ADJ
ap-8672	141	32	to	to	ADP
ap-8672	141	33	the	the	DET
ap-8672	141	34	forearm	forearm	NOUN
ap-8672	141	35	-	-	PUNCT
ap-8672	141	36	link	link	NOUN
ap-8672	141	37	.	.	PUNCT
ap-8672	142	1	▷	▷	ADV
ap-8672	142	2	calculate	calculate	VERB
ap-8672	142	3	the	the	DET
ap-8672	142	4	coordinate	coordinate	NOUN
ap-8672	142	5	of	of	ADP
ap-8672	142	6	the	the	DET
ap-8672	142	7	closest	close	ADJ
ap-8672	142	8	point	point	NOUN
ap-8672	142	9	ph	ph	NOUN
ap-8672	142	10	on	on	ADP
ap-8672	142	11	q	q	NOUN
ap-8672	142	12	-	-	NOUN
ap-8672	142	13	plane	plane	NOUN
ap-8672	142	14	at	at	ADP
ap-8672	142	15	the	the	DET
ap-8672	142	16	original	original	ADJ
ap-8672	142	17	frame	frame	NOUN
ap-8672	142	18	f0	f0	PROPN
ap-8672	142	19	.	.	PUNCT
ap-8672	143	1	▷	▷	ADV
ap-8672	143	2	determine	determine	VERB
ap-8672	143	3	the	the	DET
ap-8672	143	4	circle	circle	NOUN
ap-8672	143	5	on	on	ADP
ap-8672	143	6	the	the	DET
ap-8672	143	7	q	q	NOUN
ap-8672	143	8	-	-	NOUN
ap-8672	143	9	plane	plane	NOUN
ap-8672	143	10	in	in	ADP
ap-8672	143	11	which	which	PRON
ap-8672	143	12	the	the	DET
ap-8672	143	13	wrist	wrist	NOUN
ap-8672	143	14	poin	poin	VERB
ap-8672	143	15	pw	pw	PROPN
ap-8672	143	16	and	and	CCONJ
ap-8672	143	17	the	the	DET
ap-8672	143	18	length	length	NOUN
ap-8672	143	19	of	of	ADP
ap-8672	143	20	forearm	forearm	NOUN
ap-8672	143	21	(	(	PUNCT
ap-8672	143	22	lf	lf	NOUN
ap-8672	143	23	)	)	PUNCT
ap-8672	143	24	are	be	AUX
ap-8672	143	25	its	its	PRON
ap-8672	143	26	centre	centre	NOUN
ap-8672	143	27	and	and	CCONJ
ap-8672	143	28	radius	radius	NOUN
ap-8672	143	29	,	,	PUNCT
ap-8672	143	30	respectively	respectively	ADV
ap-8672	143	31	.	.	PUNCT
ap-8672	144	1	▷	▷	ADV
ap-8672	144	2	calculate	calculate	VERB
ap-8672	144	3	the	the	DET
ap-8672	144	4	coordinate	coordinate	NOUN
ap-8672	144	5	point	point	NOUN
ap-8672	144	6	of	of	ADP
ap-8672	144	7	elbow	elbow	NOUN
ap-8672	144	8	(	(	PUNCT
ap-8672	144	9	pe	pe	NOUN
ap-8672	144	10	)	)	PUNCT
ap-8672	144	11	.	.	PUNCT
ap-8672	145	1	according	accord	VERB
ap-8672	145	2	to	to	PART
ap-8672	145	3	figure	figure	NOUN
ap-8672	145	4	3	3	NUM
ap-8672	145	5	,	,	PUNCT
ap-8672	145	6	the	the	DET
ap-8672	145	7	frame	frame	NOUN
ap-8672	145	8	f6	f6	PROPN
ap-8672	145	9	of	of	ADP
ap-8672	145	10	the	the	DET
ap-8672	145	11	rotational	rotational	ADJ
ap-8672	145	12	joint	joint	ADJ
ap-8672	145	13	q6	q6	PROPN
ap-8672	145	14	maintains	maintain	VERB
ap-8672	145	15	the	the	DET
ap-8672	145	16	same	same	ADJ
ap-8672	145	17	orientation	orientation	NOUN
ap-8672	145	18	as	as	ADP
ap-8672	145	19	the	the	DET
ap-8672	145	20	frame	frame	NOUN
ap-8672	145	21	f7	f7	PROPN
ap-8672	145	22	;	;	PUNCT
ap-8672	145	23	therefore	therefore	ADV
ap-8672	145	24	,	,	PUNCT
ap-8672	145	25	the	the	DET
ap-8672	145	26	position	position	NOUN
ap-8672	145	27	of	of	ADP
ap-8672	145	28	the	the	DET
ap-8672	145	29	wrist	wrist	NOUN
ap-8672	145	30	is	be	AUX
ap-8672	145	31	determined	determine	VERB
ap-8672	145	32	by	by	ADP
ap-8672	145	33	the	the	DET
ap-8672	145	34	following	follow	VERB
ap-8672	145	35	equation	equation	NOUN
ap-8672	145	36	(	(	PUNCT
ap-8672	145	37	9	9	NUM
ap-8672	145	38	)	)	PUNCT
ap-8672	145	39	,	,	PUNCT
ap-8672	145	40	using	use	VERB
ap-8672	145	41	the	the	DET
ap-8672	145	42	given	give	VERB
ap-8672	145	43	vector	vector	NOUN
ap-8672	145	44	,	,	PUNCT
ap-8672	145	45	−→	−→	ADJ
ap-8672	145	46	s6	s6	PROPN
ap-8672	145	47	=	=	SYM
ap-8672	145	48	(	(	PUNCT
ap-8672	145	49	s6x	s6x	PROPN
ap-8672	145	50	,	,	PUNCT
ap-8672	145	51	s6y	s6y	ADJ
ap-8672	145	52	,	,	PUNCT
ap-8672	145	53	s6z)t	s6z)t	PROPN
ap-8672	145	54	,	,	PUNCT
ap-8672	145	55	in	in	ADP
ap-8672	145	56	th	th	NOUN
ap-8672	145	57	matrix	matrix	NOUN
ap-8672	145	58	(	(	PUNCT
ap-8672	145	59	t	t	NOUN
ap-8672	145	60	)	)	PUNCT
ap-8672	145	61	of	of	ADP
ap-8672	145	62	the	the	DET
ap-8672	145	63	end	end	NOUN
ap-8672	145	64	-	-	PUNCT
ap-8672	145	65	effector	effector	NOUN
ap-8672	145	66	.	.	PUNCT
ap-8672	146	1	−−→	−−→	PROPN
ap-8672	146	2	opw	opw	PROPN
ap-8672	146	3	=	=	PROPN
ap-8672	146	4	−−→	−−→	PROPN
ap-8672	146	5	opd	opd	PROPN
ap-8672	146	6	−	−	PROPN
ap-8672	146	7	lh	lh	PROPN
ap-8672	146	8	−→	−→	PROPN
ap-8672	146	9	s6	s6	PROPN
ap-8672	146	10	,	,	PUNCT
ap-8672	146	11	(	(	PUNCT
ap-8672	146	12	9	9	NUM
ap-8672	146	13	)	)	PUNCT
ap-8672	147	1	where	where	SCONJ
ap-8672	147	2	:	:	PUNCT
ap-8672	147	3	−−→	−−→	PROPN
ap-8672	147	4	opw	opw	PROPN
ap-8672	147	5	=	=	X
ap-8672	147	6	(	(	PUNCT
ap-8672	147	7	pwx	pwx	PROPN
ap-8672	147	8	,	,	PUNCT
ap-8672	147	9	pwy	pwy	NOUN
ap-8672	147	10	,	,	PUNCT
ap-8672	147	11	pwz)t	pwz)t	PROPN
ap-8672	147	12	and	and	CCONJ
ap-8672	147	13	−−→	−−→	PROPN
ap-8672	147	14	opd	opd	PROPN
ap-8672	148	1	=	=	SYM
ap-8672	149	1	(	(	PUNCT
ap-8672	149	2	pdx	pdx	PROPN
ap-8672	149	3	,	,	PUNCT
ap-8672	149	4	pdy	pdy	PROPN
ap-8672	149	5	,	,	PUNCT
ap-8672	149	6	pdz)t	pdz)t	PROPN
ap-8672	149	7	are	be	AUX
ap-8672	149	8	the	the	DET
ap-8672	149	9	coordinates	coordinate	NOUN
ap-8672	149	10	of	of	ADP
ap-8672	149	11	the	the	DET
ap-8672	149	12	wrist	wrist	NOUN
ap-8672	149	13	position	position	NOUN
ap-8672	149	14	and	and	CCONJ
ap-8672	149	15	the	the	DET
ap-8672	149	16	desired	desire	VERB
ap-8672	149	17	position	position	NOUN
ap-8672	149	18	of	of	ADP
ap-8672	149	19	the	the	DET
ap-8672	149	20	end	end	NOUN
ap-8672	149	21	-	-	PUNCT
ap-8672	149	22	effector	effector	NOUN
ap-8672	149	23	,	,	PUNCT
ap-8672	149	24	respectively	respectively	ADV
ap-8672	149	25	.	.	PUNCT
ap-8672	150	1	from	from	ADP
ap-8672	150	2	figure	figure	NOUN
ap-8672	150	3	3	3	NUM
ap-8672	150	4	,	,	PUNCT
ap-8672	150	5	we	we	PRON
ap-8672	150	6	derived	derive	VERB
ap-8672	150	7	the	the	DET
ap-8672	150	8	tetrahedron	tetrahedron	NOUN
ap-8672	150	9	form	form	NOUN
ap-8672	150	10	,	,	PUNCT
ap-8672	150	11	which	which	PRON
ap-8672	150	12	consists	consist	VERB
ap-8672	150	13	of	of	ADP
ap-8672	150	14	two	two	NUM
ap-8672	150	15	right	right	ADJ
ap-8672	150	16	-	-	PUNCT
ap-8672	150	17	angled	angle	VERB
ap-8672	150	18	triangles	triangle	NOUN
ap-8672	150	19	∆(ps	∆(ps	NOUN
ap-8672	150	20	,	,	PUNCT
ap-8672	150	21	ph	ph	NOUN
ap-8672	150	22	,	,	PUNCT
ap-8672	150	23	pe	pe	ADJ
ap-8672	150	24	)	)	PUNCT
ap-8672	150	25	and	and	CCONJ
ap-8672	150	26	∆(ps	∆(ps	NOUN
ap-8672	150	27	,	,	PUNCT
ap-8672	150	28	ph	ph	NOUN
ap-8672	150	29	,	,	PUNCT
ap-8672	150	30	pw	pw	PROPN
ap-8672	150	31	)	)	PUNCT
ap-8672	150	32	,	,	PUNCT
ap-8672	150	33	which	which	PRON
ap-8672	150	34	are	be	AUX
ap-8672	150	35	defined	define	VERB
ap-8672	150	36	as	as	SCONJ
ap-8672	150	37	shown	show	VERB
ap-8672	150	38	in	in	ADP
ap-8672	150	39	figure	figure	NOUN
ap-8672	150	40	4	4	NUM
ap-8672	150	41	.	.	PUNCT
ap-8672	150	42	௘ܲ	௘ܲ	ADJ
ap-8672	150	43	௛ܲ	௛ܲ	NOUN
ap-8672	150	44	௔ܮ	௔ܮ	PROPN
ap-8672	150	45	௦ܲ	௦ܲ	PROPN
ap-8672	150	46	௪ܲ	௪ܲ	PROPN
ap-8672	150	47	௙ܮ	௙ܮ	NOUN
ap-8672	151	1	r	r	NOUN
ap-8672	151	2	(	(	PUNCT
ap-8672	151	3	a	a	NOUN
ap-8672	151	4	)	)	PUNCT
ap-8672	151	5	.	.	PUNCT
ap-8672	152	1	initial	initial	ADJ
ap-8672	152	2	form	form	NOUN
ap-8672	152	3	.	.	PUNCT
ap-8672	153	1	௔ܮ	௔ܮ	NUM
ap-8672	153	2	௪ܲܮ௙	௪ܲܮ௙	NOUN
ap-8672	153	3	௘ܲ	௘ܲ	ADJ
ap-8672	153	4	௛ܲ	௛ܲ	NOUN
ap-8672	153	5	௦ܲ	௦ܲ	ADJ
ap-8672	153	6	r	r	NOUN
ap-8672	153	7	௛௘ܮ	௛௘ܮ	NOUN
ap-8672	153	8	௛௪ܮ	௛௪ܮ	NOUN
ap-8672	153	9	௘ܲ	௘ܲ	VERB
ap-8672	153	10	௛௪ܮ	௛௪ܮ	NOUN
ap-8672	153	11	௛௘ܮ	௛௘ܮ	NOUN
ap-8672	153	12	ܪ	ܪ	X
ap-8672	153	13	(	(	PUNCT
ap-8672	153	14	b	b	NOUN
ap-8672	153	15	)	)	PUNCT
ap-8672	153	16	.	.	PUNCT
ap-8672	154	1	decomposed	decompose	VERB
ap-8672	154	2	form	form	NOUN
ap-8672	154	3	.	.	PUNCT
ap-8672	155	1	figure	figure	NOUN
ap-8672	155	2	4	4	NUM
ap-8672	155	3	.	.	NOUN
ap-8672	155	4	tetrahedron	tetrahedron	NOUN
ap-8672	155	5	form	form	NOUN
ap-8672	155	6	obtained	obtain	VERB
ap-8672	155	7	from	from	ADP
ap-8672	155	8	the	the	DET
ap-8672	155	9	derived	derived	ADJ
ap-8672	155	10	geometry	geometry	NOUN
ap-8672	155	11	space	space	NOUN
ap-8672	155	12	of	of	ADP
ap-8672	155	13	robot	robot	NOUN
ap-8672	155	14	.	.	PUNCT
ap-8672	156	1	ps	ps	PROPN
ap-8672	156	2	,	,	PUNCT
ap-8672	156	3	pe	pe	X
ap-8672	156	4	,	,	PUNCT
ap-8672	156	5	pw	pw	PROPN
ap-8672	156	6	and	and	CCONJ
ap-8672	156	7	ph	ph	PROPN
ap-8672	156	8	are	be	AUX
ap-8672	156	9	the	the	DET
ap-8672	156	10	points	point	NOUN
ap-8672	156	11	designating	designating	NOUN
ap-8672	156	12	:	:	PUNCT
ap-8672	156	13	shoulder	shoulder	NOUN
ap-8672	156	14	,	,	PUNCT
ap-8672	156	15	elbow	elbow	NOUN
ap-8672	156	16	,	,	PUNCT
ap-8672	156	17	wrist	wrist	NOUN
ap-8672	156	18	,	,	PUNCT
ap-8672	156	19	and	and	CCONJ
ap-8672	156	20	the	the	DET
ap-8672	156	21	closest	close	ADJ
ap-8672	156	22	point	point	NOUN
ap-8672	156	23	on	on	ADP
ap-8672	156	24	q	q	ADJ
ap-8672	156	25	-	-	NOUN
ap-8672	156	26	plane	plane	NOUN
ap-8672	156	27	to	to	ADP
ap-8672	156	28	the	the	DET
ap-8672	156	29	shoulder	shoulder	NOUN
ap-8672	156	30	frame	frame	NOUN
ap-8672	156	31	(	(	PUNCT
ap-8672	156	32	f0	f0	PROPN
ap-8672	156	33	)	)	PUNCT
ap-8672	156	34	,	,	PUNCT
ap-8672	156	35	respectively	respectively	ADV
ap-8672	156	36	.	.	PUNCT
ap-8672	157	1	from	from	ADP
ap-8672	157	2	figure	figure	NOUN
ap-8672	157	3	4	4	NUM
ap-8672	157	4	,	,	PUNCT
ap-8672	157	5	the	the	DET
ap-8672	157	6	length	length	NOUN
ap-8672	157	7	between	between	ADP
ap-8672	157	8	the	the	DET
ap-8672	157	9	origin	origin	NOUN
ap-8672	157	10	and	and	CCONJ
ap-8672	157	11	the	the	DET
ap-8672	157	12	wrist	wrist	NOUN
ap-8672	157	13	can	can	AUX
ap-8672	157	14	be	be	AUX
ap-8672	157	15	calculated	calculate	VERB
ap-8672	157	16	by	by	ADP
ap-8672	157	17	equation	equation	NOUN
ap-8672	157	18	(	(	PUNCT
ap-8672	157	19	10	10	NUM
ap-8672	157	20	)	)	PUNCT
ap-8672	157	21	.	.	PUNCT
ap-8672	158	1	r	r	NOUN
ap-8672	158	2	=	=	PUNCT
ap-8672	158	3	√	√	PROPN
ap-8672	158	4	p	p	NOUN
ap-8672	158	5	2	2	NUM
ap-8672	158	6	wx	wx	NOUN
ap-8672	158	7	+	+	X
ap-8672	158	8	p	p	NOUN
ap-8672	158	9	2	2	NUM
ap-8672	158	10	wy	wy	PROPN
ap-8672	158	11	+	+	CCONJ
ap-8672	158	12	p	p	NOUN
ap-8672	158	13	2	2	NUM
ap-8672	158	14	wz	wz	NOUN
ap-8672	158	15	,	,	PUNCT
ap-8672	158	16	(	(	PUNCT
ap-8672	158	17	10	10	NUM
ap-8672	158	18	)	)	PUNCT
ap-8672	158	19	where	where	SCONJ
ap-8672	158	20	pwx	pwx	NOUN
ap-8672	158	21	,	,	PUNCT
ap-8672	158	22	pwy	pwy	PROPN
ap-8672	158	23	,	,	PUNCT
ap-8672	158	24	pwz	pwz	NOUN
ap-8672	158	25	are	be	AUX
ap-8672	158	26	the	the	DET
ap-8672	158	27	coordinates	coordinate	NOUN
ap-8672	158	28	of	of	ADP
ap-8672	158	29	the	the	DET
ap-8672	158	30	vector	vector	NOUN
ap-8672	158	31	(	(	PUNCT
ap-8672	158	32	−−→	−−→	PROPN
ap-8672	158	33	opw	opw	PROPN
ap-8672	158	34	)	)	PUNCT
ap-8672	158	35	obtained	obtain	VERB
ap-8672	158	36	in	in	ADP
ap-8672	158	37	equation	equation	NOUN
ap-8672	158	38	(	(	PUNCT
ap-8672	158	39	9	9	NUM
ap-8672	158	40	)	)	PUNCT
ap-8672	158	41	.	.	PUNCT
ap-8672	159	1	q	q	X
ap-8672	159	2	-	-	PUNCT
ap-8672	159	3	plane	plane	NOUN
ap-8672	159	4	equation	equation	NOUN
ap-8672	159	5	obtained	obtain	VERB
ap-8672	159	6	via	via	ADP
ap-8672	159	7	the	the	DET
ap-8672	159	8	normal	normal	ADJ
ap-8672	159	9	vector	vector	NOUN
ap-8672	159	10	−→	−→	NOUN
ap-8672	159	11	a6	a6	NOUN
ap-8672	159	12	=	=	SYM
ap-8672	159	13	(	(	PUNCT
ap-8672	159	14	ax	ax	NOUN
ap-8672	159	15	,	,	PUNCT
ap-8672	159	16	ay	ay	INTJ
ap-8672	159	17	,	,	PUNCT
ap-8672	159	18	az)t	az)t	PROPN
ap-8672	159	19	of	of	ADP
ap-8672	159	20	z6	z6	NOUN
ap-8672	159	21	-	-	PUNCT
ap-8672	159	22	axis	axis	NOUN
ap-8672	159	23	of	of	ADP
ap-8672	159	24	the	the	DET
ap-8672	159	25	frame	frame	NOUN
ap-8672	159	26	f6	f6	PROPN
ap-8672	159	27	is	be	AUX
ap-8672	159	28	:	:	PUNCT
ap-8672	159	29	axx	axx	PROPN
ap-8672	159	30	+	+	CCONJ
ap-8672	159	31	ayy	ayy	PROPN
ap-8672	160	1	+	+	NOUN
ap-8672	160	2	azz	azz	NOUN
ap-8672	160	3	−	−	PROPN
ap-8672	160	4	d	d	NOUN
ap-8672	160	5	=	=	SYM
ap-8672	160	6	0	0	NUM
ap-8672	160	7	,	,	PUNCT
ap-8672	160	8	(	(	PUNCT
ap-8672	160	9	11	11	NUM
ap-8672	160	10	)	)	PUNCT
ap-8672	160	11	where	where	SCONJ
ap-8672	160	12	d	d	NOUN
ap-8672	160	13	=	=	SYM
ap-8672	160	14	(	(	PUNCT
ap-8672	160	15	axpwx	axpwx	NOUN
ap-8672	160	16	+	+	CCONJ
ap-8672	160	17	aypwy	aypwy	ADJ
ap-8672	160	18	+	+	CCONJ
ap-8672	160	19	azpwz	azpwz	NOUN
ap-8672	160	20	)	)	PUNCT
ap-8672	160	21	is	be	AUX
ap-8672	160	22	the	the	DET
ap-8672	160	23	parameter	parameter	NOUN
ap-8672	160	24	of	of	ADP
ap-8672	160	25	the	the	DET
ap-8672	160	26	plane	plane	NOUN
ap-8672	160	27	equation	equation	NOUN
ap-8672	160	28	.	.	PUNCT
ap-8672	161	1	from	from	ADP
ap-8672	161	2	equation	equation	NOUN
ap-8672	161	3	(	(	PUNCT
ap-8672	161	4	11	11	NUM
ap-8672	161	5	)	)	PUNCT
ap-8672	161	6	,	,	PUNCT
ap-8672	161	7	the	the	DET
ap-8672	161	8	closest	close	ADJ
ap-8672	161	9	distance	distance	NOUN
ap-8672	161	10	,	,	PUNCT
ap-8672	161	11	h	h	NOUN
ap-8672	161	12	,	,	PUNCT
ap-8672	161	13	between	between	ADP
ap-8672	161	14	the	the	DET
ap-8672	161	15	origin	origin	NOUN
ap-8672	161	16	and	and	CCONJ
ap-8672	161	17	q	q	NOUN
ap-8672	161	18	-	-	PUNCT
ap-8672	161	19	plane	plane	NOUN
ap-8672	161	20	can	can	AUX
ap-8672	161	21	be	be	AUX
ap-8672	161	22	calculated	calculate	VERB
ap-8672	161	23	as	as	ADP
ap-8672	161	24	:	:	PUNCT
ap-8672	161	25	h	h	NOUN
ap-8672	161	26	=	=	PUNCT
ap-8672	161	27	|axpwx	|axpwx	ADV
ap-8672	162	1	+	+	CCONJ
ap-8672	162	2	aypwy	aypwy	PROPN
ap-8672	162	3	+	+	CCONJ
ap-8672	162	4	azpwz|√	azpwz|√	NOUN
ap-8672	162	5	a2	a2	PROPN
ap-8672	162	6	x	x	PUNCT
ap-8672	163	1	+	+	CCONJ
ap-8672	163	2	a2	a2	PROPN
ap-8672	163	3	y	y	PROPN
ap-8672	163	4	+	+	PROPN
ap-8672	163	5	a2	a2	PROPN
ap-8672	163	6	z	z	PROPN
ap-8672	163	7	.	.	PUNCT
ap-8672	164	1	(	(	PUNCT
ap-8672	164	2	12	12	NUM
ap-8672	164	3	)	)	PUNCT
ap-8672	164	4	331	331	NUM
ap-8672	164	5	n.	n.	NOUN
ap-8672	164	6	hadidi	hadidi	PROPN
ap-8672	164	7	,	,	PUNCT
ap-8672	164	8	m.	m.	NOUN
ap-8672	164	9	bouaziz	bouaziz	PROPN
ap-8672	164	10	,	,	PUNCT
ap-8672	164	11	c.	c.	PROPN
ap-8672	164	12	mahfoudi	mahfoudi	PROPN
ap-8672	164	13	,	,	PUNCT
ap-8672	164	14	m.	m.	NOUN
ap-8672	164	15	zaharuddin	zaharuddin	PROPN
ap-8672	164	16	acta	acta	PROPN
ap-8672	164	17	polytechnica	polytechnica	PROPN
ap-8672	164	18	and	and	CCONJ
ap-8672	164	19	the	the	DET
ap-8672	164	20	corresponding	corresponding	ADJ
ap-8672	164	21	coordinates	coordinate	NOUN
ap-8672	164	22	of	of	ADP
ap-8672	164	23	the	the	DET
ap-8672	164	24	closest	close	ADJ
ap-8672	164	25	point	point	NOUN
ap-8672	164	26	on	on	ADP
ap-8672	164	27	q	q	NOUN
ap-8672	164	28	-	-	NOUN
ap-8672	164	29	plane	plane	NOUN
ap-8672	164	30	from	from	ADP
ap-8672	164	31	the	the	DET
ap-8672	164	32	origin	origin	NOUN
ap-8672	164	33	is	be	AUX
ap-8672	164	34	given	give	VERB
ap-8672	164	35	by	by	ADP
ap-8672	164	36	:	:	PUNCT
ap-8672	164	37	phx	phx	PROPN
ap-8672	164	38	=	=	PROPN
ap-8672	164	39	axd	axd	NOUN
ap-8672	164	40	a2	a2	PROPN
ap-8672	164	41	x	x	PUNCT
ap-8672	164	42	+	+	PUNCT
ap-8672	164	43	a2	a2	PROPN
ap-8672	164	44	y	y	PROPN
ap-8672	164	45	+	+	PROPN
ap-8672	164	46	a2	a2	PROPN
ap-8672	164	47	z	z	PROPN
ap-8672	164	48	,	,	PUNCT
ap-8672	164	49	phy	phy	NOUN
ap-8672	164	50	=	=	SYM
ap-8672	164	51	ayd	ayd	PROPN
ap-8672	164	52	a2	a2	PROPN
ap-8672	164	53	x	x	PUNCT
ap-8672	165	1	+	+	PUNCT
ap-8672	165	2	a2	a2	PROPN
ap-8672	165	3	y	y	PROPN
ap-8672	165	4	+	+	PROPN
ap-8672	165	5	a2	a2	PROPN
ap-8672	165	6	z	z	PROPN
ap-8672	165	7	,	,	PUNCT
ap-8672	165	8	(	(	PUNCT
ap-8672	165	9	13	13	NUM
ap-8672	165	10	)	)	PUNCT
ap-8672	165	11	phz	phz	NOUN
ap-8672	165	12	=	=	PUNCT
ap-8672	165	13	azd	azd	PROPN
ap-8672	165	14	a2	a2	PROPN
ap-8672	165	15	x	x	PUNCT
ap-8672	166	1	+	+	CCONJ
ap-8672	166	2	a2	a2	PROPN
ap-8672	166	3	y	y	PROPN
ap-8672	166	4	+	+	PROPN
ap-8672	166	5	a2	a2	PROPN
ap-8672	166	6	z	z	PROPN
ap-8672	166	7	.	.	PUNCT
ap-8672	167	1	from	from	ADP
ap-8672	167	2	figure	figure	NOUN
ap-8672	167	3	4	4	NUM
ap-8672	167	4	,	,	PUNCT
ap-8672	167	5	the	the	DET
ap-8672	167	6	length	length	NOUN
ap-8672	167	7	lhe	lhe	PROPN
ap-8672	167	8	is	be	AUX
ap-8672	167	9	defined	define	VERB
ap-8672	167	10	as	as	ADP
ap-8672	167	11	the	the	DET
ap-8672	167	12	distance	distance	NOUN
ap-8672	167	13	between	between	ADP
ap-8672	167	14	ph	ph	NOUN
ap-8672	167	15	(	(	PUNCT
ap-8672	167	16	the	the	DET
ap-8672	167	17	closest	close	ADJ
ap-8672	167	18	point	point	NOUN
ap-8672	167	19	to	to	ADP
ap-8672	167	20	the	the	DET
ap-8672	167	21	shoulder	shoulder	NOUN
ap-8672	167	22	frame	frame	NOUN
ap-8672	167	23	on	on	ADP
ap-8672	167	24	q	q	ADJ
ap-8672	167	25	-	-	NOUN
ap-8672	167	26	plane	plane	NOUN
ap-8672	167	27	)	)	PUNCT
ap-8672	167	28	and	and	CCONJ
ap-8672	167	29	pe	pe	INTJ
ap-8672	167	30	(	(	PUNCT
ap-8672	167	31	the	the	DET
ap-8672	167	32	elbow	elbow	PROPN
ap-8672	167	33	position	position	NOUN
ap-8672	167	34	)	)	PUNCT
ap-8672	167	35	.	.	PUNCT
ap-8672	168	1	similarly	similarly	ADV
ap-8672	168	2	,	,	PUNCT
ap-8672	168	3	lhw	lhw	PROPN
ap-8672	168	4	is	be	AUX
ap-8672	168	5	defined	define	VERB
ap-8672	168	6	between	between	ADP
ap-8672	168	7	points	point	NOUN
ap-8672	168	8	ph	ph	ADJ
ap-8672	168	9	and	and	CCONJ
ap-8672	168	10	pw	pw	PROPN
ap-8672	168	11	(	(	PUNCT
ap-8672	168	12	the	the	DET
ap-8672	168	13	wrist	wrist	NOUN
ap-8672	168	14	position	position	NOUN
ap-8672	168	15	)	)	PUNCT
ap-8672	168	16	.	.	PUNCT
ap-8672	169	1	consequently	consequently	ADV
ap-8672	169	2	,	,	PUNCT
ap-8672	169	3	using	use	VERB
ap-8672	169	4	the	the	DET
ap-8672	169	5	results	result	NOUN
ap-8672	169	6	obtained	obtain	VERB
ap-8672	169	7	in	in	ADP
ap-8672	169	8	equations	equation	NOUN
ap-8672	169	9	(	(	PUNCT
ap-8672	169	10	10	10	NUM
ap-8672	169	11	)	)	PUNCT
ap-8672	169	12	to	to	ADP
ap-8672	169	13	(	(	PUNCT
ap-8672	169	14	13	13	NUM
ap-8672	169	15	)	)	PUNCT
ap-8672	169	16	,	,	PUNCT
ap-8672	169	17	the	the	DET
ap-8672	169	18	two	two	NUM
ap-8672	169	19	lengths	length	NOUN
ap-8672	169	20	,	,	PUNCT
ap-8672	169	21	lhe	lhe	NOUN
ap-8672	169	22	and	and	CCONJ
ap-8672	169	23	lhw	lhw	PROPN
ap-8672	169	24	,	,	PUNCT
ap-8672	169	25	can	can	AUX
ap-8672	169	26	be	be	AUX
ap-8672	169	27	obtained	obtain	VERB
ap-8672	169	28	by	by	ADP
ap-8672	169	29	the	the	DET
ap-8672	169	30	following	follow	VERB
ap-8672	169	31	relationships	relationship	NOUN
ap-8672	169	32	:	:	PUNCT
ap-8672	169	33	lhe	lhe	PROPN
ap-8672	169	34	=	=	PUNCT
ap-8672	169	35	√	√	ADP
ap-8672	169	36	l2	l2	NOUN
ap-8672	169	37	f	f	NOUN
ap-8672	170	1	−	−	PROPN
ap-8672	170	2	h2	h2	PROPN
ap-8672	170	3	,	,	PUNCT
ap-8672	170	4	(	(	PUNCT
ap-8672	170	5	14	14	NUM
ap-8672	170	6	)	)	PUNCT
ap-8672	170	7	lhw	lhw	NOUN
ap-8672	170	8	=	=	SYM
ap-8672	170	9	√	√	PROPN
ap-8672	170	10	r2	r2	PROPN
ap-8672	170	11	−	−	PROPN
ap-8672	170	12	h2	h2	PROPN
ap-8672	170	13	.	.	PUNCT
ap-8672	171	1	(	(	PUNCT
ap-8672	171	2	15	15	NUM
ap-8672	171	3	)	)	PUNCT
ap-8672	171	4	thus	thus	ADV
ap-8672	171	5	,	,	PUNCT
ap-8672	171	6	based	base	VERB
ap-8672	171	7	on	on	ADP
ap-8672	171	8	equations	equation	NOUN
ap-8672	171	9	(	(	PUNCT
ap-8672	171	10	14	14	NUM
ap-8672	171	11	)	)	PUNCT
ap-8672	171	12	and	and	CCONJ
ap-8672	171	13	(	(	PUNCT
ap-8672	171	14	15	15	NUM
ap-8672	171	15	)	)	PUNCT
ap-8672	171	16	and	and	CCONJ
ap-8672	171	17	from	from	ADP
ap-8672	171	18	the	the	DET
ap-8672	171	19	triangle	triangle	NOUN
ap-8672	171	20	∆(pe	∆(pe	NOUN
ap-8672	171	21	,	,	PUNCT
ap-8672	171	22	ph	ph	VERB
ap-8672	171	23	,	,	PUNCT
ap-8672	171	24	pw	pw	NOUN
ap-8672	171	25	)	)	PUNCT
ap-8672	171	26	shown	show	VERB
ap-8672	171	27	in	in	ADP
ap-8672	171	28	figure	figure	NOUN
ap-8672	171	29	3	3	NUM
ap-8672	171	30	,	,	PUNCT
ap-8672	171	31	the	the	DET
ap-8672	171	32	angle	angle	NOUN
ap-8672	171	33	α1	α1	PROPN
ap-8672	171	34	formed	form	VERB
ap-8672	171	35	by	by	ADP
ap-8672	171	36	the	the	DET
ap-8672	171	37	points	point	NOUN
ap-8672	171	38	(	(	PUNCT
ap-8672	171	39	pe	pe	INTJ
ap-8672	171	40	,	,	PUNCT
ap-8672	171	41	p̂w	p̂w	ADV
ap-8672	171	42	,	,	PUNCT
ap-8672	171	43	ph	ph	VERB
ap-8672	171	44	)	)	PUNCT
ap-8672	171	45	can	can	AUX
ap-8672	171	46	be	be	AUX
ap-8672	171	47	calculated	calculate	VERB
ap-8672	171	48	by	by	ADP
ap-8672	171	49	the	the	DET
ap-8672	171	50	cosine	cosine	NOUN
ap-8672	171	51	law	law	NOUN
ap-8672	171	52	as	as	ADP
ap-8672	171	53	:	:	PUNCT
ap-8672	171	54	α1	α1	PROPN
ap-8672	171	55	=	=	SYM
ap-8672	171	56	(	(	PUNCT
ap-8672	171	57	pe	pe	INTJ
ap-8672	171	58	,	,	PUNCT
ap-8672	171	59	p̂w	p̂w	ADV
ap-8672	171	60	,	,	PUNCT
ap-8672	171	61	ph	ph	PROPN
ap-8672	171	62	)	)	PUNCT
ap-8672	171	63	=	=	SYM
ap-8672	171	64	a	a	DET
ap-8672	171	65	cos	cos	PROPN
ap-8672	171	66	(	(	PUNCT
ap-8672	171	67	l2	l2	VERB
ap-8672	171	68	hw	hw	PRON
ap-8672	171	69	+	+	CCONJ
ap-8672	171	70	l2	l2	VERB
ap-8672	171	71	f	f	NOUN
ap-8672	171	72	−	−	NOUN
ap-8672	171	73	l2	l2	NOUN
ap-8672	171	74	he	he	PRON
ap-8672	171	75	2lf	2lf	ADJ
ap-8672	171	76	lhe	lhe	PROPN
ap-8672	171	77	)	)	PUNCT
ap-8672	171	78	.	.	PUNCT
ap-8672	172	1	(	(	PUNCT
ap-8672	172	2	16	16	NUM
ap-8672	172	3	)	)	PUNCT
ap-8672	172	4	in	in	ADP
ap-8672	172	5	addition	addition	NOUN
ap-8672	172	6	,	,	PUNCT
ap-8672	172	7	the	the	DET
ap-8672	172	8	circle	circle	NOUN
ap-8672	172	9	equation	equation	NOUN
ap-8672	172	10	of	of	ADP
ap-8672	172	11	radius	radius	NOUN
ap-8672	172	12	lf	lf	PROPN
ap-8672	172	13	and	and	CCONJ
ap-8672	172	14	centre	centre	NOUN
ap-8672	172	15	point	point	NOUN
ap-8672	172	16	pw	pw	PROPN
ap-8672	172	17	on	on	ADP
ap-8672	172	18	the	the	DET
ap-8672	172	19	q	q	NOUN
ap-8672	172	20	-	-	PUNCT
ap-8672	172	21	plane	plane	NOUN
ap-8672	172	22	is	be	AUX
ap-8672	172	23	defined	define	VERB
ap-8672	172	24	in	in	ADP
ap-8672	172	25	equation	equation	NOUN
ap-8672	172	26	(	(	PUNCT
ap-8672	172	27	17	17	NUM
ap-8672	172	28	)	)	PUNCT
ap-8672	172	29	.	.	PUNCT
ap-8672	173	1	−−→	−−→	PROPN
ap-8672	173	2	opc	opc	PROPN
ap-8672	173	3	=	=	PROPN
ap-8672	173	4	−−→	−−→	PROPN
ap-8672	173	5	opw	opw	PROPN
ap-8672	173	6	+	+	PROPN
ap-8672	173	7	lf	lf	PROPN
ap-8672	173	8	cos(ϕ)−→s6	cos(ϕ)−→s6	PROPN
ap-8672	173	9	+	+	CCONJ
ap-8672	173	10	lf	lf	NOUN
ap-8672	173	11	sin(ϕ)−→n6	sin(ϕ)−→n6	NOUN
ap-8672	173	12	,	,	PUNCT
ap-8672	173	13	(	(	PUNCT
ap-8672	173	14	17	17	NUM
ap-8672	173	15	)	)	PUNCT
ap-8672	173	16	where	where	SCONJ
ap-8672	173	17	−−→	−−→	PROPN
ap-8672	173	18	opc	opc	PROPN
ap-8672	173	19	=	=	SYM
ap-8672	173	20	(	(	PUNCT
ap-8672	173	21	pcx	pcx	PROPN
ap-8672	173	22	,	,	PUNCT
ap-8672	173	23	pcy	pcy	PROPN
ap-8672	173	24	,	,	PUNCT
ap-8672	173	25	pcz)t	pcz)t	PROPN
ap-8672	173	26	and	and	CCONJ
ap-8672	173	27	−−→	−−→	PROPN
ap-8672	173	28	opw	opw	PROPN
ap-8672	173	29	=	=	PROPN
ap-8672	173	30	(	(	PUNCT
ap-8672	173	31	pwx	pwx	PROPN
ap-8672	173	32	,	,	PUNCT
ap-8672	173	33	pwy	pwy	VERB
ap-8672	173	34	,	,	PUNCT
ap-8672	173	35	pwz)t	pwz)t	PROPN
ap-8672	173	36	are	be	AUX
ap-8672	173	37	the	the	DET
ap-8672	173	38	coordinates	coordinate	NOUN
ap-8672	173	39	of	of	ADP
ap-8672	173	40	circle	circle	PROPN
ap-8672	173	41	’s	’s	PART
ap-8672	173	42	circumference	circumference	NOUN
ap-8672	173	43	and	and	CCONJ
ap-8672	173	44	circle	circle	PROPN
ap-8672	173	45	’s	’s	PART
ap-8672	173	46	centre	centre	NOUN
ap-8672	173	47	respectively	respectively	ADV
ap-8672	173	48	.	.	PUNCT
ap-8672	174	1	−→	−→	PROPN
ap-8672	174	2	s6	s6	PROPN
ap-8672	174	3	and	and	CCONJ
ap-8672	174	4	−→	−→	PROPN
ap-8672	174	5	n6	n6	PROPN
ap-8672	174	6	are	be	AUX
ap-8672	174	7	the	the	DET
ap-8672	174	8	unit	unit	NOUN
ap-8672	174	9	vectors	vector	NOUN
ap-8672	174	10	of	of	ADP
ap-8672	174	11	x6	x6	NOUN
ap-8672	174	12	-	-	PUNCT
ap-8672	174	13	axis	axis	NOUN
ap-8672	174	14	and	and	CCONJ
ap-8672	174	15	y6	y6	ADJ
ap-8672	174	16	-	-	PUNCT
ap-8672	174	17	axis	axis	NOUN
ap-8672	174	18	of	of	ADP
ap-8672	174	19	frame	frame	NOUN
ap-8672	174	20	f6	f6	PROPN
ap-8672	174	21	,	,	PUNCT
ap-8672	174	22	respectively	respectively	ADV
ap-8672	174	23	,	,	PUNCT
ap-8672	174	24	and	and	CCONJ
ap-8672	174	25	ϕ	ϕ	X
ap-8672	174	26	=	=	PROPN
ap-8672	174	27	α1	α1	PROPN
ap-8672	174	28	+	+	CCONJ
ap-8672	174	29	α2	α2	ADJ
ap-8672	174	30	is	be	AUX
ap-8672	174	31	the	the	DET
ap-8672	174	32	angle	angle	NOUN
ap-8672	174	33	between	between	ADP
ap-8672	174	34	x6	x6	NOUN
ap-8672	174	35	-	-	PUNCT
ap-8672	174	36	axis	axis	NOUN
ap-8672	174	37	and	and	CCONJ
ap-8672	174	38	−−→	−−→	PROPN
ap-8672	174	39	vwe	vwe	PROPN
ap-8672	174	40	(	(	PUNCT
ap-8672	174	41	the	the	DET
ap-8672	174	42	vector	vector	NOUN
ap-8672	174	43	between	between	ADP
ap-8672	174	44	the	the	DET
ap-8672	174	45	wrist	wrist	NOUN
ap-8672	174	46	and	and	CCONJ
ap-8672	174	47	the	the	DET
ap-8672	174	48	elbow	elbow	NOUN
ap-8672	174	49	point	point	NOUN
ap-8672	174	50	)	)	PUNCT
ap-8672	174	51	.	.	PUNCT
ap-8672	175	1	additionally	additionally	ADV
ap-8672	175	2	,	,	PUNCT
ap-8672	175	3	the	the	DET
ap-8672	175	4	value	value	NOUN
ap-8672	175	5	α1	α1	PROPN
ap-8672	175	6	=	=	SYM
ap-8672	175	7	(	(	PUNCT
ap-8672	175	8	pe	pe	INTJ
ap-8672	175	9	,	,	PUNCT
ap-8672	175	10	p̂w	p̂w	ADV
ap-8672	175	11	,	,	PUNCT
ap-8672	175	12	ph	ph	VERB
ap-8672	175	13	)	)	PUNCT
ap-8672	175	14	is	be	AUX
ap-8672	175	15	calculated	calculate	VERB
ap-8672	175	16	by	by	ADP
ap-8672	175	17	equation	equation	NOUN
ap-8672	175	18	(	(	PUNCT
ap-8672	175	19	16	16	NUM
ap-8672	175	20	)	)	PUNCT
ap-8672	175	21	and	and	CCONJ
ap-8672	175	22	the	the	DET
ap-8672	175	23	α2	α2	ADJ
ap-8672	175	24	magnitude	magnitude	NOUN
ap-8672	175	25	is	be	AUX
ap-8672	175	26	given	give	VERB
ap-8672	175	27	by	by	ADP
ap-8672	175	28	the	the	DET
ap-8672	175	29	cosine	cosine	NOUN
ap-8672	175	30	law	law	NOUN
ap-8672	175	31	:	:	PUNCT
ap-8672	176	1	cos(α2	cos(α2	PROPN
ap-8672	176	2	)	)	PUNCT
ap-8672	176	3	=	=	SYM
ap-8672	176	4	−→	−→	NOUN
ap-8672	176	5	s6.−−→nwh	s6.−−→nwh	PROPN
ap-8672	176	6	|	|	ADV
ap-8672	176	7	−→	−→	ADJ
ap-8672	176	8	s6|−−→nwh|	s6|−−→nwh|	NOUN
ap-8672	176	9	,	,	PUNCT
ap-8672	176	10	(	(	PUNCT
ap-8672	176	11	18	18	NUM
ap-8672	176	12	)	)	PUNCT
ap-8672	176	13	where	where	SCONJ
ap-8672	176	14	−−→nwh	−−→nwh	NOUN
ap-8672	176	15	and	and	CCONJ
ap-8672	176	16	|−−→nwh|	|−−→nwh|	PROPN
ap-8672	176	17	are	be	AUX
ap-8672	176	18	normalised	normalise	VERB
ap-8672	176	19	vectors	vector	NOUN
ap-8672	176	20	of	of	ADP
ap-8672	176	21	−−→	−−→	PROPN
ap-8672	176	22	vwh	vwh	NOUN
ap-8672	176	23	and	and	CCONJ
ap-8672	176	24	its	its	PRON
ap-8672	176	25	modulus	modulus	NOUN
ap-8672	176	26	,	,	PUNCT
ap-8672	176	27	respectively	respectively	ADV
ap-8672	176	28	.	.	PUNCT
ap-8672	177	1	referring	refer	VERB
ap-8672	177	2	to	to	PART
ap-8672	177	3	figure	figure	VERB
ap-8672	177	4	3b	3b	NUM
ap-8672	177	5	,	,	PUNCT
ap-8672	177	6	where	where	SCONJ
ap-8672	177	7	the	the	DET
ap-8672	177	8	vectors	vector	NOUN
ap-8672	177	9	−→	−→	NOUN
ap-8672	177	10	s6	s6	PROPN
ap-8672	177	11	and	and	CCONJ
ap-8672	177	12	−−→	−−→	NUM
ap-8672	177	13	vwh	vwh	NOUN
ap-8672	177	14	(	(	PUNCT
ap-8672	177	15	wrist	wrist	NOUN
ap-8672	177	16	-	-	PUNCT
ap-8672	177	17	closest	close	ADJ
ap-8672	177	18	point	point	NOUN
ap-8672	177	19	on	on	ADP
ap-8672	177	20	the	the	DET
ap-8672	177	21	q	q	NOUN
ap-8672	177	22	-	-	NOUN
ap-8672	177	23	plane	plane	NOUN
ap-8672	177	24	to	to	ADP
ap-8672	177	25	the	the	DET
ap-8672	177	26	shoulder	shoulder	NOUN
ap-8672	177	27	frame	frame	NOUN
ap-8672	177	28	)	)	PUNCT
ap-8672	177	29	are	be	AUX
ap-8672	177	30	both	both	PRON
ap-8672	177	31	inside	inside	ADP
ap-8672	177	32	the	the	DET
ap-8672	177	33	q	q	NOUN
ap-8672	177	34	-	-	NOUN
ap-8672	177	35	plane	plane	NOUN
ap-8672	177	36	,	,	PUNCT
ap-8672	177	37	the	the	DET
ap-8672	177	38	orientation	orientation	NOUN
ap-8672	177	39	of	of	ADP
ap-8672	177	40	α2	α2	PROPN
ap-8672	177	41	can	can	AUX
ap-8672	177	42	be	be	AUX
ap-8672	177	43	determined	determine	VERB
ap-8672	177	44	by	by	ADP
ap-8672	177	45	the	the	DET
ap-8672	177	46	determinant	determinant	NOUN
ap-8672	177	47	of	of	ADP
ap-8672	177	48	these	these	DET
ap-8672	177	49	three	three	NUM
ap-8672	177	50	vectors	vector	NOUN
ap-8672	177	51	:	:	PUNCT
ap-8672	177	52	−→	−→	NOUN
ap-8672	177	53	a6	a6	NOUN
ap-8672	177	54	,	,	PUNCT
ap-8672	177	55	−−→nwh	−−→nwh	X
ap-8672	177	56	and	and	CCONJ
ap-8672	177	57	−→	−→	NOUN
ap-8672	177	58	s6	s6	PROPN
ap-8672	177	59	as	as	SCONJ
ap-8672	177	60	shown	show	VERB
ap-8672	177	61	in	in	ADP
ap-8672	177	62	equation	equation	NOUN
ap-8672	177	63	(	(	PUNCT
ap-8672	177	64	19	19	NUM
ap-8672	177	65	):	):	PUNCT
ap-8672	178	1	det	det	PROPN
ap-8672	178	2	α2	α2	PROPN
ap-8672	178	3	=	=	SYM
ap-8672	178	4	det	det	PROPN
ap-8672	179	1	[	[	X
ap-8672	179	2	−→	−→	NOUN
ap-8672	179	3	a6	a6	NOUN
ap-8672	179	4	−−→nwh	−−→nwh	NOUN
ap-8672	179	5	−→	−→	PROPN
ap-8672	179	6	s6	s6	PROPN
ap-8672	179	7	]	]	X
ap-8672	179	8	t	t	PROPN
ap-8672	179	9	.	.	PUNCT
ap-8672	180	1	(	(	PUNCT
ap-8672	180	2	19	19	NUM
ap-8672	180	3	)	)	PUNCT
ap-8672	180	4	hence	hence	ADV
ap-8672	180	5	,	,	PUNCT
ap-8672	180	6	based	base	VERB
ap-8672	180	7	on	on	ADP
ap-8672	180	8	equations	equation	NOUN
ap-8672	180	9	(	(	PUNCT
ap-8672	180	10	18	18	NUM
ap-8672	180	11	)	)	PUNCT
ap-8672	180	12	and	and	CCONJ
ap-8672	180	13	(	(	PUNCT
ap-8672	180	14	19	19	NUM
ap-8672	180	15	)	)	PUNCT
ap-8672	180	16	,	,	PUNCT
ap-8672	180	17	the	the	DET
ap-8672	180	18	angle	angle	NOUN
ap-8672	180	19	α2	α2	PROPN
ap-8672	180	20	is	be	AUX
ap-8672	180	21	given	give	VERB
ap-8672	180	22	by	by	ADP
ap-8672	180	23	the	the	DET
ap-8672	180	24	next	next	ADJ
ap-8672	180	25	equation	equation	NOUN
ap-8672	180	26	:	:	PUNCT
ap-8672	180	27	α2	α2	PROPN
ap-8672	180	28	=	=	PUNCT
ap-8672	180	29	atan2(det	atan2(det	NOUN
ap-8672	180	30	α2	α2	PROPN
ap-8672	180	31	,	,	PUNCT
ap-8672	180	32	cos(α2	cos(α2	PROPN
ap-8672	180	33	)	)	PUNCT
ap-8672	180	34	)	)	PUNCT
ap-8672	180	35	.	.	PUNCT
ap-8672	181	1	(	(	PUNCT
ap-8672	181	2	20	20	NUM
ap-8672	181	3	)	)	PUNCT
ap-8672	181	4	then	then	ADV
ap-8672	181	5	,	,	PUNCT
ap-8672	181	6	the	the	DET
ap-8672	181	7	angle	angle	NOUN
ap-8672	181	8	ϕ	ϕ	NOUN
ap-8672	181	9	is	be	AUX
ap-8672	181	10	calculated	calculate	VERB
ap-8672	181	11	by	by	ADP
ap-8672	181	12	the	the	DET
ap-8672	181	13	equations	equation	NOUN
ap-8672	181	14	(	(	PUNCT
ap-8672	181	15	16	16	NUM
ap-8672	181	16	)	)	PUNCT
ap-8672	181	17	and	and	CCONJ
ap-8672	181	18	(	(	PUNCT
ap-8672	181	19	20	20	NUM
ap-8672	181	20	)	)	PUNCT
ap-8672	181	21	.	.	PUNCT
ap-8672	182	1	ϕ	ϕ	NOUN
ap-8672	182	2	=	=	PUNCT
ap-8672	182	3	α1	α1	PROPN
ap-8672	182	4	+	+	CCONJ
ap-8672	182	5	α2	α2	ADJ
ap-8672	182	6	.	.	PUNCT
ap-8672	183	1	(	(	PUNCT
ap-8672	183	2	21	21	NUM
ap-8672	183	3	)	)	PUNCT
ap-8672	183	4	finally	finally	ADV
ap-8672	183	5	substituting	substitute	VERB
ap-8672	183	6	equation	equation	NOUN
ap-8672	183	7	(	(	PUNCT
ap-8672	183	8	21	21	NUM
ap-8672	183	9	)	)	PUNCT
ap-8672	183	10	in	in	ADP
ap-8672	183	11	equation	equation	NOUN
ap-8672	183	12	(	(	PUNCT
ap-8672	183	13	17	17	NUM
ap-8672	183	14	)	)	PUNCT
ap-8672	183	15	,	,	PUNCT
ap-8672	183	16	the	the	DET
ap-8672	183	17	elbow	elbow	NOUN
ap-8672	183	18	position	position	NOUN
ap-8672	183	19	is	be	AUX
ap-8672	183	20	determined	determine	VERB
ap-8672	183	21	by	by	ADP
ap-8672	183	22	the	the	DET
ap-8672	183	23	coordinate	coordinate	NOUN
ap-8672	183	24	’s	’s	PART
ap-8672	183	25	vector	vector	NOUN
ap-8672	183	26	(	(	PUNCT
ap-8672	183	27	22	22	NUM
ap-8672	183	28	):	):	PUNCT
ap-8672	183	29	−→	−→	PROPN
ap-8672	183	30	voe	voe	PROPN
ap-8672	183	31	=	=	SYM
ap-8672	183	32	(	(	PUNCT
ap-8672	183	33	pex	pex	PROPN
ap-8672	183	34	,	,	PUNCT
ap-8672	183	35	pey	pey	PROPN
ap-8672	183	36	,	,	PUNCT
ap-8672	183	37	pez)t	pez)t	PROPN
ap-8672	183	38	.	.	PUNCT
ap-8672	184	1	(	(	PUNCT
ap-8672	184	2	22	22	NUM
ap-8672	184	3	)	)	PUNCT
ap-8672	184	4	after	after	ADP
ap-8672	184	5	determining	determine	VERB
ap-8672	184	6	the	the	DET
ap-8672	184	7	necessary	necessary	ADJ
ap-8672	184	8	geometric	geometric	ADJ
ap-8672	184	9	entities	entity	NOUN
ap-8672	184	10	for	for	ADP
ap-8672	184	11	calculating	calculate	VERB
ap-8672	184	12	the	the	DET
ap-8672	184	13	joint	joint	ADJ
ap-8672	184	14	angles	angle	NOUN
ap-8672	184	15	,	,	PUNCT
ap-8672	184	16	we	we	PRON
ap-8672	184	17	proceed	proceed	VERB
ap-8672	184	18	to	to	ADP
ap-8672	184	19	their	their	PRON
ap-8672	184	20	identifications	identification	NOUN
ap-8672	184	21	.	.	PUNCT
ap-8672	185	1	332	332	NUM
ap-8672	185	2	vol	vol	NOUN
ap-8672	185	3	.	.	PUNCT
ap-8672	185	4	63	63	NUM
ap-8672	185	5	no	no	NOUN
ap-8672	185	6	.	.	PUNCT
ap-8672	186	1	5/2023	5/2023	NUM
ap-8672	186	2	geometric	geometric	ADJ
ap-8672	186	3	approach	approach	NOUN
ap-8672	186	4	to	to	ADP
ap-8672	186	5	solving	solve	VERB
ap-8672	186	6	inverse	inverse	ADJ
ap-8672	186	7	kinematics	kinematic	NOUN
ap-8672	186	8	of	of	ADP
ap-8672	186	9	six	six	NUM
ap-8672	186	10	dof	dof	NOUN
ap-8672	186	11	robot	robot	NOUN
ap-8672	186	12	4.2.2	4.2.2	NOUN
ap-8672	186	13	.	.	PUNCT
ap-8672	186	14	calculate	calculate	VERB
ap-8672	186	15	the	the	DET
ap-8672	186	16	joint	joint	ADJ
ap-8672	186	17	angles	angle	NOUN
ap-8672	186	18	of	of	ADP
ap-8672	186	19	the	the	DET
ap-8672	186	20	robot	robot	NOUN
ap-8672	186	21	the	the	DET
ap-8672	186	22	geometric	geometric	ADJ
ap-8672	186	23	vectors	vector	NOUN
ap-8672	186	24	needed	need	VERB
ap-8672	186	25	to	to	PART
ap-8672	186	26	calculate	calculate	VERB
ap-8672	186	27	the	the	DET
ap-8672	186	28	joint	joint	ADJ
ap-8672	186	29	angles	angle	NOUN
ap-8672	186	30	are	be	AUX
ap-8672	186	31	obtained	obtain	VERB
ap-8672	186	32	in	in	ADP
ap-8672	186	33	phase	phase	NOUN
ap-8672	186	34	1	1	NUM
ap-8672	186	35	.	.	PUNCT
ap-8672	187	1	therefore	therefore	ADV
ap-8672	187	2	,	,	PUNCT
ap-8672	187	3	the	the	DET
ap-8672	187	4	joint	joint	ADJ
ap-8672	187	5	angle	angle	NOUN
ap-8672	187	6	equations	equation	NOUN
ap-8672	187	7	are	be	AUX
ap-8672	187	8	calculable	calculable	ADJ
ap-8672	187	9	(	(	PUNCT
ap-8672	187	10	βi	βi	PROPN
ap-8672	187	11	,	,	PUNCT
ap-8672	187	12	i	i	NOUN
ap-8672	187	13	=	=	NOUN
ap-8672	187	14	1	1	NUM
ap-8672	187	15	,	,	PUNCT
ap-8672	187	16	.	.	PUNCT
ap-8672	187	17	.	.	PUNCT
ap-8672	188	1	.	.	PUNCT
ap-8672	189	1	,	,	PUNCT
ap-8672	189	2	6	6	NUM
ap-8672	189	3	)	)	PUNCT
ap-8672	189	4	.	.	PUNCT
ap-8672	190	1	geometrically	geometrically	ADV
ap-8672	190	2	,	,	PUNCT
ap-8672	190	3	each	each	DET
ap-8672	190	4	joint	joint	ADJ
ap-8672	190	5	angle	angle	NOUN
ap-8672	190	6	is	be	AUX
ap-8672	190	7	described	describe	VERB
ap-8672	190	8	by	by	ADP
ap-8672	190	9	three	three	NUM
ap-8672	190	10	vectors	vector	NOUN
ap-8672	190	11	(	(	PUNCT
ap-8672	190	12	see	see	VERB
ap-8672	190	13	figure	figure	NOUN
ap-8672	190	14	5a-5f	5a-5f	NOUN
ap-8672	190	15	)	)	PUNCT
ap-8672	190	16	,	,	PUNCT
ap-8672	190	17	two	two	NUM
ap-8672	190	18	mathematical	mathematical	ADJ
ap-8672	190	19	arguments	argument	NOUN
ap-8672	190	20	(	(	PUNCT
ap-8672	190	21	arg1	arg1	PROPN
ap-8672	190	22	,	,	PUNCT
ap-8672	190	23	arg2	arg2	PROPN
ap-8672	190	24	)	)	PUNCT
ap-8672	190	25	are	be	AUX
ap-8672	190	26	expressed	express	VERB
ap-8672	190	27	which	which	PRON
ap-8672	190	28	are	be	AUX
ap-8672	190	29	used	use	VERB
ap-8672	190	30	in	in	ADP
ap-8672	190	31	equation	equation	NOUN
ap-8672	190	32	(	(	PUNCT
ap-8672	190	33	6	6	NUM
ap-8672	190	34	)	)	PUNCT
ap-8672	190	35	in	in	ADP
ap-8672	190	36	the	the	DET
ap-8672	190	37	form	form	NOUN
ap-8672	190	38	atan2(arg1	atan2(arg1	PROPN
ap-8672	190	39	,	,	PUNCT
ap-8672	190	40	arg2	arg2	PROPN
ap-8672	190	41	)	)	PUNCT
ap-8672	190	42	.	.	PUNCT
ap-8672	191	1	푛	푛	X
ap-8672	191	2	푛	푛	X
ap-8672	191	3	푛	푛	X
ap-8672	191	4	⃗	⃗	PROPN
ap-8672	191	5	푃	푃	X
ap-8672	191	6	푦	푦	X
ap-8672	191	7	푥	푥	PRON
ap-8672	191	8	푧	푧	X
ap-8672	191	9	훽	훽	X
ap-8672	191	10	표	표	NOUN
ap-8672	191	11	푛	푛	X
ap-8672	191	12	⃗	⃗	PROPN
ap-8672	191	13	휷ퟏ	휷ퟏ	NOUN
ap-8672	191	14	푃	푃	X
ap-8672	191	15	푃	푃	X
ap-8672	191	16	푄	푄	X
ap-8672	191	17	(	(	PUNCT
ap-8672	191	18	a	a	NOUN
ap-8672	191	19	)	)	PUNCT
ap-8672	191	20	.	.	PUNCT
ap-8672	192	1	β1	β1	PROPN
ap-8672	192	2	.	.	PUNCT
ap-8672	193	1	푛	푛	X
ap-8672	193	2	⃗	⃗	PROPN
ap-8672	193	3	푃	푃	PROPN
ap-8672	193	4	푃	푃	PROPN
ap-8672	193	5	푦	푦	X
ap-8672	193	6	푧	푧	X
ap-8672	193	7	푃	푃	X
ap-8672	193	8	표	표	X
ap-8672	193	9	훽	훽	X
ap-8672	193	10	푛	푛	X
ap-8672	193	11	⃗	⃗	PROPN
ap-8672	193	12	푛	푛	X
ap-8672	193	13	⃗	⃗	PROPN
ap-8672	193	14	휷ퟐ	휷ퟐ	NOUN
ap-8672	193	15	훾	훾	X
ap-8672	193	16	푥	푥	INTJ
ap-8672	193	17	푄	푄	X
ap-8672	193	18	(	(	PUNCT
ap-8672	193	19	b	b	NOUN
ap-8672	193	20	)	)	PUNCT
ap-8672	193	21	.	.	PUNCT
ap-8672	194	1	β2	β2	PROPN
ap-8672	194	2	.	.	PUNCT
ap-8672	195	1	푥	푥	INTJ
ap-8672	195	2	푛	푛	X
ap-8672	195	3	⃗	⃗	PROPN
ap-8672	195	4	휷ퟑ	휷ퟑ	NOUN
ap-8672	195	5	푃	푃	PROPN
ap-8672	195	6	푃	푃	X
ap-8672	195	7	푦	푦	X
ap-8672	195	8	푧	푧	X
ap-8672	195	9	푛	푛	X
ap-8672	195	10	⃗	⃗	PROPN
ap-8672	195	11	표	표	X
ap-8672	195	12	푛	푛	X
ap-8672	195	13	⃗	⃗	PROPN
ap-8672	195	14	푉	푉	ADP
ap-8672	195	15	⃗	⃗	PROPN
ap-8672	195	16	훽	훽	X
ap-8672	195	17	(	(	PUNCT
ap-8672	195	18	c	c	NOUN
ap-8672	195	19	)	)	PUNCT
ap-8672	195	20	.	.	PUNCT
ap-8672	196	1	β3	β3	PROPN
ap-8672	196	2	.	.	PUNCT
ap-8672	197	1	푃	푃	PROPN
ap-8672	197	2	푃	푃	PROPN
ap-8672	197	3	푦	푦	X
ap-8672	197	4	푧	푧	X
ap-8672	197	5	푃	푃	PROPN
ap-8672	197	6	표	표	PROPN
ap-8672	197	7	푉	푉	ADP
ap-8672	197	8	⃗	⃗	PROPN
ap-8672	197	9	휷ퟒ	휷ퟒ	NOUN
ap-8672	197	10	푥	푥	INTJ
ap-8672	197	11	훽	훽	X
ap-8672	197	12	푉	푉	ADP
ap-8672	197	13	⃗	⃗	PROPN
ap-8672	197	14	(	(	PUNCT
ap-8672	197	15	d	d	NOUN
ap-8672	197	16	)	)	PUNCT
ap-8672	197	17	.	.	PUNCT
ap-8672	198	1	β4	β4	PROPN
ap-8672	198	2	.	.	PUNCT
ap-8672	199	1	퐴⃗	퐴⃗	PROPN
ap-8672	199	2	훽	훽	X
ap-8672	199	3	푃	푃	X
ap-8672	199	4	푃	푃	PROPN
ap-8672	199	5	푦	푦	X
ap-8672	199	6	푥	푥	X
ap-8672	199	7	푧	푧	X
ap-8672	199	8	푛	푛	X
ap-8672	199	9	⃗	⃗	X
ap-8672	199	10	푛	푛	X
ap-8672	199	11	⃗	⃗	PROPN
ap-8672	199	12	휷ퟓ	휷ퟓ	INTJ
ap-8672	199	13	푉	푉	ADP
ap-8672	199	14	⃗	⃗	PROPN
ap-8672	199	15	푄	푄	X
ap-8672	199	16	(	(	PUNCT
ap-8672	199	17	e	e	NOUN
ap-8672	199	18	)	)	PUNCT
ap-8672	199	19	.	.	PUNCT
ap-8672	200	1	β5	β5	NOUN
ap-8672	200	2	.	.	PUNCT
ap-8672	201	1	퐴⃗	퐴⃗	PROPN
ap-8672	201	2	푃	푃	X
ap-8672	201	3	푃	푃	PROPN
ap-8672	201	4	푦	푦	X
ap-8672	201	5	푥	푥	X
ap-8672	201	6	푧	푧	X
ap-8672	201	7	휷ퟔ	휷ퟔ	NOUN
ap-8672	201	8	푃	푃	PROPN
ap-8672	201	9	푉	푉	ADP
ap-8672	201	10	⃗	⃗	PROPN
ap-8672	201	11	푆⃗	푆⃗	NOUN
ap-8672	201	12	(	(	PUNCT
ap-8672	201	13	f	f	NOUN
ap-8672	201	14	)	)	PUNCT
ap-8672	201	15	.	.	PUNCT
ap-8672	202	1	β6	β6	PROPN
ap-8672	202	2	.	.	PUNCT
ap-8672	203	1	figure	figure	VERB
ap-8672	203	2	5	5	NUM
ap-8672	203	3	.	.	PUNCT
ap-8672	203	4	vectorial	vectorial	ADJ
ap-8672	203	5	description	description	NOUN
ap-8672	203	6	of	of	ADP
ap-8672	203	7	robot	robot	NOUN
ap-8672	203	8	’s	’s	PART
ap-8672	203	9	joint	joint	ADJ
ap-8672	203	10	angles	angle	NOUN
ap-8672	203	11	.	.	PUNCT
ap-8672	204	1	a.	a.	NOUN
ap-8672	204	2	joint	joint	PROPN
ap-8672	204	3	angle	angle	NOUN
ap-8672	204	4	β1	β1	PROPN
ap-8672	204	5	:	:	PUNCT
ap-8672	204	6	figure	figure	NOUN
ap-8672	204	7	5a	5a	NUM
ap-8672	204	8	shows	show	VERB
ap-8672	204	9	the	the	DET
ap-8672	204	10	vectorial	vectorial	ADJ
ap-8672	204	11	description	description	NOUN
ap-8672	204	12	of	of	ADP
ap-8672	204	13	the	the	DET
ap-8672	204	14	joint	joint	ADJ
ap-8672	204	15	angle	angle	NOUN
ap-8672	204	16	β1	β1	PROPN
ap-8672	204	17	.	.	PUNCT
ap-8672	205	1	the	the	DET
ap-8672	205	2	angle	angle	NOUN
ap-8672	205	3	is	be	AUX
ap-8672	205	4	defined	define	VERB
ap-8672	205	5	by	by	ADP
ap-8672	205	6	the	the	DET
ap-8672	205	7	normal	normal	ADJ
ap-8672	205	8	vector	vector	NOUN
ap-8672	205	9	obtained	obtain	VERB
ap-8672	205	10	from	from	ADP
ap-8672	205	11	the	the	DET
ap-8672	205	12	cross	cross	NOUN
ap-8672	205	13	product	product	NOUN
ap-8672	205	14	of	of	ADP
ap-8672	205	15	vectors	vector	NOUN
ap-8672	205	16	−−→	−−→	PROPN
ap-8672	205	17	voz0	voz0	PROPN
ap-8672	205	18	and	and	CCONJ
ap-8672	205	19	−→	−→	PROPN
ap-8672	205	20	voe	voe	PROPN
ap-8672	205	21	.	.	PUNCT
ap-8672	206	1	−→nq1	−→nq1	PART
ap-8672	206	2	is	be	AUX
ap-8672	206	3	the	the	DET
ap-8672	206	4	axis	axis	NOUN
ap-8672	206	5	collinear	collinear	ADJ
ap-8672	206	6	with	with	ADP
ap-8672	206	7	the	the	DET
ap-8672	206	8	rotational	rotational	ADJ
ap-8672	206	9	joint	joint	ADJ
ap-8672	206	10	q2	q2	NOUN
ap-8672	206	11	-	-	PUNCT
ap-8672	206	12	axis	axis	NOUN
ap-8672	206	13	.	.	PUNCT
ap-8672	207	1	furthermore	furthermore	ADV
ap-8672	207	2	,	,	PUNCT
ap-8672	207	3	−→nq1	−→nq1	ADV
ap-8672	207	4	revolves	revolve	VERB
ap-8672	207	5	in	in	ADP
ap-8672	207	6	a	a	DET
ap-8672	207	7	plane	plane	NOUN
ap-8672	207	8	parallel	parallel	NOUN
ap-8672	207	9	to	to	ADP
ap-8672	207	10	plane	plane	NOUN
ap-8672	207	11	qxoy	qxoy	NOUN
ap-8672	207	12	.	.	PUNCT
ap-8672	208	1	therefore	therefore	ADV
ap-8672	208	2	,	,	PUNCT
ap-8672	208	3	n1x	n1x	PROPN
ap-8672	208	4	=	=	SYM
ap-8672	208	5	cos(−−→	cos(−−→	NUM
ap-8672	208	6	vox0	vox0	NOUN
ap-8672	208	7	,	,	PUNCT
ap-8672	208	8	−−→nq1	−−→nq1	ADJ
ap-8672	208	9	)	)	PUNCT
ap-8672	208	10	|−−→nq1|	|−−→nq1|	ADV
ap-8672	208	11	and	and	CCONJ
ap-8672	208	12	n1y	n1y	NUM
ap-8672	208	13	=	=	PUNCT
ap-8672	208	14	sin(−−→	sin(−−→	NUM
ap-8672	208	15	vox0	vox0	NOUN
ap-8672	208	16	,	,	PUNCT
ap-8672	208	17	−−→nq1	−−→nq1	NOUN
ap-8672	208	18	)	)	PUNCT
ap-8672	208	19	|−−→nq1|	|−−→nq1|	ADV
ap-8672	208	20	,	,	PUNCT
ap-8672	208	21	where	where	SCONJ
ap-8672	208	22	:	:	PUNCT
ap-8672	208	23	−−→	−−→	NOUN
ap-8672	208	24	vox0	vox0	NOUN
ap-8672	208	25	and	and	CCONJ
ap-8672	208	26	−−→	−−→	PROPN
ap-8672	208	27	voz0	voz0	PROPN
ap-8672	208	28	:	:	PUNCT
ap-8672	208	29	the	the	DET
ap-8672	208	30	unit	unit	NOUN
ap-8672	208	31	vectors	vector	NOUN
ap-8672	208	32	of	of	ADP
ap-8672	208	33	x0	x0	PROPN
ap-8672	208	34	-	-	PUNCT
ap-8672	208	35	axis	axis	ADJ
ap-8672	208	36	and	and	CCONJ
ap-8672	208	37	z0	z0	NOUN
ap-8672	208	38	-	-	PUNCT
ap-8672	208	39	axis	axis	NOUN
ap-8672	208	40	,	,	PUNCT
ap-8672	208	41	respectively	respectively	ADV
ap-8672	208	42	,	,	PUNCT
ap-8672	208	43	of	of	ADP
ap-8672	208	44	frame	frame	NOUN
ap-8672	208	45	f0	f0	PROPN
ap-8672	208	46	,	,	PUNCT
ap-8672	208	47	−→nq1	−→nq1	ADV
ap-8672	208	48	:	:	PUNCT
ap-8672	208	49	the	the	DET
ap-8672	208	50	normalised	normalise	VERB
ap-8672	208	51	and	and	CCONJ
ap-8672	208	52	normal	normal	ADJ
ap-8672	208	53	vector	vector	NOUN
ap-8672	208	54	of	of	ADP
ap-8672	208	55	q1	q1	NOUN
ap-8672	208	56	-	-	PUNCT
ap-8672	208	57	plan	plan	NOUN
ap-8672	208	58	obtained	obtain	VERB
ap-8672	208	59	from	from	ADP
ap-8672	208	60	cross	cross	NOUN
ap-8672	208	61	product	product	NOUN
ap-8672	208	62	−−→	−−→	PROPN
ap-8672	208	63	voz0	voz0	PROPN
ap-8672	208	64	∧	∧	PROPN
ap-8672	208	65	−→	−→	PROPN
ap-8672	208	66	voe	voe	PROPN
ap-8672	208	67	,	,	PUNCT
ap-8672	208	68	−→	−→	PROPN
ap-8672	208	69	voe	voe	PROPN
ap-8672	208	70	:	:	PUNCT
ap-8672	208	71	the	the	DET
ap-8672	208	72	vector	vector	NOUN
ap-8672	208	73	between	between	ADP
ap-8672	208	74	the	the	DET
ap-8672	208	75	two	two	NUM
ap-8672	208	76	points	point	NOUN
ap-8672	208	77	(	(	PUNCT
ap-8672	208	78	origin	origin	NOUN
ap-8672	208	79	-	-	PUNCT
ap-8672	208	80	elbow	elbow	NOUN
ap-8672	208	81	)	)	PUNCT
ap-8672	208	82	,	,	PUNCT
ap-8672	208	83	qxoy	qxoy	NOUN
ap-8672	208	84	:	:	PUNCT
ap-8672	208	85	the	the	DET
ap-8672	208	86	plane	plane	NOUN
ap-8672	208	87	defined	define	VERB
ap-8672	208	88	by	by	ADP
ap-8672	208	89	two	two	NUM
ap-8672	208	90	unit	unit	NOUN
ap-8672	208	91	vectors	vector	NOUN
ap-8672	208	92	of	of	ADP
ap-8672	208	93	axes	axis	NOUN
ap-8672	208	94	,	,	PUNCT
ap-8672	208	95	x0	x0	PROPN
ap-8672	208	96	-	-	PUNCT
ap-8672	208	97	axis	axis	NOUN
ap-8672	208	98	and	and	CCONJ
ap-8672	208	99	y0	y0	NOUN
ap-8672	208	100	-	-	PUNCT
ap-8672	208	101	axis	axis	NOUN
ap-8672	208	102	.	.	PUNCT
ap-8672	209	1	as	as	SCONJ
ap-8672	209	2	the	the	DET
ap-8672	209	3	normal	normal	ADJ
ap-8672	209	4	vector	vector	NOUN
ap-8672	209	5	−→nq1	−→nq1	ADV
ap-8672	209	6	is	be	AUX
ap-8672	209	7	normalised	normalise	VERB
ap-8672	209	8	to	to	ADP
ap-8672	209	9	a	a	DET
ap-8672	209	10	unit	unit	NOUN
ap-8672	209	11	vector	vector	NOUN
ap-8672	209	12	(	(	PUNCT
ap-8672	209	13	|−→nq1|	|−→nq1|	NUM
ap-8672	209	14	=	=	SYM
ap-8672	209	15	1	1	NUM
ap-8672	209	16	)	)	PUNCT
ap-8672	209	17	,	,	PUNCT
ap-8672	209	18	the	the	DET
ap-8672	209	19	equations	equation	NOUN
ap-8672	209	20	can	can	AUX
ap-8672	209	21	be	be	AUX
ap-8672	209	22	written	write	VERB
ap-8672	209	23	as	as	ADP
ap-8672	209	24	:	:	PUNCT
ap-8672	209	25	n1x	n1x	PROPN
ap-8672	209	26	=	=	PUNCT
ap-8672	209	27	cos(−−→	cos(−−→	NOUN
ap-8672	209	28	vox0	vox0	NOUN
ap-8672	209	29	,	,	PUNCT
ap-8672	209	30	−→nq1	−→nq1	ADV
ap-8672	209	31	)	)	PUNCT
ap-8672	209	32	and	and	CCONJ
ap-8672	209	33	n1y	n1y	NUM
ap-8672	209	34	=	=	PUNCT
ap-8672	209	35	sin(−−→	sin(−−→	NUM
ap-8672	209	36	vox0	vox0	NOUN
ap-8672	209	37	,	,	PUNCT
ap-8672	209	38	−→nq1	−→nq1	ADV
ap-8672	209	39	)	)	PUNCT
ap-8672	209	40	.	.	PUNCT
ap-8672	210	1	therefore	therefore	ADV
ap-8672	210	2	,	,	PUNCT
ap-8672	210	3	the	the	DET
ap-8672	210	4	joint	joint	ADJ
ap-8672	210	5	angle	angle	NOUN
ap-8672	210	6	is	be	AUX
ap-8672	210	7	obtained	obtain	VERB
ap-8672	210	8	by	by	ADP
ap-8672	210	9	formula	formula	NOUN
ap-8672	210	10	:	:	PUNCT
ap-8672	210	11	β1	β1	PROPN
ap-8672	210	12	=	=	SYM
ap-8672	210	13	atan2(n1y	atan2(n1y	PROPN
ap-8672	210	14	,	,	PUNCT
ap-8672	210	15	n1x	n1x	PROPN
ap-8672	210	16	)	)	PUNCT
ap-8672	210	17	.	.	PUNCT
ap-8672	211	1	(	(	PUNCT
ap-8672	211	2	23	23	NUM
ap-8672	211	3	)	)	PUNCT
ap-8672	211	4	b.	b.	NOUN
ap-8672	211	5	joint	joint	PROPN
ap-8672	211	6	angle	angle	NOUN
ap-8672	211	7	β2	β2	NOUN
ap-8672	211	8	:	:	PUNCT
ap-8672	211	9	figure	figure	NOUN
ap-8672	211	10	5b	5b	PROPN
ap-8672	211	11	shows	show	VERB
ap-8672	211	12	the	the	DET
ap-8672	211	13	vectorial	vectorial	ADJ
ap-8672	211	14	description	description	NOUN
ap-8672	211	15	of	of	ADP
ap-8672	211	16	the	the	DET
ap-8672	211	17	joint	joint	ADJ
ap-8672	211	18	angle	angle	NOUN
ap-8672	211	19	β2	β2	NOUN
ap-8672	211	20	.	.	PUNCT
ap-8672	212	1	it	it	PRON
ap-8672	212	2	is	be	AUX
ap-8672	212	3	defined	define	VERB
ap-8672	212	4	by	by	ADP
ap-8672	212	5	two	two	NUM
ap-8672	212	6	vectors,−−→	vectors,−−→	NOUN
ap-8672	212	7	voz0	voz0	PROPN
ap-8672	212	8	and	and	CCONJ
ap-8672	212	9	−→	−→	PROPN
ap-8672	212	10	voe	voe	PROPN
ap-8672	212	11	,	,	PUNCT
ap-8672	212	12	where	where	SCONJ
ap-8672	212	13	,	,	PUNCT
ap-8672	212	14	−−→noz0	−−→noz0	PROPN
ap-8672	212	15	and	and	CCONJ
ap-8672	212	16	−→noe	−→noe	PROPN
ap-8672	212	17	are	be	AUX
ap-8672	212	18	their	their	PRON
ap-8672	212	19	normal	normal	ADJ
ap-8672	212	20	vectors	vector	NOUN
ap-8672	212	21	,	,	PUNCT
ap-8672	212	22	respectively	respectively	ADV
ap-8672	212	23	.	.	PUNCT
ap-8672	213	1	333	333	NUM
ap-8672	213	2	n.	n.	NOUN
ap-8672	213	3	hadidi	hadidi	PROPN
ap-8672	213	4	,	,	PUNCT
ap-8672	213	5	m.	m.	NOUN
ap-8672	213	6	bouaziz	bouaziz	PROPN
ap-8672	213	7	,	,	PUNCT
ap-8672	213	8	c.	c.	PROPN
ap-8672	213	9	mahfoudi	mahfoudi	PROPN
ap-8672	213	10	,	,	PUNCT
ap-8672	213	11	m.	m.	NOUN
ap-8672	213	12	zaharuddin	zaharuddin	PROPN
ap-8672	213	13	acta	acta	PROPN
ap-8672	213	14	polytechnica	polytechnica	PROPN
ap-8672	213	15	from	from	ADP
ap-8672	213	16	figure	figure	NOUN
ap-8672	213	17	5b	5b	NUM
ap-8672	213	18	,	,	PUNCT
ap-8672	213	19	β2	β2	PROPN
ap-8672	213	20	can	can	AUX
ap-8672	213	21	be	be	AUX
ap-8672	213	22	written	write	VERB
ap-8672	213	23	as	as	ADP
ap-8672	213	24	:	:	PUNCT
ap-8672	213	25	β2	β2	NOUN
ap-8672	213	26	=	=	PROPN
ap-8672	213	27	π	π	PROPN
ap-8672	213	28	2	2	NUM
ap-8672	213	29	−	−	NOUN
ap-8672	213	30	γ2	γ2	NOUN
ap-8672	213	31	,	,	PUNCT
ap-8672	213	32	(	(	PUNCT
ap-8672	213	33	24	24	NUM
ap-8672	213	34	)	)	PUNCT
ap-8672	213	35	where	where	SCONJ
ap-8672	213	36	γ2	γ2	PROPN
ap-8672	213	37	is	be	AUX
ap-8672	213	38	expressed	express	VERB
ap-8672	213	39	by	by	ADP
ap-8672	213	40	the	the	DET
ap-8672	213	41	equation	equation	NOUN
ap-8672	213	42	γ2	γ2	NOUN
ap-8672	213	43	=	=	PUNCT
ap-8672	213	44	atan2(det	atan2(det	NOUN
ap-8672	213	45	γ2	γ2	NOUN
ap-8672	213	46	,	,	PUNCT
ap-8672	213	47	cos(γ2	cos(γ2	NOUN
ap-8672	213	48	)	)	PUNCT
ap-8672	213	49	)	)	PUNCT
ap-8672	213	50	,	,	PUNCT
ap-8672	213	51	where	where	SCONJ
ap-8672	213	52	cos(γ2	cos(γ2	NOUN
ap-8672	213	53	)	)	PUNCT
ap-8672	213	54	=	=	SYM
ap-8672	213	55	−−→	−−→	PROPN
ap-8672	213	56	voz0	voz0	PROPN
ap-8672	213	57	.−→noe	.−→noe	PROPN
ap-8672	213	58	and	and	CCONJ
ap-8672	213	59	det	det	PROPN
ap-8672	213	60	γ2	γ2	PROPN
ap-8672	213	61	=	=	SYM
ap-8672	213	62	det	det	PROPN
ap-8672	214	1	[	[	X
ap-8672	214	2	−→nq1	−→nq1	ADV
ap-8672	214	3	−−→noz0	−−→noz0	DET
ap-8672	214	4	−→noe]t	−→noe]t	NOUN
ap-8672	214	5	in	in	ADP
ap-8672	214	6	which	which	PRON
ap-8672	214	7	−−→noz0	−−→noz0	PROPN
ap-8672	214	8	=	=	SYM
ap-8672	214	9	(	(	PUNCT
ap-8672	214	10	0	0	NUM
ap-8672	214	11	0	0	NUM
ap-8672	214	12	1)t	1)t	PROPN
ap-8672	214	13	,	,	PUNCT
ap-8672	214	14	−→noe	−→noe	PROPN
ap-8672	214	15	=	=	PUNCT
ap-8672	214	16	(	(	PUNCT
ap-8672	214	17	nex	nex	PROPN
ap-8672	214	18	ney	ney	NOUN
ap-8672	214	19	nez)t	nez)t	PROPN
ap-8672	214	20	and	and	CCONJ
ap-8672	214	21	−→nq1	−→nq1	ADV
ap-8672	214	22	=	=	SYM
ap-8672	214	23	(	(	PUNCT
ap-8672	214	24	n1x	n1x	PROPN
ap-8672	214	25	n1y	n1y	PRON
ap-8672	214	26	0)t	0)t	PROPN
ap-8672	214	27	.	.	PUNCT
ap-8672	215	1	c.	c.	PROPN
ap-8672	215	2	joint	joint	PROPN
ap-8672	215	3	angle	angle	NOUN
ap-8672	215	4	β3	β3	PROPN
ap-8672	215	5	:	:	PUNCT
ap-8672	215	6	the	the	DET
ap-8672	215	7	joint	joint	ADJ
ap-8672	215	8	angle	angle	NOUN
ap-8672	215	9	β3	β3	PROPN
ap-8672	215	10	is	be	AUX
ap-8672	215	11	the	the	DET
ap-8672	215	12	angle	angle	NOUN
ap-8672	215	13	between	between	ADP
ap-8672	215	14	the	the	DET
ap-8672	215	15	two	two	NUM
ap-8672	215	16	planes	plane	NOUN
ap-8672	215	17	q1	q1	NOUN
ap-8672	215	18	-	-	PUNCT
ap-8672	215	19	plane	plane	NOUN
ap-8672	215	20	(	(	PUNCT
ap-8672	215	21	defined	define	VERB
ap-8672	215	22	by	by	ADP
ap-8672	215	23	vectors	vector	NOUN
ap-8672	215	24	−−→	−−→	PROPN
ap-8672	215	25	voz0	voz0	PROPN
ap-8672	215	26	and	and	CCONJ
ap-8672	215	27	−→	−→	PROPN
ap-8672	215	28	voe	voe	PROPN
ap-8672	215	29	)	)	PUNCT
ap-8672	215	30	and	and	CCONJ
ap-8672	215	31	q2	q2	NOUN
ap-8672	215	32	-	-	PUNCT
ap-8672	215	33	plane	plane	NOUN
ap-8672	215	34	(	(	PUNCT
ap-8672	215	35	defined	define	VERB
ap-8672	215	36	by	by	ADP
ap-8672	215	37	the	the	DET
ap-8672	215	38	three	three	NUM
ap-8672	215	39	points	point	NOUN
ap-8672	215	40	of	of	ADP
ap-8672	215	41	the	the	DET
ap-8672	215	42	robot	robot	NOUN
ap-8672	215	43	’s	’s	PART
ap-8672	215	44	links	link	NOUN
ap-8672	215	45	:	:	PUNCT
ap-8672	215	46	shoulder	shoulder	NOUN
ap-8672	215	47	-	-	PUNCT
ap-8672	215	48	elbow	elbow	NOUN
ap-8672	215	49	-	-	PUNCT
ap-8672	215	50	wrist	wrist	NOUN
ap-8672	215	51	)	)	PUNCT
ap-8672	215	52	as	as	SCONJ
ap-8672	215	53	shown	show	VERB
ap-8672	215	54	in	in	ADP
ap-8672	215	55	figure	figure	NOUN
ap-8672	215	56	5c	5c	NOUN
ap-8672	215	57	,	,	PUNCT
ap-8672	215	58	where	where	SCONJ
ap-8672	215	59	−→nq1	−→nq1	ADV
ap-8672	215	60	and	and	CCONJ
ap-8672	215	61	−→nq2	−→nq2	NUM
ap-8672	215	62	are	be	AUX
ap-8672	215	63	their	their	PRON
ap-8672	215	64	normal	normal	ADJ
ap-8672	215	65	vectors	vector	NOUN
ap-8672	215	66	,	,	PUNCT
ap-8672	215	67	respectively	respectively	ADV
ap-8672	215	68	.	.	PUNCT
ap-8672	216	1	thus	thus	ADV
ap-8672	216	2	,	,	PUNCT
ap-8672	216	3	β3	β3	NOUN
ap-8672	216	4	can	can	AUX
ap-8672	216	5	be	be	AUX
ap-8672	216	6	further	far	ADV
ap-8672	216	7	expressed	express	VERB
ap-8672	216	8	as	as	SCONJ
ap-8672	216	9	follows	follow	VERB
ap-8672	216	10	:	:	PUNCT
ap-8672	216	11	β3	β3	PROPN
ap-8672	216	12	=	=	SYM
ap-8672	216	13	atan2(det	atan2(det	NOUN
ap-8672	216	14	β3	β3	PROPN
ap-8672	216	15	,	,	PUNCT
ap-8672	216	16	cos(β3	cos(β3	PROPN
ap-8672	216	17	)	)	PUNCT
ap-8672	216	18	)	)	PUNCT
ap-8672	216	19	,	,	PUNCT
ap-8672	216	20	(	(	PUNCT
ap-8672	216	21	25	25	NUM
ap-8672	216	22	)	)	PUNCT
ap-8672	216	23	where	where	SCONJ
ap-8672	216	24	cos(β3	cos(β3	X
ap-8672	216	25	)	)	PUNCT
ap-8672	217	1	=	=	SYM
ap-8672	218	1	−→nq1.−→nq2	−→nq1.−→nq2	NOUN
ap-8672	218	2	and	and	CCONJ
ap-8672	218	3	the	the	DET
ap-8672	218	4	determinant	determinant	ADJ
ap-8672	218	5	is	be	AUX
ap-8672	218	6	:	:	PUNCT
ap-8672	218	7	det	det	NOUN
ap-8672	218	8	β3	β3	PROPN
ap-8672	218	9	=	=	SYM
ap-8672	218	10	det	det	PROPN
ap-8672	219	1	[	[	X
ap-8672	219	2	−→noe	−→noe	PROPN
ap-8672	219	3	−→nq1	−→nq1	ADV
ap-8672	219	4	−→nq2]t	−→nq2]t	PUNCT
ap-8672	219	5	.	.	PUNCT
ap-8672	220	1	d.	d.	PROPN
ap-8672	220	2	joint	joint	PROPN
ap-8672	220	3	angle	angle	PROPN
ap-8672	220	4	β4	β4	PROPN
ap-8672	220	5	:	:	PUNCT
ap-8672	220	6	the	the	DET
ap-8672	220	7	joint	joint	ADJ
ap-8672	220	8	angle	angle	NOUN
ap-8672	220	9	β4	β4	PROPN
ap-8672	220	10	is	be	AUX
ap-8672	220	11	an	an	DET
ap-8672	220	12	angle	angle	NOUN
ap-8672	220	13	between	between	ADP
ap-8672	220	14	−→	−→	PROPN
ap-8672	220	15	voe	voe	PROPN
ap-8672	220	16	(	(	PUNCT
ap-8672	220	17	arm	arm	PROPN
ap-8672	220	18	)	)	PUNCT
ap-8672	220	19	and	and	CCONJ
ap-8672	220	20	−−→	−−→	PROPN
ap-8672	220	21	vew	vew	INTJ
ap-8672	220	22	(	(	PUNCT
ap-8672	220	23	forearm	forearm	NOUN
ap-8672	220	24	)	)	PUNCT
ap-8672	220	25	as	as	SCONJ
ap-8672	220	26	shown	show	VERB
ap-8672	220	27	in	in	ADP
ap-8672	220	28	figure	figure	NOUN
ap-8672	220	29	5d	5d	NUM
ap-8672	220	30	.	.	PUNCT
ap-8672	221	1	−→noe	−→noe	PROPN
ap-8672	221	2	and	and	CCONJ
ap-8672	221	3	−−→new	−−→new	NOUN
ap-8672	221	4	are	be	AUX
ap-8672	221	5	the	the	DET
ap-8672	221	6	normalised	normalise	VERB
ap-8672	221	7	vectors	vector	NOUN
ap-8672	221	8	of	of	ADP
ap-8672	221	9	−→	−→	PROPN
ap-8672	221	10	voe	voe	PROPN
ap-8672	221	11	and	and	CCONJ
ap-8672	221	12	−−→	−−→	PROPN
ap-8672	221	13	vew	vew	PROPN
ap-8672	221	14	,	,	PUNCT
ap-8672	221	15	respectively	respectively	ADV
ap-8672	221	16	.	.	PUNCT
ap-8672	222	1	the	the	DET
ap-8672	222	2	angle	angle	NOUN
ap-8672	222	3	can	can	AUX
ap-8672	222	4	be	be	AUX
ap-8672	222	5	calculated	calculate	VERB
ap-8672	222	6	by	by	ADP
ap-8672	222	7	the	the	DET
ap-8672	222	8	formula	formula	NOUN
ap-8672	222	9	below	below	ADV
ap-8672	222	10	:	:	PUNCT
ap-8672	222	11	β4	β4	PROPN
ap-8672	222	12	=	=	PUNCT
ap-8672	222	13	atan2(det	atan2(det	PROPN
ap-8672	222	14	β4	β4	PROPN
ap-8672	222	15	,	,	PUNCT
ap-8672	222	16	cos(β4	cos(β4	NOUN
ap-8672	222	17	)	)	PUNCT
ap-8672	222	18	)	)	PUNCT
ap-8672	222	19	,	,	PUNCT
ap-8672	222	20	(	(	PUNCT
ap-8672	222	21	26	26	NUM
ap-8672	222	22	)	)	PUNCT
ap-8672	222	23	where	where	SCONJ
ap-8672	222	24	the	the	DET
ap-8672	222	25	cos(β4	cos(β4	NOUN
ap-8672	222	26	)	)	PUNCT
ap-8672	222	27	=	=	PUNCT
ap-8672	223	1	−→noe.−−→new	−→noe.−−→new	PRON
ap-8672	223	2	and	and	CCONJ
ap-8672	223	3	the	the	DET
ap-8672	223	4	determinant	determinant	NOUN
ap-8672	223	5	of	of	ADP
ap-8672	223	6	β4	β4	PROPN
ap-8672	223	7	can	can	AUX
ap-8672	223	8	be	be	AUX
ap-8672	223	9	obtained	obtain	VERB
ap-8672	223	10	by	by	ADP
ap-8672	223	11	:	:	PUNCT
ap-8672	223	12	det	det	PROPN
ap-8672	223	13	β4	β4	PROPN
ap-8672	223	14	=	=	SYM
ap-8672	223	15	det	det	PROPN
ap-8672	224	1	[	[	X
ap-8672	224	2	−→nq1	−→nq1	X
ap-8672	224	3	−→noe	−→noe	PROPN
ap-8672	224	4	−−→new]t	−−→new]t	NOUN
ap-8672	224	5	.	.	PUNCT
ap-8672	225	1	e.	e.	PROPN
ap-8672	225	2	joint	joint	PROPN
ap-8672	225	3	angle	angle	PROPN
ap-8672	225	4	β5	β5	PROPN
ap-8672	225	5	:	:	PUNCT
ap-8672	225	6	the	the	DET
ap-8672	225	7	joint	joint	ADJ
ap-8672	225	8	angle	angle	NOUN
ap-8672	225	9	β5	β5	NOUN
ap-8672	225	10	is	be	AUX
ap-8672	225	11	defined	define	VERB
ap-8672	225	12	as	as	ADP
ap-8672	225	13	the	the	DET
ap-8672	225	14	angle	angle	NOUN
ap-8672	225	15	between	between	ADP
ap-8672	225	16	the	the	DET
ap-8672	225	17	vectors	vector	NOUN
ap-8672	225	18	−→nq2	−→nq2	ADJ
ap-8672	225	19	and	and	CCONJ
ap-8672	225	20	−→	−→	NOUN
ap-8672	225	21	a6	a6	NOUN
ap-8672	225	22	=	=	SYM
ap-8672	225	23	(	(	PUNCT
ap-8672	225	24	ax	ax	NOUN
ap-8672	225	25	,	,	PUNCT
ap-8672	225	26	ay	ay	INTJ
ap-8672	225	27	,	,	PUNCT
ap-8672	225	28	az)t	az)t	PROPN
ap-8672	225	29	of	of	ADP
ap-8672	225	30	the	the	DET
ap-8672	225	31	z6	z6	NOUN
ap-8672	225	32	-	-	PUNCT
ap-8672	225	33	axis	axis	NOUN
ap-8672	225	34	as	as	SCONJ
ap-8672	225	35	shown	show	VERB
ap-8672	225	36	in	in	ADP
ap-8672	225	37	figure	figure	NOUN
ap-8672	225	38	5e	5e	NOUN
ap-8672	225	39	.	.	PUNCT
ap-8672	226	1	so	so	ADV
ap-8672	226	2	the	the	DET
ap-8672	226	3	arguments	argument	NOUN
ap-8672	226	4	of	of	ADP
ap-8672	226	5	β5	β5	NOUN
ap-8672	226	6	can	can	AUX
ap-8672	226	7	be	be	AUX
ap-8672	226	8	expressed	express	VERB
ap-8672	226	9	by	by	ADP
ap-8672	226	10	cos(β5	cos(β5	NOUN
ap-8672	226	11	)	)	PUNCT
ap-8672	226	12	=	=	PUNCT
ap-8672	227	1	−→nq2	−→nq2	ADJ
ap-8672	227	2	.	.	PUNCT
ap-8672	228	1	−→	−→	NOUN
ap-8672	228	2	a6	a6	NOUN
ap-8672	228	3	and	and	CCONJ
ap-8672	228	4	det	det	PROPN
ap-8672	228	5	β5	β5	PROPN
ap-8672	228	6	=	=	SYM
ap-8672	228	7	det	det	PROPN
ap-8672	229	1	[	[	X
ap-8672	229	2	−−→	−−→	X
ap-8672	229	3	vwe	vwe	PROPN
ap-8672	229	4	−→nq2	−→nq2	VERB
ap-8672	229	5	−→	−→	NOUN
ap-8672	229	6	a6	a6	NOUN
ap-8672	229	7	]	]	X
ap-8672	229	8	t	t	PROPN
ap-8672	229	9	.	.	PUNCT
ap-8672	230	1	finally	finally	ADV
ap-8672	230	2	,	,	PUNCT
ap-8672	230	3	β5	β5	PROPN
ap-8672	230	4	can	can	AUX
ap-8672	230	5	be	be	AUX
ap-8672	230	6	expressed	express	VERB
ap-8672	230	7	by	by	ADP
ap-8672	230	8	equation	equation	NOUN
ap-8672	230	9	(	(	PUNCT
ap-8672	230	10	27	27	NUM
ap-8672	230	11	):	):	PUNCT
ap-8672	230	12	β5	β5	PROPN
ap-8672	230	13	=	=	PUNCT
ap-8672	230	14	atan2(det	atan2(det	NOUN
ap-8672	230	15	β5	β5	NOUN
ap-8672	230	16	,	,	PUNCT
ap-8672	230	17	cos(β5	cos(β5	PROPN
ap-8672	230	18	)	)	PUNCT
ap-8672	230	19	)	)	PUNCT
ap-8672	230	20	.	.	PUNCT
ap-8672	231	1	(	(	PUNCT
ap-8672	231	2	27	27	NUM
ap-8672	231	3	)	)	PUNCT
ap-8672	231	4	f.	f.	PROPN
ap-8672	231	5	joint	joint	PROPN
ap-8672	231	6	angle	angle	PROPN
ap-8672	231	7	β6	β6	PROPN
ap-8672	231	8	:	:	PUNCT
ap-8672	231	9	the	the	DET
ap-8672	231	10	joint	joint	ADJ
ap-8672	231	11	angle	angle	NOUN
ap-8672	231	12	β6	β6	PROPN
ap-8672	231	13	is	be	AUX
ap-8672	231	14	the	the	DET
ap-8672	231	15	angle	angle	NOUN
ap-8672	231	16	between	between	ADP
ap-8672	231	17	the	the	DET
ap-8672	231	18	forearm	forearm	NOUN
ap-8672	231	19	and	and	CCONJ
ap-8672	231	20	the	the	DET
ap-8672	231	21	hand	hand	NOUN
ap-8672	231	22	of	of	ADP
ap-8672	231	23	the	the	DET
ap-8672	231	24	robot	robot	NOUN
ap-8672	231	25	,	,	PUNCT
ap-8672	231	26	which	which	PRON
ap-8672	231	27	is	be	AUX
ap-8672	231	28	defined	define	VERB
ap-8672	231	29	by	by	ADP
ap-8672	231	30	the	the	DET
ap-8672	231	31	vectors	vector	NOUN
ap-8672	231	32	−−→	−−→	X
ap-8672	231	33	vew	vew	INTJ
ap-8672	231	34	(	(	PUNCT
ap-8672	231	35	elbow	elbow	NOUN
ap-8672	231	36	-	-	PUNCT
ap-8672	231	37	wrist	wrist	NOUN
ap-8672	231	38	)	)	PUNCT
ap-8672	231	39	and	and	CCONJ
ap-8672	231	40	−−→	−−→	PROPN
ap-8672	231	41	vwd	vwd	PROPN
ap-8672	231	42	(	(	PUNCT
ap-8672	231	43	wrist	wrist	NOUN
ap-8672	231	44	-	-	PUNCT
ap-8672	231	45	desired	desire	VERB
ap-8672	231	46	position	position	NOUN
ap-8672	231	47	)	)	PUNCT
ap-8672	231	48	,	,	PUNCT
ap-8672	231	49	respectively	respectively	ADV
ap-8672	231	50	,	,	PUNCT
ap-8672	231	51	see	see	VERB
ap-8672	231	52	figure	figure	NOUN
ap-8672	231	53	5f	5f	NOUN
ap-8672	231	54	.	.	PUNCT
ap-8672	232	1	therefore	therefore	ADV
ap-8672	232	2	,	,	PUNCT
ap-8672	232	3	β6	β6	PROPN
ap-8672	232	4	is	be	AUX
ap-8672	232	5	the	the	DET
ap-8672	232	6	angle	angle	NOUN
ap-8672	232	7	between	between	ADP
ap-8672	232	8	two	two	NUM
ap-8672	232	9	vectors	vector	NOUN
ap-8672	232	10	:	:	PUNCT
ap-8672	232	11	−−→new	−−→new	ADJ
ap-8672	232	12	=	=	SYM
ap-8672	232	13	1	1	NUM
ap-8672	232	14	|	|	ADV
ap-8672	232	15	−−→	−−→	PROPN
ap-8672	232	16	vew|	vew|	PROPN
ap-8672	232	17	−−→	−−→	PROPN
ap-8672	232	18	vew	vew	NOUN
ap-8672	232	19	and	and	CCONJ
ap-8672	232	20	−→	−→	NOUN
ap-8672	232	21	s6	s6	PROPN
ap-8672	232	22	=	=	SYM
ap-8672	232	23	(	(	PUNCT
ap-8672	232	24	sx	sx	PROPN
ap-8672	232	25	,	,	PUNCT
ap-8672	232	26	sy	sy	PROPN
ap-8672	232	27	,	,	PUNCT
ap-8672	232	28	sz)t	sz)t	PROPN
ap-8672	232	29	.	.	PUNCT
ap-8672	233	1	thus	thus	ADV
ap-8672	233	2	,	,	PUNCT
ap-8672	233	3	the	the	DET
ap-8672	233	4	two	two	NUM
ap-8672	233	5	arguments	argument	NOUN
ap-8672	233	6	of	of	ADP
ap-8672	233	7	β6	β6	PROPN
ap-8672	233	8	are	be	AUX
ap-8672	233	9	:	:	PUNCT
ap-8672	233	10	cos(β6	cos(β6	NOUN
ap-8672	233	11	)	)	PUNCT
ap-8672	233	12	=	=	PUNCT
ap-8672	233	13	−−→new	−−→new	ADJ
ap-8672	233	14	.	.	PUNCT
ap-8672	234	1	−→	−→	PROPN
ap-8672	234	2	s6	s6	PROPN
ap-8672	234	3	and	and	CCONJ
ap-8672	234	4	det	det	PROPN
ap-8672	234	5	β6	β6	PROPN
ap-8672	234	6	=	=	SYM
ap-8672	234	7	det	det	PROPN
ap-8672	235	1	[	[	X
ap-8672	235	2	−→	−→	NOUN
ap-8672	235	3	a6	a6	NOUN
ap-8672	235	4	−−→new	−−→new	ADJ
ap-8672	235	5	−→	−→	ADJ
ap-8672	235	6	s6	s6	PROPN
ap-8672	235	7	]	]	X
ap-8672	235	8	t	t	PROPN
ap-8672	235	9	.	.	PUNCT
ap-8672	236	1	consequently	consequently	ADV
ap-8672	236	2	,	,	PUNCT
ap-8672	236	3	β6	β6	PROPN
ap-8672	236	4	can	can	AUX
ap-8672	236	5	be	be	AUX
ap-8672	236	6	obtained	obtain	VERB
ap-8672	236	7	by	by	ADP
ap-8672	236	8	the	the	DET
ap-8672	236	9	following	follow	VERB
ap-8672	236	10	formula	formula	NOUN
ap-8672	236	11	:	:	PUNCT
ap-8672	236	12	β6	β6	PROPN
ap-8672	236	13	=	=	PUNCT
ap-8672	236	14	atan2(det	atan2(det	NOUN
ap-8672	236	15	β6	β6	PROPN
ap-8672	236	16	,	,	PUNCT
ap-8672	236	17	cos(β6	cos(β6	NOUN
ap-8672	236	18	)	)	PUNCT
ap-8672	236	19	)	)	PUNCT
ap-8672	236	20	.	.	PUNCT
ap-8672	237	1	(	(	PUNCT
ap-8672	237	2	28	28	NUM
ap-8672	237	3	)	)	PUNCT
ap-8672	237	4	5	5	NUM
ap-8672	237	5	.	.	NOUN
ap-8672	237	6	simulations	simulation	NOUN
ap-8672	237	7	and	and	CCONJ
ap-8672	237	8	results	result	NOUN
ap-8672	237	9	in	in	ADP
ap-8672	237	10	this	this	DET
ap-8672	237	11	study	study	NOUN
ap-8672	237	12	,	,	PUNCT
ap-8672	237	13	simulations	simulation	NOUN
ap-8672	237	14	have	have	AUX
ap-8672	237	15	been	be	AUX
ap-8672	237	16	performed	perform	VERB
ap-8672	237	17	to	to	PART
ap-8672	237	18	verify	verify	VERB
ap-8672	237	19	the	the	DET
ap-8672	237	20	performance	performance	NOUN
ap-8672	237	21	of	of	ADP
ap-8672	237	22	the	the	DET
ap-8672	237	23	proposed	propose	VERB
ap-8672	237	24	approach	approach	NOUN
ap-8672	237	25	for	for	ADP
ap-8672	237	26	solving	solve	VERB
ap-8672	237	27	the	the	DET
ap-8672	237	28	inverse	inverse	NOUN
ap-8672	237	29	kinematics	kinematic	NOUN
ap-8672	237	30	(	(	PUNCT
ap-8672	237	31	ik	ik	ADJ
ap-8672	237	32	)	)	PUNCT
ap-8672	237	33	problem	problem	NOUN
ap-8672	237	34	.	.	PUNCT
ap-8672	238	1	to	to	PART
ap-8672	238	2	achieve	achieve	VERB
ap-8672	238	3	this	this	PRON
ap-8672	238	4	,	,	PUNCT
ap-8672	238	5	a	a	DET
ap-8672	238	6	program	program	NOUN
ap-8672	238	7	was	be	AUX
ap-8672	238	8	developed	develop	VERB
ap-8672	238	9	using	use	VERB
ap-8672	238	10	matlab	matlab	PROPN
ap-8672	238	11	based	base	VERB
ap-8672	238	12	on	on	ADP
ap-8672	238	13	the	the	DET
ap-8672	238	14	ik	ik	PROPN
ap-8672	238	15	results	result	NOUN
ap-8672	238	16	presented	present	VERB
ap-8672	238	17	in	in	ADP
ap-8672	238	18	equations	equation	NOUN
ap-8672	238	19	(	(	PUNCT
ap-8672	238	20	23	23	NUM
ap-8672	238	21	)	)	PUNCT
ap-8672	238	22	to	to	ADP
ap-8672	238	23	(	(	PUNCT
ap-8672	238	24	28	28	NUM
ap-8672	238	25	)	)	PUNCT
ap-8672	238	26	for	for	ADP
ap-8672	238	27	the	the	DET
ap-8672	238	28	simulation	simulation	NOUN
ap-8672	238	29	case	case	NOUN
ap-8672	238	30	.	.	PUNCT
ap-8672	239	1	figure	figure	NOUN
ap-8672	239	2	6	6	NUM
ap-8672	239	3	illustrates	illustrate	VERB
ap-8672	239	4	a	a	DET
ap-8672	239	5	freely	freely	ADV
ap-8672	239	6	chosen	choose	VERB
ap-8672	239	7	predefined	predefine	VERB
ap-8672	239	8	path	path	NOUN
ap-8672	239	9	for	for	ADP
ap-8672	239	10	the	the	DET
ap-8672	239	11	end	end	NOUN
ap-8672	239	12	-	-	PUNCT
ap-8672	239	13	effector	effector	NOUN
ap-8672	239	14	.	.	PUNCT
ap-8672	240	1	the	the	DET
ap-8672	240	2	robot	robot	NOUN
ap-8672	240	3	should	should	AUX
ap-8672	240	4	therefore	therefore	ADV
ap-8672	240	5	be	be	AUX
ap-8672	240	6	able	able	ADJ
ap-8672	240	7	to	to	PART
ap-8672	240	8	follow	follow	VERB
ap-8672	240	9	these	these	DET
ap-8672	240	10	trajectories	trajectory	NOUN
ap-8672	240	11	accurately	accurately	ADV
ap-8672	240	12	.	.	PUNCT
ap-8672	241	1	each	each	DET
ap-8672	241	2	part	part	NOUN
ap-8672	241	3	of	of	ADP
ap-8672	241	4	the	the	DET
ap-8672	241	5	end	end	NOUN
ap-8672	241	6	-	-	PUNCT
ap-8672	241	7	effector	effector	NOUN
ap-8672	241	8	’s	’s	PART
ap-8672	241	9	path	path	NOUN
ap-8672	241	10	has	have	AUX
ap-8672	241	11	been	be	AUX
ap-8672	241	12	characterised	characterise	VERB
ap-8672	241	13	as	as	ADP
ap-8672	241	14	an	an	DET
ap-8672	241	15	arc	arc	NOUN
ap-8672	241	16	of	of	ADP
ap-8672	241	17	a	a	DET
ap-8672	241	18	circle	circle	NOUN
ap-8672	241	19	defined	define	VERB
ap-8672	241	20	by	by	ADP
ap-8672	241	21	a	a	DET
ap-8672	241	22	set	set	NOUN
ap-8672	241	23	of	of	ADP
ap-8672	241	24	cartesian	cartesian	ADJ
ap-8672	241	25	coordinates	coordinate	NOUN
ap-8672	241	26	.	.	PUNCT
ap-8672	242	1	only	only	ADV
ap-8672	242	2	the	the	DET
ap-8672	242	3	path	path	NOUN
ap-8672	242	4	’s	’s	PART
ap-8672	242	5	part	part	NOUN
ap-8672	242	6	9→10	9→10	PROPN
ap-8672	242	7	is	be	AUX
ap-8672	242	8	a	a	DET
ap-8672	242	9	circular	circular	ADJ
ap-8672	242	10	trajectory	trajectory	NOUN
ap-8672	242	11	defined	define	VERB
ap-8672	242	12	by	by	ADP
ap-8672	242	13	its	its	PRON
ap-8672	242	14	equation	equation	NOUN
ap-8672	242	15	(	(	PUNCT
ap-8672	242	16	see	see	VERB
ap-8672	242	17	appendix	appendix	NOUN
ap-8672	242	18	a.2	a.2	PUNCT
ap-8672	242	19	)	)	PUNCT
ap-8672	242	20	.	.	PUNCT
ap-8672	243	1	as	as	SCONJ
ap-8672	243	2	mentioned	mention	VERB
ap-8672	243	3	in	in	ADP
ap-8672	243	4	table	table	NOUN
ap-8672	243	5	3	3	NUM
ap-8672	243	6	,	,	PUNCT
ap-8672	243	7	the	the	DET
ap-8672	243	8	robot	robot	NOUN
ap-8672	243	9	’s	’s	PART
ap-8672	243	10	end	end	NOUN
ap-8672	243	11	-	-	PUNCT
ap-8672	243	12	effector	effector	NOUN
ap-8672	243	13	will	will	AUX
ap-8672	243	14	start	start	VERB
ap-8672	243	15	from	from	ADP
ap-8672	243	16	the	the	DET
ap-8672	243	17	point	point	NOUN
ap-8672	243	18	with	with	ADP
ap-8672	243	19	coordinates	coordinate	NOUN
ap-8672	243	20	(	(	PUNCT
ap-8672	243	21	0,-0.6,0	0,-0.6,0	NUM
ap-8672	243	22	)	)	PUNCT
ap-8672	243	23	m	m	PROPN
ap-8672	243	24	,	,	PUNCT
ap-8672	243	25	following	follow	VERB
ap-8672	243	26	the	the	DET
ap-8672	243	27	trajectories	trajectory	NOUN
ap-8672	243	28	indicated	indicate	VERB
ap-8672	243	29	by	by	ADP
ap-8672	243	30	the	the	DET
ap-8672	243	31	following	follow	VERB
ap-8672	243	32	numbered	number	VERB
ap-8672	243	33	points	point	NOUN
ap-8672	243	34	order	order	NOUN
ap-8672	243	35	:	:	PUNCT
ap-8672	243	36	p0	p0	NOUN
ap-8672	243	37	→	→	SYM
ap-8672	243	38	p1	p1	PROPN
ap-8672	243	39	→	→	SYM
ap-8672	243	40	p2	p2	PROPN
ap-8672	243	41	→	→	SYM
ap-8672	243	42	p3	p3	PROPN
ap-8672	243	43	→	→	SYM
ap-8672	243	44	p4	p4	ADJ
ap-8672	243	45	→	→	SYM
ap-8672	243	46	p5	p5	ADJ
ap-8672	243	47	→	→	SYM
ap-8672	243	48	p6	p6	ADJ
ap-8672	243	49	→	→	SYM
ap-8672	243	50	p7	p7	PROPN
ap-8672	243	51	→	→	SYM
ap-8672	243	52	p8	p8	PROPN
ap-8672	243	53	→	→	SYM
ap-8672	243	54	p9	p9	PROPN
ap-8672	243	55	→	→	SYM
ap-8672	243	56	p10	p10	NOUN
ap-8672	243	57	→	→	SYM
ap-8672	243	58	p11	p11	NOUN
ap-8672	243	59	the	the	DET
ap-8672	243	60	orientation	orientation	NOUN
ap-8672	243	61	of	of	ADP
ap-8672	243	62	the	the	DET
ap-8672	243	63	end	end	NOUN
ap-8672	243	64	-	-	PUNCT
ap-8672	243	65	effector	effector	NOUN
ap-8672	243	66	is	be	AUX
ap-8672	243	67	expressed	express	VERB
ap-8672	243	68	by	by	ADP
ap-8672	243	69	a	a	DET
ap-8672	243	70	given	give	VERB
ap-8672	243	71	matrix	matrix	NOUN
ap-8672	243	72	as	as	SCONJ
ap-8672	243	73	shown	show	VERB
ap-8672	243	74	below	below	ADV
ap-8672	243	75	:	:	PUNCT
ap-8672	244	1	[	[	X
ap-8672	244	2	s	s	X
ap-8672	244	3	n	n	PRON
ap-8672	244	4	a	a	NOUN
ap-8672	244	5	]	]	X
ap-8672	244	6	=	=	SYM
ap-8672	244	7			NOUN
ap-8672	244	8	0	0	NUM
ap-8672	244	9	1	1	NUM
ap-8672	244	10	0	0	NUM
ap-8672	244	11	−1	−1	NOUN
ap-8672	244	12	0	0	NUM
ap-8672	244	13	0	0	NUM
ap-8672	244	14	0	0	NUM
ap-8672	244	15	0	0	NUM
ap-8672	244	16	1	1	NUM
ap-8672	244	17			NOUN
ap-8672	244	18	.	.	PUNCT
ap-8672	245	1	334	334	NUM
ap-8672	245	2	vol	vol	NOUN
ap-8672	245	3	.	.	PUNCT
ap-8672	245	4	63	63	NUM
ap-8672	245	5	no	no	NOUN
ap-8672	245	6	.	.	PUNCT
ap-8672	246	1	5/2023	5/2023	NUM
ap-8672	246	2	geometric	geometric	ADJ
ap-8672	246	3	approach	approach	NOUN
ap-8672	246	4	to	to	ADP
ap-8672	246	5	solving	solve	VERB
ap-8672	246	6	inverse	inverse	ADJ
ap-8672	246	7	kinematics	kinematic	NOUN
ap-8672	246	8	of	of	ADP
ap-8672	246	9	six	six	NUM
ap-8672	246	10	dof	dof	NOUN
ap-8672	246	11	robot	robot	NOUN
ap-8672	246	12	figure	figure	NOUN
ap-8672	246	13	6	6	NUM
ap-8672	246	14	.	.	PUNCT
ap-8672	246	15	predefined	predefine	VERB
ap-8672	246	16	trajectories	trajectory	NOUN
ap-8672	246	17	of	of	ADP
ap-8672	246	18	end	end	NOUN
ap-8672	246	19	-	-	PUNCT
ap-8672	246	20	effector	effector	NOUN
ap-8672	246	21	’s	’s	PART
ap-8672	246	22	path	path	NOUN
ap-8672	246	23	.	.	PUNCT
ap-8672	247	1	points	point	NOUN
ap-8672	247	2	coordinates	coordinate	NOUN
ap-8672	247	3	(	(	PUNCT
ap-8672	247	4	x	x	X
ap-8672	247	5	,	,	PUNCT
ap-8672	247	6	y	y	PROPN
ap-8672	247	7	,	,	PUNCT
ap-8672	247	8	z	z	NOUN
ap-8672	247	9	)	)	PUNCT
ap-8672	248	1	[	[	X
ap-8672	248	2	m	m	X
ap-8672	248	3	]	]	X
ap-8672	248	4	p0	p0	NOUN
ap-8672	248	5	(	(	PUNCT
ap-8672	248	6	0.00	0.00	NUM
ap-8672	248	7	-0.60	-0.60	NUM
ap-8672	248	8	0.00	0.00	NUM
ap-8672	248	9	)	)	PUNCT
ap-8672	248	10	p1	p1	NOUN
ap-8672	248	11	(	(	PUNCT
ap-8672	248	12	0.00	0.00	NUM
ap-8672	248	13	-0.59	-0.59	NUM
ap-8672	248	14	0.12	0.12	NUM
ap-8672	248	15	)	)	PUNCT
ap-8672	248	16	p2	p2	PROPN
ap-8672	248	17	(	(	PUNCT
ap-8672	248	18	0.40	0.40	NUM
ap-8672	248	19	-0.45	-0.45	NUM
ap-8672	248	20	0.12	0.12	NUM
ap-8672	248	21	)	)	PUNCT
ap-8672	248	22	p3	p3	NOUN
ap-8672	248	23	(	(	PUNCT
ap-8672	248	24	0.00	0.00	NUM
ap-8672	248	25	-0.59	-0.59	NUM
ap-8672	248	26	0.12	0.12	NUM
ap-8672	248	27	)	)	PUNCT
ap-8672	248	28	p4	p4	NOUN
ap-8672	248	29	(	(	PUNCT
ap-8672	248	30	0.00	0.00	NUM
ap-8672	248	31	-0.60	-0.60	NUM
ap-8672	248	32	0.00	0.00	NUM
ap-8672	248	33	)	)	PUNCT
ap-8672	248	34	p5	p5	PROPN
ap-8672	248	35	(	(	PUNCT
ap-8672	248	36	0.23	0.23	NUM
ap-8672	248	37	-0.50	-0.50	NUM
ap-8672	248	38	0.23	0.23	NUM
ap-8672	248	39	)	)	PUNCT
ap-8672	248	40	p6	p6	PROPN
ap-8672	248	41	(	(	PUNCT
ap-8672	248	42	0.32	0.32	NUM
ap-8672	248	43	-0.01	-0.01	NUM
ap-8672	248	44	0.32	0.32	NUM
ap-8672	248	45	)	)	PUNCT
ap-8672	248	46	p7	p7	NOUN
ap-8672	248	47	(	(	PUNCT
ap-8672	248	48	0.23	0.23	NUM
ap-8672	248	49	-0.50	-0.50	NUM
ap-8672	248	50	0.23	0.23	NUM
ap-8672	248	51	)	)	PUNCT
ap-8672	248	52	p8	p8	PROPN
ap-8672	248	53	(	(	PUNCT
ap-8672	248	54	0.00	0.00	NUM
ap-8672	248	55	-0.60	-0.60	NUM
ap-8672	248	56	0.00	0.00	NUM
ap-8672	248	57	)	)	PUNCT
ap-8672	248	58	p9	p9	PROPN
ap-8672	248	59	(	(	PUNCT
ap-8672	248	60	0.00	0.00	NUM
ap-8672	248	61	-0.59	-0.59	NUM
ap-8672	248	62	0.12	0.12	NUM
ap-8672	248	63	)	)	PUNCT
ap-8672	248	64	p10	p10	NOUN
ap-8672	248	65	(	(	PUNCT
ap-8672	248	66	0.00	0.00	NUM
ap-8672	248	67	-0.59	-0.59	NUM
ap-8672	248	68	0.12	0.12	NUM
ap-8672	248	69	)	)	PUNCT
ap-8672	248	70	p11	p11	NOUN
ap-8672	248	71	(	(	PUNCT
ap-8672	248	72	0.00	0.00	NUM
ap-8672	248	73	-0.60	-0.60	NUM
ap-8672	248	74	0.00	0.00	NUM
ap-8672	248	75	)	)	PUNCT
ap-8672	248	76	table	table	NOUN
ap-8672	248	77	3	3	NUM
ap-8672	248	78	.	.	PUNCT
ap-8672	248	79	coordinate	coordinate	NOUN
ap-8672	248	80	points	point	NOUN
ap-8672	248	81	of	of	ADP
ap-8672	248	82	each	each	DET
ap-8672	248	83	limit	limit	NOUN
ap-8672	248	84	path	path	NOUN
ap-8672	248	85	section	section	NOUN
ap-8672	248	86	.	.	PUNCT
ap-8672	249	1	a	a	DET
ap-8672	249	2	simulation	simulation	NOUN
ap-8672	249	3	is	be	AUX
ap-8672	249	4	used	use	VERB
ap-8672	249	5	to	to	PART
ap-8672	249	6	assess	assess	VERB
ap-8672	249	7	the	the	DET
ap-8672	249	8	effectiveness	effectiveness	NOUN
ap-8672	249	9	of	of	ADP
ap-8672	249	10	the	the	DET
ap-8672	249	11	current	current	ADJ
ap-8672	249	12	method	method	NOUN
ap-8672	249	13	.	.	PUNCT
ap-8672	250	1	specifically	specifically	ADV
ap-8672	250	2	,	,	PUNCT
ap-8672	250	3	the	the	DET
ap-8672	250	4	angles	angle	NOUN
ap-8672	250	5	obtained	obtain	VERB
ap-8672	250	6	for	for	ADP
ap-8672	250	7	the	the	DET
ap-8672	250	8	six	six	NUM
ap-8672	250	9	joint	joint	ADJ
ap-8672	250	10	articulations	articulation	NOUN
ap-8672	250	11	using	use	VERB
ap-8672	250	12	the	the	DET
ap-8672	250	13	current	current	ADJ
ap-8672	250	14	method	method	NOUN
ap-8672	250	15	are	be	AUX
ap-8672	250	16	simulated	simulate	VERB
ap-8672	250	17	using	use	VERB
ap-8672	250	18	forward	forward	ADV
ap-8672	250	19	kinematics	kinematic	NOUN
ap-8672	250	20	(	(	PUNCT
ap-8672	250	21	fk	fk	INTJ
ap-8672	250	22	)	)	PUNCT
ap-8672	250	23	equations	equation	NOUN
ap-8672	250	24	within	within	ADP
ap-8672	250	25	the	the	DET
ap-8672	250	26	developed	develop	VERB
ap-8672	250	27	matlab	matlab	PROPN
ap-8672	250	28	program	program	NOUN
ap-8672	250	29	.	.	PUNCT
ap-8672	251	1	the	the	DET
ap-8672	251	2	robot	robot	NOUN
ap-8672	251	3	’s	’s	PART
ap-8672	251	4	end	end	NOUN
ap-8672	251	5	-	-	PUNCT
ap-8672	251	6	effector	effector	NOUN
ap-8672	251	7	demonstrates	demonstrate	VERB
ap-8672	251	8	the	the	DET
ap-8672	251	9	capability	capability	NOUN
ap-8672	251	10	to	to	PART
ap-8672	251	11	accurately	accurately	ADV
ap-8672	251	12	follow	follow	VERB
ap-8672	251	13	the	the	DET
ap-8672	251	14	prescribed	prescribed	ADJ
ap-8672	251	15	trajectories	trajectory	NOUN
ap-8672	251	16	,	,	PUNCT
ap-8672	251	17	as	as	SCONJ
ap-8672	251	18	shown	show	VERB
ap-8672	251	19	in	in	ADP
ap-8672	251	20	figure	figure	NOUN
ap-8672	251	21	7	7	NUM
ap-8672	251	22	.	.	PUNCT
ap-8672	251	23	from	from	ADP
ap-8672	251	24	figure	figure	NOUN
ap-8672	251	25	7	7	NUM
ap-8672	251	26	,	,	PUNCT
ap-8672	251	27	it	it	PRON
ap-8672	251	28	can	can	AUX
ap-8672	251	29	be	be	AUX
ap-8672	251	30	seen	see	VERB
ap-8672	251	31	that	that	SCONJ
ap-8672	251	32	the	the	DET
ap-8672	251	33	robot	robot	NOUN
ap-8672	251	34	’s	’s	PART
ap-8672	251	35	end	end	NOUN
ap-8672	251	36	-	-	PUNCT
ap-8672	251	37	effector	effector	NOUN
ap-8672	251	38	has	have	AUX
ap-8672	251	39	followed	follow	VERB
ap-8672	251	40	exactly	exactly	ADV
ap-8672	251	41	the	the	DET
ap-8672	251	42	predefined	predefine	VERB
ap-8672	251	43	trajectory	trajectory	NOUN
ap-8672	251	44	that	that	PRON
ap-8672	251	45	is	be	AUX
ap-8672	251	46	divided	divide	VERB
ap-8672	251	47	into	into	ADP
ap-8672	251	48	ten	ten	NUM
ap-8672	251	49	paths	path	NOUN
ap-8672	251	50	as	as	SCONJ
ap-8672	251	51	numbered	number	VERB
ap-8672	251	52	above	above	ADV
ap-8672	251	53	in	in	ADP
ap-8672	251	54	figure	figure	NOUN
ap-8672	251	55	6	6	NUM
ap-8672	251	56	.	.	SYM
ap-8672	251	57	335	335	NUM
ap-8672	251	58	n.	n.	NOUN
ap-8672	251	59	hadidi	hadidi	PROPN
ap-8672	251	60	,	,	PUNCT
ap-8672	251	61	m.	m.	NOUN
ap-8672	251	62	bouaziz	bouaziz	PROPN
ap-8672	251	63	,	,	PUNCT
ap-8672	251	64	c.	c.	PROPN
ap-8672	251	65	mahfoudi	mahfoudi	PROPN
ap-8672	251	66	,	,	PUNCT
ap-8672	252	1	m.	m.	NOUN
ap-8672	252	2	zaharuddin	zaharuddin	PROPN
ap-8672	252	3	acta	acta	PROPN
ap-8672	252	4	polytechnica	polytechnica	PROPN
ap-8672	252	5	−0.2	−0.2	PROPN
ap-8672	253	1	−0.1	−0.1	PROPN
ap-8672	253	2	0	0	PUNCT
ap-8672	254	1	−0.5	−0.5	NUM
ap-8672	254	2	−0.4	−0.4	NUM
ap-8672	255	1	−0.3	−0.3	NOUN
ap-8672	255	2	−0.2	−0.2	PROPN
ap-8672	256	1	−0.1	−0.1	NOUN
ap-8672	256	2	0	0	NUM
ap-8672	256	3	0	0	NUM
ap-8672	256	4	0.05	0.05	NUM
ap-8672	256	5	0.1	0.1	NUM
ap-8672	256	6	z[m	z[m	NOUN
ap-8672	256	7	]	]	X
ap-8672	256	8	x[m	x[m	PROPN
ap-8672	256	9	]	]	X
ap-8672	256	10	y	y	PROPN
ap-8672	256	11	[	[	X
ap-8672	256	12	m	m	X
ap-8672	256	13	]	]	X
ap-8672	256	14	(	(	PUNCT
ap-8672	256	15	a	a	NOUN
ap-8672	256	16	)	)	PUNCT
ap-8672	256	17	.	.	PUNCT
ap-8672	257	1	forward	forward	ADJ
ap-8672	257	2	p0	p0	PROPN
ap-8672	257	3	→	→	SYM
ap-8672	257	4	p1	p1	PROPN
ap-8672	257	5	,	,	PUNCT
ap-8672	257	6	p8	p8	PROPN
ap-8672	257	7	→	→	SYM
ap-8672	257	8	p9	p9	PROPN
ap-8672	257	9	(	(	PUNCT
ap-8672	257	10	returned	return	VERB
ap-8672	257	11	p3	p3	PROPN
ap-8672	257	12	→	→	SYM
ap-8672	257	13	p4	p4	ADJ
ap-8672	257	14	,	,	PUNCT
ap-8672	257	15	p10	p10	NOUN
ap-8672	257	16	→	→	SYM
ap-8672	257	17	p11	p11	NOUN
ap-8672	257	18	)	)	PUNCT
ap-8672	257	19	.	.	PUNCT
ap-8672	258	1	−0.2	−0.2	PROPN
ap-8672	258	2	0	0	NUM
ap-8672	258	3	0.2	0.2	NUM
ap-8672	258	4	0.4	0.4	NUM
ap-8672	258	5	−0.5	−0.5	NUM
ap-8672	258	6	−0.4	−0.4	NUM
ap-8672	259	1	−0.3	−0.3	NOUN
ap-8672	259	2	−0.2	−0.2	PROPN
ap-8672	260	1	−0.1	−0.1	NOUN
ap-8672	260	2	0	0	PUNCT
ap-8672	260	3	0	0	NUM
ap-8672	260	4	0.050.1z[m]x[m	0.050.1z[m]x[m	NUM
ap-8672	260	5	]	]	X
ap-8672	260	6	y	y	PROPN
ap-8672	260	7	[	[	X
ap-8672	260	8	m	m	X
ap-8672	260	9	]	]	X
ap-8672	260	10	(	(	PUNCT
ap-8672	260	11	b	b	NOUN
ap-8672	260	12	)	)	PUNCT
ap-8672	260	13	.	.	PUNCT
ap-8672	261	1	forward	forward	PROPN
ap-8672	261	2	p1	p1	PROPN
ap-8672	261	3	→	→	SYM
ap-8672	261	4	p2	p2	PROPN
ap-8672	261	5	(	(	PUNCT
ap-8672	261	6	returned	return	VERB
ap-8672	261	7	p2	p2	PROPN
ap-8672	261	8	→	→	SYM
ap-8672	261	9	p3	p3	PROPN
ap-8672	261	10	)	)	PUNCT
ap-8672	261	11	.	.	PUNCT
ap-8672	262	1	−0.2	−0.2	PROPN
ap-8672	262	2	0	0	NUM
ap-8672	262	3	0.2	0.2	NUM
ap-8672	262	4	0.4	0.4	NUM
ap-8672	262	5	−0.5	−0.5	NUM
ap-8672	262	6	−0.4	−0.4	NUM
ap-8672	263	1	−0.3	−0.3	NOUN
ap-8672	263	2	−0.2	−0.2	PROPN
ap-8672	264	1	−0.1	−0.1	NOUN
ap-8672	264	2	0	0	NUM
ap-8672	264	3	0.1	0.1	NUM
ap-8672	264	4	0	0	NUM
ap-8672	264	5	0.10.2	0.10.2	NUM
ap-8672	264	6	0.3	0.3	NUM
ap-8672	264	7	z[m	z[m	NOUN
ap-8672	264	8	]	]	X
ap-8672	264	9	x[m	x[m	PROPN
ap-8672	264	10	]	]	X
ap-8672	264	11	y	y	PROPN
ap-8672	264	12	[	[	X
ap-8672	264	13	m	m	X
ap-8672	264	14	]	]	X
ap-8672	264	15	(	(	PUNCT
ap-8672	264	16	c	c	NOUN
ap-8672	264	17	)	)	PUNCT
ap-8672	264	18	.	.	PUNCT
ap-8672	265	1	forward	forward	ADV
ap-8672	265	2	p4	p4	ADJ
ap-8672	265	3	→	→	SYM
ap-8672	265	4	p5	p5	ADJ
ap-8672	265	5	→	→	SYM
ap-8672	265	6	p6	p6	PROPN
ap-8672	265	7	(	(	PUNCT
ap-8672	265	8	returned	return	VERB
ap-8672	265	9	p6	p6	PROPN
ap-8672	265	10	→	→	SYM
ap-8672	265	11	p7	p7	PROPN
ap-8672	265	12	→	→	SYM
ap-8672	265	13	p8	p8	PROPN
ap-8672	265	14	)	)	PUNCT
ap-8672	265	15	.	.	PUNCT
ap-8672	266	1	−0.2	−0.2	PROPN
ap-8672	266	2	0	0	NUM
ap-8672	266	3	0.2	0.2	NUM
ap-8672	266	4	−0.5	−0.5	NUM
ap-8672	266	5	−0.4	−0.4	NUM
ap-8672	267	1	−0.3	−0.3	NOUN
ap-8672	267	2	−0.2	−0.2	PROPN
ap-8672	268	1	−0.1	−0.1	NOUN
ap-8672	268	2	0	0	NUM
ap-8672	268	3	0	0	NUM
ap-8672	268	4	0.1	0.1	NUM
ap-8672	268	5	0.2	0.2	NUM
ap-8672	268	6	z[m	z[m	NOUN
ap-8672	268	7	]	]	X
ap-8672	268	8	x[m	x[m	PROPN
ap-8672	268	9	]	]	X
ap-8672	268	10	y	y	PROPN
ap-8672	268	11	[	[	X
ap-8672	268	12	m	m	X
ap-8672	268	13	]	]	X
ap-8672	268	14	(	(	PUNCT
ap-8672	268	15	d	d	NOUN
ap-8672	268	16	)	)	PUNCT
ap-8672	268	17	.	.	PUNCT
ap-8672	269	1	movement	movement	PROPN
ap-8672	269	2	p9	p9	PROPN
ap-8672	269	3	→	→	SYM
ap-8672	269	4	p10	p10	PROPN
ap-8672	269	5	.	.	PROPN
ap-8672	269	6	figure	figure	NOUN
ap-8672	269	7	7	7	NUM
ap-8672	269	8	.	.	PUNCT
ap-8672	269	9	matlab	matlab	PROPN
ap-8672	269	10	simulations	simulation	NOUN
ap-8672	269	11	of	of	ADP
ap-8672	269	12	the	the	DET
ap-8672	269	13	robot	robot	NOUN
ap-8672	269	14	’s	’s	PART
ap-8672	269	15	end	end	NOUN
ap-8672	269	16	-	-	PUNCT
ap-8672	269	17	effector	effector	NOUN
ap-8672	269	18	following	follow	VERB
ap-8672	269	19	predefined	predefine	VERB
ap-8672	269	20	trajectories	trajectory	NOUN
ap-8672	269	21	.	.	PUNCT
ap-8672	270	1	6	6	X
ap-8672	270	2	.	.	X
ap-8672	270	3	experiments	experiment	NOUN
ap-8672	270	4	in	in	ADP
ap-8672	270	5	this	this	DET
ap-8672	270	6	study	study	NOUN
ap-8672	270	7	,	,	PUNCT
ap-8672	270	8	experiments	experiment	NOUN
ap-8672	270	9	have	have	AUX
ap-8672	270	10	been	be	AUX
ap-8672	270	11	conducted	conduct	VERB
ap-8672	270	12	to	to	PART
ap-8672	270	13	demonstrate	demonstrate	VERB
ap-8672	270	14	the	the	DET
ap-8672	270	15	applicability	applicability	NOUN
ap-8672	270	16	of	of	ADP
ap-8672	270	17	the	the	DET
ap-8672	270	18	proposed	propose	VERB
ap-8672	270	19	approach	approach	NOUN
ap-8672	270	20	for	for	ADP
ap-8672	270	21	solving	solve	VERB
ap-8672	270	22	the	the	DET
ap-8672	270	23	inverse	inverse	NOUN
ap-8672	270	24	kinematics	kinematic	NOUN
ap-8672	270	25	(	(	PUNCT
ap-8672	270	26	ik	ik	ADJ
ap-8672	270	27	)	)	PUNCT
ap-8672	270	28	problem	problem	NOUN
ap-8672	270	29	.	.	PUNCT
ap-8672	271	1	in	in	ADP
ap-8672	271	2	order	order	NOUN
ap-8672	271	3	to	to	PART
ap-8672	271	4	achieve	achieve	VERB
ap-8672	271	5	this	this	DET
ap-8672	271	6	objective	objective	NOUN
ap-8672	271	7	,	,	PUNCT
ap-8672	271	8	by	by	ADP
ap-8672	271	9	exploring	explore	VERB
ap-8672	271	10	the	the	DET
ap-8672	271	11	results	result	NOUN
ap-8672	271	12	of	of	ADP
ap-8672	271	13	ik	ik	PROPN
ap-8672	271	14	solutions	solution	NOUN
ap-8672	271	15	given	give	VERB
ap-8672	271	16	in	in	ADP
ap-8672	271	17	section	section	NOUN
ap-8672	271	18	4	4	NUM
ap-8672	271	19	,	,	PUNCT
ap-8672	271	20	an	an	DET
ap-8672	271	21	arduino	arduino	NOUN
ap-8672	271	22	code	code	NOUN
ap-8672	271	23	has	have	AUX
ap-8672	271	24	been	be	AUX
ap-8672	271	25	developed	develop	VERB
ap-8672	271	26	and	and	CCONJ
ap-8672	271	27	implemented	implement	VERB
ap-8672	271	28	into	into	ADP
ap-8672	271	29	an	an	DET
ap-8672	271	30	arduino	arduino	NOUN
ap-8672	271	31	board	board	NOUN
ap-8672	271	32	2650	2650	NUM
ap-8672	271	33	.	.	PUNCT
ap-8672	272	1	this	this	DET
ap-8672	272	2	board	board	NOUN
ap-8672	272	3	serves	serve	VERB
ap-8672	272	4	as	as	ADP
ap-8672	272	5	an	an	DET
ap-8672	272	6	input	input	NOUN
ap-8672	272	7	/	/	SYM
ap-8672	272	8	output	output	NOUN
ap-8672	272	9	device	device	NOUN
ap-8672	272	10	between	between	ADP
ap-8672	272	11	the	the	DET
ap-8672	272	12	computer	computer	NOUN
ap-8672	272	13	and	and	CCONJ
ap-8672	272	14	the	the	DET
ap-8672	272	15	robot	robot	NOUN
ap-8672	272	16	’s	’s	PART
ap-8672	272	17	actuators	actuator	NOUN
ap-8672	272	18	,	,	PUNCT
ap-8672	272	19	as	as	SCONJ
ap-8672	272	20	shows	show	NOUN
ap-8672	272	21	in	in	ADP
ap-8672	272	22	the	the	DET
ap-8672	272	23	schematic	schematic	ADJ
ap-8672	272	24	circuit	circuit	NOUN
ap-8672	272	25	of	of	ADP
ap-8672	272	26	the	the	DET
ap-8672	272	27	control	control	NOUN
ap-8672	272	28	and	and	CCONJ
ap-8672	272	29	connection	connection	NOUN
ap-8672	272	30	between	between	ADP
ap-8672	272	31	devices	device	NOUN
ap-8672	272	32	in	in	ADP
ap-8672	272	33	figure	figure	NOUN
ap-8672	272	34	8	8	NUM
ap-8672	272	35	.	.	PUNCT
ap-8672	272	36	tools	tool	NOUN
ap-8672	272	37	and	and	CCONJ
ap-8672	272	38	materials	material	NOUN
ap-8672	272	39	for	for	ADP
ap-8672	272	40	the	the	DET
ap-8672	272	41	experiment	experiment	NOUN
ap-8672	272	42	:	:	PUNCT
ap-8672	272	43	the	the	DET
ap-8672	272	44	design	design	NOUN
ap-8672	272	45	of	of	ADP
ap-8672	272	46	the	the	DET
ap-8672	272	47	robot	robot	NOUN
ap-8672	272	48	was	be	AUX
ap-8672	272	49	created	create	VERB
ap-8672	272	50	using	use	VERB
ap-8672	272	51	solidworks	solidworks	PROPN
ap-8672	272	52	software	software	NOUN
ap-8672	272	53	and	and	CCONJ
ap-8672	272	54	its	its	PRON
ap-8672	272	55	parts	part	NOUN
ap-8672	272	56	were	be	AUX
ap-8672	272	57	3d	3d	NUM
ap-8672	272	58	printed	print	VERB
ap-8672	272	59	using	use	VERB
ap-8672	272	60	a	a	DET
ap-8672	272	61	3d	3d	NUM
ap-8672	272	62	printer	printer	NOUN
ap-8672	272	63	.	.	PUNCT
ap-8672	273	1	the	the	DET
ap-8672	273	2	robot	robot	NOUN
ap-8672	273	3	is	be	AUX
ap-8672	273	4	equipped	equip	VERB
ap-8672	273	5	with	with	ADP
ap-8672	273	6	six	six	NUM
ap-8672	273	7	stepper	stepper	NOUN
ap-8672	273	8	motors	motor	NOUN
ap-8672	273	9	at	at	ADP
ap-8672	273	10	the	the	DET
ap-8672	273	11	joint	joint	ADJ
ap-8672	273	12	articulations	articulation	NOUN
ap-8672	273	13	,	,	PUNCT
ap-8672	273	14	each	each	PRON
ap-8672	273	15	controlled	control	VERB
ap-8672	273	16	by	by	ADP
ap-8672	273	17	a	a	DET
ap-8672	273	18	dedicated	dedicated	ADJ
ap-8672	273	19	motor	motor	NOUN
ap-8672	273	20	driver	driver	NOUN
ap-8672	273	21	.	.	PUNCT
ap-8672	274	1	the	the	DET
ap-8672	274	2	control	control	NOUN
ap-8672	274	3	of	of	ADP
ap-8672	274	4	these	these	DET
ap-8672	274	5	motors	motor	NOUN
ap-8672	274	6	is	be	AUX
ap-8672	274	7	managed	manage	VERB
ap-8672	274	8	by	by	ADP
ap-8672	274	9	an	an	DET
ap-8672	274	10	arduino	arduino	NOUN
ap-8672	274	11	board	board	NOUN
ap-8672	274	12	mega	mega	PROPN
ap-8672	274	13	2650	2650	NUM
ap-8672	274	14	,	,	PUNCT
ap-8672	274	15	which	which	PRON
ap-8672	274	16	is	be	AUX
ap-8672	274	17	programmed	program	VERB
ap-8672	274	18	accordingly	accordingly	ADV
ap-8672	274	19	.	.	PUNCT
ap-8672	275	1	the	the	DET
ap-8672	275	2	setup	setup	NOUN
ap-8672	275	3	also	also	ADV
ap-8672	275	4	includes	include	VERB
ap-8672	275	5	a	a	DET
ap-8672	275	6	ramps	ramp	NOUN
ap-8672	275	7	1.4	1.4	NUM
ap-8672	275	8	board	board	NOUN
ap-8672	275	9	and	and	CCONJ
ap-8672	275	10	power	power	NOUN
ap-8672	275	11	supplies	supply	NOUN
ap-8672	275	12	that	that	PRON
ap-8672	275	13	provides	provide	VERB
ap-8672	275	14	both	both	DET
ap-8672	275	15	12	12	NUM
ap-8672	275	16	v	v	NOUN
ap-8672	275	17	and	and	CCONJ
ap-8672	275	18	24	24	NUM
ap-8672	275	19	v.	v.	CCONJ
ap-8672	275	20	336	336	NUM
ap-8672	275	21	vol	vol	NOUN
ap-8672	275	22	.	.	PUNCT
ap-8672	276	1	63	63	NUM
ap-8672	277	1	no	no	NOUN
ap-8672	277	2	.	.	PUNCT
ap-8672	278	1	5/2023	5/2023	NUM
ap-8672	278	2	geometric	geometric	ADJ
ap-8672	278	3	approach	approach	NOUN
ap-8672	278	4	to	to	ADP
ap-8672	278	5	solving	solve	VERB
ap-8672	278	6	inverse	inverse	ADJ
ap-8672	278	7	kinematics	kinematic	NOUN
ap-8672	278	8	of	of	ADP
ap-8672	278	9	six	six	NUM
ap-8672	278	10	dof	dof	NOUN
ap-8672	278	11	robot	robot	NOUN
ap-8672	278	12	figure	figure	NOUN
ap-8672	278	13	8	8	NUM
ap-8672	278	14	.	.	PUNCT
ap-8672	278	15	schematic	schematic	ADJ
ap-8672	278	16	circuit	circuit	NOUN
ap-8672	278	17	of	of	ADP
ap-8672	278	18	control	control	NOUN
ap-8672	278	19	and	and	CCONJ
ap-8672	278	20	connection	connection	NOUN
ap-8672	278	21	between	between	ADP
ap-8672	278	22	devices	device	NOUN
ap-8672	278	23	.	.	PUNCT
ap-8672	279	1	figure	figure	NOUN
ap-8672	279	2	8	8	NUM
ap-8672	279	3	shows	show	VERB
ap-8672	279	4	a	a	DET
ap-8672	279	5	schematic	schematic	ADJ
ap-8672	279	6	diagram	diagram	NOUN
ap-8672	279	7	of	of	ADP
ap-8672	279	8	the	the	DET
ap-8672	279	9	main	main	ADJ
ap-8672	279	10	devices	device	NOUN
ap-8672	279	11	used	use	VERB
ap-8672	279	12	to	to	PART
ap-8672	279	13	control	control	VERB
ap-8672	279	14	the	the	DET
ap-8672	279	15	robots	robot	NOUN
ap-8672	279	16	and	and	CCONJ
ap-8672	279	17	their	their	PRON
ap-8672	279	18	corresponding	corresponding	ADJ
ap-8672	279	19	wiring	wiring	NOUN
ap-8672	279	20	.	.	PUNCT
ap-8672	280	1	as	as	ADP
ap-8672	280	2	part	part	NOUN
ap-8672	280	3	of	of	ADP
ap-8672	280	4	further	further	ADJ
ap-8672	280	5	validation	validation	NOUN
ap-8672	280	6	,	,	PUNCT
ap-8672	280	7	we	we	PRON
ap-8672	280	8	deliberately	deliberately	ADV
ap-8672	280	9	instructed	instruct	VERB
ap-8672	280	10	the	the	DET
ap-8672	280	11	robot	robot	NOUN
ap-8672	280	12	to	to	PART
ap-8672	280	13	return	return	VERB
ap-8672	280	14	along	along	ADP
ap-8672	280	15	the	the	DET
ap-8672	280	16	same	same	ADJ
ap-8672	280	17	path	path	NOUN
ap-8672	280	18	in	in	ADP
ap-8672	280	19	certain	certain	ADJ
ap-8672	280	20	cases	case	NOUN
ap-8672	280	21	.	.	PUNCT
ap-8672	281	1	this	this	PRON
ap-8672	281	2	included	include	VERB
ap-8672	281	3	cases	case	NOUN
ap-8672	281	4	like	like	ADP
ap-8672	281	5	p1	p1	PROPN
ap-8672	281	6	→	→	SYM
ap-8672	281	7	p2	p2	PROPN
ap-8672	281	8	and	and	CCONJ
ap-8672	281	9	p2	p2	PROPN
ap-8672	281	10	→	→	SYM
ap-8672	281	11	p3	p3	PROPN
ap-8672	281	12	,	,	PUNCT
ap-8672	281	13	as	as	ADV
ap-8672	281	14	well	well	ADV
ap-8672	281	15	as	as	ADP
ap-8672	281	16	p5	p5	ADJ
ap-8672	281	17	→	→	SYM
ap-8672	281	18	p6	p6	ADJ
ap-8672	281	19	and	and	CCONJ
ap-8672	281	20	p6	p6	PROPN
ap-8672	281	21	→	→	SYM
ap-8672	281	22	p7	p7	PROPN
ap-8672	281	23	.	.	PUNCT
ap-8672	282	1	in	in	ADP
ap-8672	282	2	practice	practice	NOUN
ap-8672	282	3	,	,	PUNCT
ap-8672	282	4	the	the	DET
ap-8672	282	5	angle	angle	NOUN
ap-8672	282	6	equations	equation	NOUN
ap-8672	282	7	of	of	ADP
ap-8672	282	8	the	the	DET
ap-8672	282	9	six	six	NUM
ap-8672	282	10	joint	joint	ADJ
ap-8672	282	11	articulations	articulation	NOUN
ap-8672	282	12	derived	derive	VERB
ap-8672	282	13	from	from	ADP
ap-8672	282	14	the	the	DET
ap-8672	282	15	current	current	ADJ
ap-8672	282	16	method	method	NOUN
ap-8672	282	17	were	be	AUX
ap-8672	282	18	directly	directly	ADV
ap-8672	282	19	used	use	VERB
ap-8672	282	20	in	in	ADP
ap-8672	282	21	the	the	DET
ap-8672	282	22	programmed	program	VERB
ap-8672	282	23	arduino	arduino	NOUN
ap-8672	282	24	code	code	NOUN
ap-8672	282	25	through	through	ADP
ap-8672	282	26	the	the	DET
ap-8672	282	27	mega2560	mega2560	PROPN
ap-8672	282	28	control	control	PROPN
ap-8672	282	29	board	board	PROPN
ap-8672	282	30	,	,	PUNCT
ap-8672	282	31	after	after	ADP
ap-8672	282	32	configuring	configure	VERB
ap-8672	282	33	the	the	DET
ap-8672	282	34	relevant	relevant	ADJ
ap-8672	282	35	robot	robot	NOUN
ap-8672	282	36	parameters	parameter	NOUN
ap-8672	282	37	.	.	PUNCT
ap-8672	283	1	based	base	VERB
ap-8672	283	2	on	on	ADP
ap-8672	283	3	the	the	DET
ap-8672	283	4	experimental	experimental	ADJ
ap-8672	283	5	observation	observation	NOUN
ap-8672	283	6	,	,	PUNCT
ap-8672	283	7	it	it	PRON
ap-8672	283	8	’s	’	VERB
ap-8672	283	9	evident	evident	ADJ
ap-8672	283	10	that	that	SCONJ
ap-8672	283	11	the	the	DET
ap-8672	283	12	robot	robot	NOUN
ap-8672	283	13	can	can	AUX
ap-8672	283	14	successfully	successfully	ADV
ap-8672	283	15	follow	follow	VERB
ap-8672	283	16	the	the	DET
ap-8672	283	17	predefined	predefine	VERB
ap-8672	283	18	trajectories	trajectory	NOUN
ap-8672	283	19	.	.	PUNCT
ap-8672	284	1	figure	figure	NOUN
ap-8672	284	2	9	9	NUM
ap-8672	284	3	displays	display	VERB
ap-8672	284	4	various	various	ADJ
ap-8672	284	5	poses	pose	NOUN
ap-8672	284	6	of	of	ADP
ap-8672	284	7	the	the	DET
ap-8672	284	8	robot	robot	NOUN
ap-8672	284	9	as	as	SCONJ
ap-8672	284	10	it	it	PRON
ap-8672	284	11	tracks	track	VERB
ap-8672	284	12	the	the	DET
ap-8672	284	13	trajectories	trajectory	NOUN
ap-8672	284	14	assigned	assign	VERB
ap-8672	284	15	to	to	ADP
ap-8672	284	16	the	the	DET
ap-8672	284	17	end	end	NOUN
ap-8672	284	18	-	-	PUNCT
ap-8672	284	19	effector	effector	NOUN
ap-8672	284	20	.	.	PUNCT
ap-8672	285	1	the	the	DET
ap-8672	285	2	six	six	NUM
ap-8672	285	3	motors	motor	NOUN
ap-8672	285	4	of	of	ADP
ap-8672	285	5	the	the	DET
ap-8672	285	6	robot	robot	NOUN
ap-8672	285	7	effectively	effectively	ADV
ap-8672	285	8	respond	respond	VERB
ap-8672	285	9	to	to	ADP
ap-8672	285	10	the	the	DET
ap-8672	285	11	signals	signal	NOUN
ap-8672	285	12	generated	generate	VERB
ap-8672	285	13	by	by	ADP
ap-8672	285	14	the	the	DET
ap-8672	285	15	inverse	inverse	NOUN
ap-8672	285	16	kinematics	kinematic	NOUN
ap-8672	285	17	(	(	PUNCT
ap-8672	285	18	ik	ik	ADJ
ap-8672	285	19	)	)	PUNCT
ap-8672	285	20	solution	solution	NOUN
ap-8672	285	21	.	.	PUNCT
ap-8672	286	1	consequently	consequently	ADV
ap-8672	286	2	,	,	PUNCT
ap-8672	286	3	the	the	DET
ap-8672	286	4	ik	ik	PROPN
ap-8672	286	5	solutions	solution	NOUN
ap-8672	286	6	obtained	obtain	VERB
ap-8672	286	7	are	be	AUX
ap-8672	286	8	validated	validate	VERB
ap-8672	286	9	.	.	PUNCT
ap-8672	287	1	however	however	ADV
ap-8672	287	2	,	,	PUNCT
ap-8672	287	3	it	it	PRON
ap-8672	287	4	’s	’	VERB
ap-8672	287	5	worth	worth	ADJ
ap-8672	287	6	noting	note	VERB
ap-8672	287	7	that	that	SCONJ
ap-8672	287	8	in	in	ADP
ap-8672	287	9	this	this	DET
ap-8672	287	10	case	case	NOUN
ap-8672	287	11	,	,	PUNCT
ap-8672	287	12	no	no	DET
ap-8672	287	13	position	position	NOUN
ap-8672	287	14	control	control	NOUN
ap-8672	287	15	system	system	NOUN
ap-8672	287	16	is	be	AUX
ap-8672	287	17	implemented	implement	VERB
ap-8672	287	18	on	on	ADP
ap-8672	287	19	the	the	DET
ap-8672	287	20	joint	joint	ADJ
ap-8672	287	21	articulations	articulation	NOUN
ap-8672	287	22	.	.	PUNCT
ap-8672	288	1	as	as	ADP
ap-8672	288	2	a	a	DET
ap-8672	288	3	result	result	NOUN
ap-8672	288	4	,	,	PUNCT
ap-8672	288	5	slight	slight	ADJ
ap-8672	288	6	fluctuations	fluctuation	NOUN
ap-8672	288	7	in	in	ADP
ap-8672	288	8	position	position	NOUN
ap-8672	288	9	and	and	CCONJ
ap-8672	288	10	orientation	orientation	NOUN
ap-8672	288	11	of	of	ADP
ap-8672	288	12	the	the	DET
ap-8672	288	13	end	end	NOUN
ap-8672	288	14	-	-	PUNCT
ap-8672	288	15	effector	effector	NOUN
ap-8672	288	16	can	can	AUX
ap-8672	288	17	be	be	AUX
ap-8672	288	18	observed	observe	VERB
ap-8672	288	19	in	in	ADP
ap-8672	288	20	some	some	DET
ap-8672	288	21	instances	instance	NOUN
ap-8672	288	22	.	.	PUNCT
ap-8672	289	1	figure	figure	VERB
ap-8672	289	2	10	10	NUM
ap-8672	289	3	illustrates	illustrate	VERB
ap-8672	289	4	the	the	DET
ap-8672	289	5	variations	variation	NOUN
ap-8672	289	6	in	in	ADP
ap-8672	289	7	the	the	DET
ap-8672	289	8	six	six	NUM
ap-8672	289	9	articulations	articulation	NOUN
ap-8672	289	10	of	of	ADP
ap-8672	289	11	the	the	DET
ap-8672	289	12	robot	robot	NOUN
ap-8672	289	13	as	as	SCONJ
ap-8672	289	14	it	it	PRON
ap-8672	289	15	moves	move	VERB
ap-8672	289	16	along	along	ADP
ap-8672	289	17	the	the	DET
ap-8672	289	18	ten	ten	NUM
ap-8672	289	19	path	path	NOUN
ap-8672	289	20	segments	segment	NOUN
ap-8672	289	21	.	.	PUNCT
ap-8672	290	1	it	it	PRON
ap-8672	290	2	can	can	AUX
ap-8672	290	3	clearly	clearly	ADV
ap-8672	290	4	be	be	AUX
ap-8672	290	5	seen	see	VERB
ap-8672	290	6	that	that	SCONJ
ap-8672	290	7	the	the	DET
ap-8672	290	8	variations	variation	NOUN
ap-8672	290	9	have	have	VERB
ap-8672	290	10	regularities	regularity	NOUN
ap-8672	290	11	,	,	PUNCT
ap-8672	290	12	notably	notably	ADV
ap-8672	290	13	in	in	ADP
ap-8672	290	14	the	the	DET
ap-8672	290	15	case	case	NOUN
ap-8672	290	16	where	where	SCONJ
ap-8672	290	17	the	the	DET
ap-8672	290	18	robot	robot	NOUN
ap-8672	290	19	returned	return	VERB
ap-8672	290	20	along	along	ADP
ap-8672	290	21	the	the	DET
ap-8672	290	22	same	same	ADJ
ap-8672	290	23	path	path	NOUN
ap-8672	290	24	(	(	PUNCT
ap-8672	290	25	p1→p2	p1→p2	NOUN
ap-8672	290	26	with	with	ADP
ap-8672	290	27	p2→p3	p2→p3	NOUN
ap-8672	290	28	,	,	PUNCT
ap-8672	290	29	p0→p1	p0→p1	NOUN
ap-8672	290	30	with	with	ADP
ap-8672	290	31	p3→p4	p3→p4	NOUN
ap-8672	290	32	,	,	PUNCT
ap-8672	290	33	.	.	PUNCT
ap-8672	290	34	.	.	PUNCT
ap-8672	290	35	.	.	PUNCT
ap-8672	290	36	)	)	PUNCT
ap-8672	290	37	.	.	PUNCT
ap-8672	291	1	also	also	ADV
ap-8672	291	2	,	,	PUNCT
ap-8672	291	3	in	in	ADP
ap-8672	291	4	the	the	DET
ap-8672	291	5	case	case	NOUN
ap-8672	291	6	of	of	ADP
ap-8672	291	7	the	the	DET
ap-8672	291	8	circular	circular	ADJ
ap-8672	291	9	path	path	NOUN
ap-8672	291	10	(	(	PUNCT
ap-8672	291	11	p9→p10	p9→p10	NOUN
ap-8672	291	12	)	)	PUNCT
ap-8672	291	13	,	,	PUNCT
ap-8672	291	14	each	each	PRON
ap-8672	291	15	of	of	ADP
ap-8672	291	16	the	the	DET
ap-8672	291	17	six	six	NUM
ap-8672	291	18	motors	motor	NOUN
ap-8672	291	19	start	start	VERB
ap-8672	291	20	and	and	CCONJ
ap-8672	291	21	end	end	VERB
ap-8672	291	22	at	at	ADP
ap-8672	291	23	the	the	DET
ap-8672	291	24	same	same	ADJ
ap-8672	291	25	points	point	NOUN
ap-8672	291	26	.	.	PUNCT
ap-8672	292	1	in	in	ADP
ap-8672	292	2	fact	fact	NOUN
ap-8672	292	3	,	,	PUNCT
ap-8672	292	4	there	there	PRON
ap-8672	292	5	is	be	VERB
ap-8672	292	6	a	a	DET
ap-8672	292	7	compatibility	compatibility	NOUN
ap-8672	292	8	between	between	ADP
ap-8672	292	9	the	the	DET
ap-8672	292	10	angular	angular	ADJ
ap-8672	292	11	variations	variation	NOUN
ap-8672	292	12	and	and	CCONJ
ap-8672	292	13	the	the	DET
ap-8672	292	14	parts	part	NOUN
ap-8672	292	15	of	of	ADP
ap-8672	292	16	the	the	DET
ap-8672	292	17	trajectories	trajectory	NOUN
ap-8672	292	18	as	as	SCONJ
ap-8672	292	19	suggested	suggest	VERB
ap-8672	292	20	in	in	ADP
ap-8672	292	21	figure	figure	NOUN
ap-8672	292	22	6	6	NUM
ap-8672	292	23	,	,	PUNCT
ap-8672	292	24	and	and	CCONJ
ap-8672	292	25	further	further	ADJ
ap-8672	292	26	confirmation	confirmation	NOUN
ap-8672	292	27	is	be	AUX
ap-8672	292	28	deduced	deduce	VERB
ap-8672	292	29	when	when	SCONJ
ap-8672	292	30	the	the	DET
ap-8672	292	31	robot	robot	NOUN
ap-8672	292	32	comes	come	VERB
ap-8672	292	33	back	back	ADV
ap-8672	292	34	on	on	ADP
ap-8672	292	35	the	the	DET
ap-8672	292	36	same	same	ADJ
ap-8672	292	37	path	path	NOUN
ap-8672	292	38	.	.	PUNCT
ap-8672	293	1	for	for	ADP
ap-8672	293	2	example	example	NOUN
ap-8672	293	3	,	,	PUNCT
ap-8672	293	4	in	in	ADP
ap-8672	293	5	the	the	DET
ap-8672	293	6	case	case	NOUN
ap-8672	293	7	when	when	SCONJ
ap-8672	293	8	the	the	DET
ap-8672	293	9	robot	robot	NOUN
ap-8672	293	10	followed	follow	VERB
ap-8672	293	11	the	the	DET
ap-8672	293	12	path	path	NOUN
ap-8672	293	13	from	from	ADP
ap-8672	293	14	p5	p5	NOUN
ap-8672	293	15	→	→	SYM
ap-8672	293	16	p6	p6	PROPN
ap-8672	293	17	and	and	CCONJ
ap-8672	293	18	retraced	retrace	VERB
ap-8672	293	19	the	the	DET
ap-8672	293	20	same	same	ADJ
ap-8672	293	21	way	way	NOUN
ap-8672	293	22	defined	define	VERB
ap-8672	293	23	in	in	ADP
ap-8672	293	24	the	the	DET
ap-8672	293	25	graph	graph	NOUN
ap-8672	293	26	via	via	ADP
ap-8672	293	27	points	point	NOUN
ap-8672	293	28	p6	p6	PROPN
ap-8672	293	29	→	→	SYM
ap-8672	293	30	p7	p7	PROPN
ap-8672	293	31	.	.	PUNCT
ap-8672	294	1	it	it	PRON
ap-8672	294	2	is	be	AUX
ap-8672	294	3	evident	evident	ADJ
ap-8672	294	4	from	from	ADP
ap-8672	294	5	the	the	DET
ap-8672	294	6	graph	graph	NOUN
ap-8672	294	7	that	that	SCONJ
ap-8672	294	8	the	the	DET
ap-8672	294	9	six	six	NUM
ap-8672	294	10	joint	joint	ADJ
ap-8672	294	11	angle	angle	NOUN
ap-8672	294	12	variations	variation	NOUN
ap-8672	294	13	exhibit	exhibit	VERB
ap-8672	294	14	perfect	perfect	ADJ
ap-8672	294	15	symmetry	symmetry	NOUN
ap-8672	294	16	with	with	ADP
ap-8672	294	17	respect	respect	NOUN
ap-8672	294	18	to	to	PART
ap-8672	294	19	point	point	NOUN
ap-8672	294	20	p6	p6	PROPN
ap-8672	294	21	.	.	PUNCT
ap-8672	295	1	this	this	PRON
ap-8672	295	2	indicates	indicate	VERB
ap-8672	295	3	that	that	SCONJ
ap-8672	295	4	the	the	DET
ap-8672	295	5	robot	robot	NOUN
ap-8672	295	6	retraced	retrace	VERB
ap-8672	295	7	the	the	DET
ap-8672	295	8	path	path	NOUN
ap-8672	295	9	with	with	ADP
ap-8672	295	10	agreat	agreat	NOUN
ap-8672	295	11	precision	precision	NOUN
ap-8672	295	12	.	.	PUNCT
ap-8672	296	1	this	this	PRON
ap-8672	296	2	proves	prove	VERB
ap-8672	296	3	the	the	DET
ap-8672	296	4	compatibility	compatibility	NOUN
ap-8672	296	5	between	between	ADP
ap-8672	296	6	variations	variation	NOUN
ap-8672	296	7	of	of	ADP
ap-8672	296	8	articulations	articulation	NOUN
ap-8672	296	9	and	and	CCONJ
ap-8672	296	10	the	the	DET
ap-8672	296	11	predefined	predefine	VERB
ap-8672	296	12	trajectories	trajectory	NOUN
ap-8672	296	13	as	as	SCONJ
ap-8672	296	14	suggested	suggest	VERB
ap-8672	296	15	in	in	ADP
ap-8672	296	16	figure	figure	NOUN
ap-8672	296	17	6	6	NUM
ap-8672	296	18	.	.	PUNCT
ap-8672	296	19	337	337	NUM
ap-8672	296	20	n.	n.	NOUN
ap-8672	296	21	hadidi	hadidi	PROPN
ap-8672	296	22	,	,	PUNCT
ap-8672	296	23	m.	m.	NOUN
ap-8672	296	24	bouaziz	bouaziz	PROPN
ap-8672	296	25	,	,	PUNCT
ap-8672	296	26	c.	c.	PROPN
ap-8672	296	27	mahfoudi	mahfoudi	PROPN
ap-8672	296	28	,	,	PUNCT
ap-8672	296	29	m.	m.	NOUN
ap-8672	296	30	zaharuddin	zaharuddin	PROPN
ap-8672	296	31	acta	acta	PROPN
ap-8672	296	32	polytechnica	polytechnica	PROPN
ap-8672	296	33	home	home	PROPN
ap-8672	296	34	position	position	NOUN
ap-8672	296	35	movement	movement	NOUN
ap-8672	296	36	p1p2p3	p1p2p3	PROPN
ap-8672	296	37	movement	movement	NOUN
ap-8672	296	38	p4p5	p4p5	PROPN
ap-8672	296	39	and	and	CCONJ
ap-8672	296	40	(	(	PUNCT
ap-8672	296	41	p7p8	p7p8	ADJ
ap-8672	296	42	)	)	PUNCT
ap-8672	296	43	movement	movement	NOUN
ap-8672	296	44	p5p6p7	p5p6p7	NOUN
ap-8672	296	45	movement	movement	NOUN
ap-8672	296	46	p9p10	p9p10	PROPN
ap-8672	296	47	(	(	PUNCT
ap-8672	296	48	a	a	NOUN
ap-8672	296	49	)	)	PUNCT
ap-8672	296	50	.	.	PUNCT
ap-8672	297	1	front	front	ADJ
ap-8672	297	2	view	view	NOUN
ap-8672	297	3	.	.	PUNCT
ap-8672	298	1	home	home	NOUN
ap-8672	298	2	position	position	NOUN
ap-8672	298	3	movement	movement	NOUN
ap-8672	298	4	p1p2p3	p1p2p3	PROPN
ap-8672	298	5	movement	movement	NOUN
ap-8672	298	6	p4p5	p4p5	PROPN
ap-8672	298	7	and	and	CCONJ
ap-8672	298	8	(	(	PUNCT
ap-8672	298	9	p7p8	p7p8	ADJ
ap-8672	298	10	)	)	PUNCT
ap-8672	298	11	movement	movement	NOUN
ap-8672	298	12	p5p6p7	p5p6p7	NOUN
ap-8672	298	13	movement	movement	NOUN
ap-8672	298	14	p9p10	p9p10	PROPN
ap-8672	298	15	(	(	PUNCT
ap-8672	298	16	b	b	NOUN
ap-8672	298	17	)	)	PUNCT
ap-8672	298	18	.	.	PUNCT
ap-8672	299	1	side	side	NOUN
ap-8672	299	2	view	view	NOUN
ap-8672	299	3	.	.	PUNCT
ap-8672	299	4	  	  	SPACE
ap-8672	300	1	home	home	NOUN
ap-8672	300	2	position	position	NOUN
ap-8672	300	3	movement	movement	NOUN
ap-8672	300	4	p1p2p3	p1p2p3	PROPN
ap-8672	300	5	movement	movement	NOUN
ap-8672	300	6	p4p5	p4p5	PROPN
ap-8672	300	7	and	and	CCONJ
ap-8672	300	8	(	(	PUNCT
ap-8672	300	9	p7p8	p7p8	ADJ
ap-8672	300	10	)	)	PUNCT
ap-8672	300	11	movement	movement	NOUN
ap-8672	300	12	p5p6p7	p5p6p7	NOUN
ap-8672	300	13	movement	movement	NOUN
ap-8672	300	14	p9p10	p9p10	PROPN
ap-8672	300	15	  	  	SPACE
ap-8672	300	16	(	(	PUNCT
ap-8672	300	17	c	c	NOUN
ap-8672	300	18	)	)	PUNCT
ap-8672	300	19	.	.	PUNCT
ap-8672	301	1	top	top	ADJ
ap-8672	301	2	view	view	NOUN
ap-8672	301	3	.	.	PUNCT
ap-8672	302	1	figure	figure	NOUN
ap-8672	302	2	9	9	NUM
ap-8672	302	3	.	.	PUNCT
ap-8672	303	1	different	different	ADJ
ap-8672	303	2	postures	posture	NOUN
ap-8672	303	3	of	of	ADP
ap-8672	303	4	the	the	DET
ap-8672	303	5	robot	robot	NOUN
ap-8672	303	6	following	follow	VERB
ap-8672	303	7	predefined	predefine	VERB
ap-8672	303	8	trajectories	trajectory	NOUN
ap-8672	303	9	.	.	PUNCT
ap-8672	304	1	figure	figure	VERB
ap-8672	304	2	10	10	NUM
ap-8672	304	3	.	.	PUNCT
ap-8672	305	1	graphs	graph	NOUN
ap-8672	305	2	of	of	ADP
ap-8672	305	3	the	the	DET
ap-8672	305	4	variations	variation	NOUN
ap-8672	305	5	of	of	ADP
ap-8672	305	6	the	the	DET
ap-8672	305	7	robot	robot	NOUN
ap-8672	305	8	’s	’s	PART
ap-8672	305	9	joint	joint	ADJ
ap-8672	305	10	angles	angle	NOUN
ap-8672	305	11	.	.	PUNCT
ap-8672	306	1	7	7	X
ap-8672	306	2	.	.	AUX
ap-8672	306	3	comparison	comparison	NOUN
ap-8672	306	4	and	and	CCONJ
ap-8672	306	5	discussion	discussion	NOUN
ap-8672	306	6	paul	paul	PROPN
ap-8672	306	7	’s	’s	PART
ap-8672	306	8	method	method	NOUN
ap-8672	306	9	is	be	AUX
ap-8672	306	10	recognised	recognise	VERB
ap-8672	306	11	as	as	ADP
ap-8672	306	12	one	one	NUM
ap-8672	306	13	of	of	ADP
ap-8672	306	14	the	the	DET
ap-8672	306	15	most	most	ADV
ap-8672	306	16	effective	effective	ADJ
ap-8672	306	17	analytical	analytical	ADJ
ap-8672	306	18	approaches	approach	NOUN
ap-8672	306	19	for	for	ADP
ap-8672	306	20	solving	solve	VERB
ap-8672	306	21	the	the	DET
ap-8672	306	22	inverse	inverse	NOUN
ap-8672	306	23	kinematics	kinematic	NOUN
ap-8672	306	24	(	(	PUNCT
ap-8672	306	25	ik	ik	ADJ
ap-8672	306	26	)	)	PUNCT
ap-8672	306	27	problem	problem	NOUN
ap-8672	306	28	in	in	ADP
ap-8672	306	29	robotics	robotic	NOUN
ap-8672	306	30	.	.	PUNCT
ap-8672	307	1	it	it	PRON
ap-8672	307	2	starts	start	VERB
ap-8672	307	3	with	with	ADP
ap-8672	307	4	the	the	DET
ap-8672	307	5	forward	forward	ADJ
ap-8672	307	6	kinematics	kinematic	NOUN
ap-8672	307	7	(	(	PUNCT
ap-8672	307	8	fk	fk	INTJ
ap-8672	307	9	)	)	PUNCT
ap-8672	307	10	model	model	NOUN
ap-8672	307	11	as	as	SCONJ
ap-8672	307	12	given	give	VERB
ap-8672	307	13	in	in	ADP
ap-8672	307	14	equation	equation	NOUN
ap-8672	307	15	(	(	PUNCT
ap-8672	307	16	7	7	NUM
ap-8672	307	17	)	)	PUNCT
ap-8672	307	18	,	,	PUNCT
ap-8672	307	19	which	which	PRON
ap-8672	307	20	leads	lead	VERB
ap-8672	307	21	to	to	ADP
ap-8672	307	22	a	a	DET
ap-8672	307	23	system	system	NOUN
ap-8672	307	24	of	of	ADP
ap-8672	307	25	nonlinear	nonlinear	ADJ
ap-8672	307	26	and	and	CCONJ
ap-8672	307	27	coupled	couple	VERB
ap-8672	307	28	equations	equation	NOUN
ap-8672	307	29	.	.	PUNCT
ap-8672	308	1	for	for	ADP
ap-8672	308	2	example	example	NOUN
ap-8672	308	3	,	,	PUNCT
ap-8672	308	4	the	the	DET
ap-8672	308	5	ik	ik	PROPN
ap-8672	308	6	problem	problem	NOUN
ap-8672	308	7	for	for	ADP
ap-8672	308	8	a	a	DET
ap-8672	308	9	robot	robot	NOUN
ap-8672	308	10	with	with	ADP
ap-8672	308	11	a	a	DET
ap-8672	308	12	6	6	NUM
ap-8672	308	13	-	-	PUNCT
ap-8672	308	14	dof	dof	NOUN
ap-8672	308	15	338	338	NUM
ap-8672	308	16	vol	vol	NOUN
ap-8672	308	17	.	.	PUNCT
ap-8672	309	1	63	63	NUM
ap-8672	309	2	no	no	NOUN
ap-8672	309	3	.	.	PUNCT
ap-8672	310	1	5/2023	5/2023	NUM
ap-8672	310	2	geometric	geometric	ADJ
ap-8672	310	3	approach	approach	NOUN
ap-8672	310	4	to	to	ADP
ap-8672	310	5	solving	solve	VERB
ap-8672	310	6	inverse	inverse	ADJ
ap-8672	310	7	kinematics	kinematic	NOUN
ap-8672	310	8	of	of	ADP
ap-8672	310	9	six	six	NUM
ap-8672	310	10	dof	dof	NOUN
ap-8672	310	11	robot	robot	NOUN
ap-8672	310	12	configuration	configuration	NOUN
ap-8672	310	13	similar	similar	ADJ
ap-8672	310	14	to	to	ADP
ap-8672	310	15	ours	ours	PRON
ap-8672	310	16	has	have	AUX
ap-8672	310	17	been	be	AUX
ap-8672	310	18	studied	study	VERB
ap-8672	310	19	and	and	CCONJ
ap-8672	310	20	presented	present	VERB
ap-8672	310	21	in	in	ADP
ap-8672	310	22	[	[	X
ap-8672	310	23	16	16	NUM
ap-8672	310	24	]	]	PUNCT
ap-8672	310	25	and	and	CCONJ
ap-8672	310	26	[	[	X
ap-8672	310	27	32	32	NUM
ap-8672	310	28	]	]	PUNCT
ap-8672	310	29	using	use	VERB
ap-8672	310	30	paul	paul	PROPN
ap-8672	310	31	’s	’s	PART
ap-8672	310	32	method	method	NOUN
ap-8672	310	33	.	.	PUNCT
ap-8672	311	1	here	here	ADV
ap-8672	311	2	are	be	AUX
ap-8672	311	3	the	the	DET
ap-8672	311	4	initial	initial	ADJ
ap-8672	311	5	key	key	ADJ
ap-8672	311	6	results	result	NOUN
ap-8672	311	7	of	of	ADP
ap-8672	311	8	the	the	DET
ap-8672	311	9	generated	generate	VERB
ap-8672	311	10	system	system	NOUN
ap-8672	311	11	of	of	ADP
ap-8672	311	12	equations	equation	NOUN
ap-8672	311	13	,	,	PUNCT
ap-8672	311	14	as	as	SCONJ
ap-8672	311	15	shown	show	VERB
ap-8672	311	16	in	in	ADP
ap-8672	311	17	equations	equation	NOUN
ap-8672	311	18	(	(	PUNCT
ap-8672	311	19	29	29	NUM
ap-8672	311	20	)	)	PUNCT
ap-8672	311	21	.	.	PUNCT
ap-8672	312	1	s1.s2.s3.c4.c5.c6	s1.s2.s3.c4.c5.c6	PROPN
ap-8672	312	2	+	+	CCONJ
ap-8672	312	3	c1.c3.c4.c5.s6	c1.c3.c4.c5.s6	PROPN
ap-8672	312	4	−	−	PROPN
ap-8672	313	1	s1.c2.s4.c5.s6	s1.c2.s4.c5.s6	PROPN
ap-8672	313	2	+	+	NUM
ap-8672	313	3	s1.s2.c3.s5.s6−	s1.s2.c3.s5.s6−	PROPN
ap-8672	313	4	c1.s3.s5.s6	c1.s3.s5.s6	PROPN
ap-8672	314	1	+	+	CCONJ
ap-8672	314	2	s1.s2.s3.s4.c6	s1.s2.s3.s4.c6	PROPN
ap-8672	314	3	+	+	CCONJ
ap-8672	314	4	c1.c3.s4.c6	c1.c3.s4.c6	PROPN
ap-8672	314	5	+	+	CCONJ
ap-8672	314	6	s1.c2.c4.c6	s1.c2.c4.c6	ADJ
ap-8672	314	7	=	=	SYM
ap-8672	314	8	sx	sx	PROPN
ap-8672	314	9	,	,	PUNCT
ap-8672	314	10	s1.s2.s3.c4.c5.c6	s1.s2.s3.c4.c5.c6	PROPN
ap-8672	314	11	+	+	CCONJ
ap-8672	314	12	c1.c3.c4.c5.c6	c1.c3.c4.c5.c6	VERB
ap-8672	314	13	−	−	PROPN
ap-8672	314	14	21.c2.s4.c5.c6	21.c2.s4.c5.c6	NUM
ap-8672	314	15	+	+	CCONJ
ap-8672	314	16	s1.s2.c3.s5.c6−	s1.s2.c3.s5.c6−	NOUN
ap-8672	314	17	c1.s3.s5.c6	c1.s3.s5.c6	NOUN
ap-8672	314	18	−	−	PROPN
ap-8672	314	19	s1.s2.s3.s4.s6	s1.s2.s3.s4.s6	PROPN
ap-8672	314	20	−	−	PROPN
ap-8672	315	1	c1.c3.s4.s6	c1.c3.s4.s6	PROPN
ap-8672	315	2	−	−	PROPN
ap-8672	315	3	s1.c2.c4.s6	s1.c2.c4.s6	PROPN
ap-8672	315	4	=	=	SYM
ap-8672	315	5	nx	nx	X
ap-8672	315	6	,	,	PUNCT
ap-8672	315	7	−	−	PROPN
ap-8672	315	8	s1.s2.s3.c4.s5	s1.s2.s3.c4.s5	PROPN
ap-8672	315	9	−	−	PROPN
ap-8672	315	10	c1.c3.c4.s5	c1.c3.c4.s5	PROPN
ap-8672	315	11	−	−	PROPN
ap-8672	315	12	s1.c2.s4.s5	s1.c2.s4.s5	PROPN
ap-8672	315	13	+	+	CCONJ
ap-8672	315	14	s1.s2.c3.c5	s1.s2.c3.c5	ADV
ap-8672	315	15	−	−	NOUN
ap-8672	315	16	c1.s3.c5	c1.s3.c5	NOUN
ap-8672	315	17	=	=	NOUN
ap-8672	315	18	ax	ax	NOUN
ap-8672	315	19	,	,	PUNCT
ap-8672	315	20	la.s1.s2.s3.s4	la.s1.s2.s3.s4	NOUN
ap-8672	315	21	+	+	CCONJ
ap-8672	315	22	la.c1.c3.s4	la.c1.c3.s4	NOUN
ap-8672	315	23	+	+	CCONJ
ap-8672	315	24	la.s1.c2.s4	la.s1.c2.s4	NOUN
ap-8672	315	25	+	+	CCONJ
ap-8672	315	26	lf	lf	NOUN
ap-8672	315	27	.s1.c2	.s1.c2	NOUN
ap-8672	316	1	=	=	SYM
ap-8672	316	2	sy	sy	PROPN
ap-8672	316	3	,	,	PUNCT
ap-8672	316	4	c1.s2.s3.c4.c5.c6	c1.s2.s3.c4.c5.c6	PROPN
ap-8672	316	5	+	+	CCONJ
ap-8672	316	6	s1.c3.c4.c5.s6	s1.c3.c4.c5.s6	PROPN
ap-8672	317	1	+	+	CCONJ
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ap-8672	317	4	c1.s2.c3.s5.s6−	c1.s2.c3.s5.s6−	PROPN
ap-8672	317	5	s1.s3.s5.s6	s1.s3.s5.s6	NOUN
ap-8672	317	6	−	−	PROPN
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ap-8672	317	8	+	+	CCONJ
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ap-8672	317	10	−	−	NOUN
ap-8672	317	11	c1.c2.c4.c6	c1.c2.c4.c6	NOUN
ap-8672	317	12	=	=	PUNCT
ap-8672	317	13	ny	ny	PROPN
ap-8672	317	14	,	,	PUNCT
ap-8672	317	15	−	−	PROPN
ap-8672	317	16	c1.s2.s3.c4.c5.c6	c1.s2.s3.c4.c5.c6	PROPN
ap-8672	317	17	+	+	CCONJ
ap-8672	317	18	s1.c3.c4.c5.c6	s1.c3.c4.c5.c6	VERB
ap-8672	317	19	+	+	NUM
ap-8672	317	20	c1.c2.s4.c5.c6	c1.c2.s4.c5.c6	NOUN
ap-8672	317	21	−	−	PROPN
ap-8672	317	22	c1.s2.c3.s5.c6−	c1.s2.c3.s5.c6−	NOUN
ap-8672	317	23	s1.s3.s5.c6	s1.s3.s5.c6	PROPN
ap-8672	318	1	+	+	CCONJ
ap-8672	318	2	c1.s2.s3.s4.s6	c1.s2.s3.s4.s6	ADJ
ap-8672	318	3	−	−	PROPN
ap-8672	319	1	s1.c3.s4.s6	s1.c3.s4.s6	PROPN
ap-8672	320	1	+	+	CCONJ
ap-8672	320	2	c1.c2.c4.s6	c1.c2.c4.s6	PROPN
ap-8672	320	3	=	=	SYM
ap-8672	320	4	ay	ay	PROPN
ap-8672	320	5	,	,	PUNCT
ap-8672	320	6	c1.s2.s3.c4.s5	c1.s2.s3.c4.s5	PROPN
ap-8672	320	7	−	−	PROPN
ap-8672	320	8	s1.c3.c4.s5	s1.c3.c4.s5	PROPN
ap-8672	320	9	−	−	PROPN
ap-8672	320	10	c1.c2.s4.s5	c1.c2.s4.s5	PROPN
ap-8672	320	11	−	−	PROPN
ap-8672	320	12	c1.s2.c3.c5	c1.s2.c3.c5	NOUN
ap-8672	320	13	−	−	X
ap-8672	320	14	s1.s3.c5	s1.s3.c5	ADJ
ap-8672	320	15	=	=	SYM
ap-8672	320	16	sz	sz	NOUN
ap-8672	320	17	,	,	PUNCT
ap-8672	320	18	−	−	PROPN
ap-8672	320	19	la.c1.s2.s3.s4	la.c1.s2.s3.s4	NOUN
ap-8672	320	20	+	+	CCONJ
ap-8672	320	21	la.s1.c3.s4	la.s1.c3.s4	NOUN
ap-8672	320	22	−	−	PROPN
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ap-8672	320	24	−	−	NOUN
ap-8672	320	25	lf	lf	NOUN
ap-8672	320	26	.c1.c2	.c1.c2	PUNCT
ap-8672	321	1	=	=	SYM
ap-8672	321	2	nz	nz	PROPN
ap-8672	321	3	,	,	PUNCT
ap-8672	321	4	c2.s3.c4.c5.c6	c2.s3.c4.c5.c6	PROPN
ap-8672	321	5	+	+	CCONJ
ap-8672	321	6	s2.s4.c5.s6	s2.s4.c5.s6	PROPN
ap-8672	321	7	+	+	SYM
ap-8672	321	8	c2.c3.s5.s6	c2.c3.s5.s6	NOUN
ap-8672	321	9	+	+	CCONJ
ap-8672	321	10	c2.s3.s4.c6	c2.s3.s4.c6	PROPN
ap-8672	321	11	−	−	PROPN
ap-8672	321	12	s2.c4.c6	s2.c4.c6	NOUN
ap-8672	321	13	=	=	SYM
ap-8672	321	14	az	az	PROPN
ap-8672	321	15	,	,	PUNCT
ap-8672	321	16	c2.s3.c4.c5.c6	c2.s3.c4.c5.c6	PROPN
ap-8672	322	1	+	+	CCONJ
ap-8672	322	2	s2.s4.c5.c6	s2.s4.c5.c6	VERB
ap-8672	322	3	+	+	CCONJ
ap-8672	322	4	c2.c3.s5.c6	c2.c3.s5.c6	VERB
ap-8672	322	5	−	−	PROPN
ap-8672	322	6	c2.s3.s4.s6	c2.s3.s4.s6	PROPN
ap-8672	323	1	+	+	CCONJ
ap-8672	323	2	s2.c4.s6	s2.c4.s6	PROPN
ap-8672	323	3	=	=	PUNCT
ap-8672	323	4	pdx	pdx	PROPN
ap-8672	323	5	,	,	PUNCT
ap-8672	323	6	−	−	PROPN
ap-8672	323	7	c2.c3.c4.s5	c2.c3.c4.s5	PROPN
ap-8672	323	8	−	−	PROPN
ap-8672	323	9	s2.s4.s5	s2.s4.s5	ADJ
ap-8672	323	10	+	+	CCONJ
ap-8672	323	11	c2.c3.c5	c2.c3.c5	NOUN
ap-8672	323	12	=	=	SYM
ap-8672	323	13	pdy	pdy	INTJ
ap-8672	323	14	,	,	PUNCT
ap-8672	324	1	−	−	PROPN
ap-8672	324	2	la.c2.s3.s4	la.c2.s3.s4	NOUN
ap-8672	324	3	−	−	NOUN
ap-8672	324	4	la.s2.c4	la.s2.c4	NOUN
ap-8672	324	5	−	−	X
ap-8672	324	6	lf	lf	INTJ
ap-8672	324	7	.s2	.s2	PUNCT
ap-8672	325	1	=	=	SYM
ap-8672	326	1	pdz	pdz	NOUN
ap-8672	326	2	,	,	PUNCT
ap-8672	326	3	(	(	PUNCT
ap-8672	326	4	29	29	NUM
ap-8672	326	5	)	)	PUNCT
ap-8672	326	6	where	where	SCONJ
ap-8672	326	7	si	si	PROPN
ap-8672	326	8	and	and	CCONJ
ap-8672	326	9	ci	ci	PROPN
ap-8672	326	10	are	be	AUX
ap-8672	326	11	sin(θi	sin(θi	NUM
ap-8672	326	12	)	)	PUNCT
ap-8672	326	13	and	and	CCONJ
ap-8672	326	14	cos(θi	cos(θi	NUM
ap-8672	326	15	)	)	PUNCT
ap-8672	326	16	for	for	ADP
ap-8672	326	17	i	i	PROPN
ap-8672	326	18	=	=	NOUN
ap-8672	326	19	1	1	NUM
ap-8672	326	20	,	,	PUNCT
ap-8672	326	21	.	.	PUNCT
ap-8672	326	22	.	.	PUNCT
ap-8672	327	1	.	.	PUNCT
ap-8672	328	1	,	,	PUNCT
ap-8672	328	2	6	6	NUM
ap-8672	328	3	,	,	PUNCT
ap-8672	328	4	respectively	respectively	ADV
ap-8672	328	5	.	.	PUNCT
ap-8672	329	1	to	to	PART
ap-8672	329	2	obtain	obtain	VERB
ap-8672	329	3	solutions	solution	NOUN
ap-8672	329	4	for	for	ADP
ap-8672	329	5	the	the	DET
ap-8672	329	6	articular	articular	ADJ
ap-8672	329	7	space	space	NOUN
ap-8672	329	8	variables	variable	NOUN
ap-8672	329	9	(	(	PUNCT
ap-8672	329	10	θ1	θ1	PROPN
ap-8672	329	11	,	,	PUNCT
ap-8672	329	12	θ2	θ2	PROPN
ap-8672	329	13	,	,	PUNCT
ap-8672	329	14	θ3	θ3	PROPN
ap-8672	329	15	,	,	PUNCT
ap-8672	329	16	θ4	θ4	NOUN
ap-8672	329	17	,	,	PUNCT
ap-8672	329	18	θ5	θ5	PROPN
ap-8672	329	19	,	,	PUNCT
ap-8672	329	20	θ6	θ6	PROPN
ap-8672	329	21	)	)	PUNCT
ap-8672	329	22	,	,	PUNCT
ap-8672	329	23	paul	paul	PROPN
ap-8672	329	24	’s	’s	PART
ap-8672	329	25	method	method	NOUN
ap-8672	329	26	relies	rely	VERB
ap-8672	329	27	on	on	ADP
ap-8672	329	28	complex	complex	ADJ
ap-8672	329	29	mathematical	mathematical	ADJ
ap-8672	329	30	operations	operation	NOUN
ap-8672	329	31	and	and	CCONJ
ap-8672	329	32	rearrangements	rearrangement	NOUN
ap-8672	329	33	to	to	PART
ap-8672	329	34	isolate	isolate	VERB
ap-8672	329	35	and	and	CCONJ
ap-8672	329	36	identify	identify	VERB
ap-8672	329	37	these	these	DET
ap-8672	329	38	variables	variable	NOUN
ap-8672	329	39	one	one	NUM
ap-8672	329	40	by	by	ADP
ap-8672	329	41	one	one	NUM
ap-8672	330	1	[	[	X
ap-8672	330	2	16	16	NUM
ap-8672	330	3	]	]	PUNCT
ap-8672	330	4	.	.	PUNCT
ap-8672	331	1	how	how	SCONJ
ap-8672	331	2	do	do	AUX
ap-8672	331	3	we	we	PRON
ap-8672	331	4	obtain	obtain	VERB
ap-8672	331	5	the	the	DET
ap-8672	331	6	solutions	solution	NOUN
ap-8672	331	7	when	when	SCONJ
ap-8672	331	8	comparing	compare	VERB
ap-8672	331	9	the	the	DET
ap-8672	331	10	two	two	NUM
ap-8672	331	11	methods	method	NOUN
ap-8672	331	12	and	and	CCONJ
ap-8672	331	13	evaluating	evaluate	VERB
ap-8672	331	14	the	the	DET
ap-8672	331	15	inverse	inverse	NOUN
ap-8672	331	16	kinematics	kinematic	NOUN
ap-8672	331	17	(	(	PUNCT
ap-8672	331	18	ik	ik	ADJ
ap-8672	331	19	)	)	PUNCT
ap-8672	331	20	problem	problem	NOUN
ap-8672	331	21	?	?	PUNCT
ap-8672	332	1	we	we	PRON
ap-8672	332	2	observe	observe	VERB
ap-8672	332	3	that	that	SCONJ
ap-8672	332	4	the	the	DET
ap-8672	332	5	solutions	solution	NOUN
ap-8672	332	6	of	of	ADP
ap-8672	332	7	the	the	DET
ap-8672	332	8	present	present	ADJ
ap-8672	332	9	approach	approach	NOUN
ap-8672	332	10	originate	originate	VERB
ap-8672	332	11	from	from	ADP
ap-8672	332	12	simple	simple	ADJ
ap-8672	332	13	linear	linear	ADJ
ap-8672	332	14	equations	equation	NOUN
ap-8672	332	15	.	.	PUNCT
ap-8672	333	1	in	in	ADP
ap-8672	333	2	contrast	contrast	NOUN
ap-8672	333	3	,	,	PUNCT
ap-8672	333	4	paul	paul	PROPN
ap-8672	333	5	’s	’s	PART
ap-8672	333	6	method	method	NOUN
ap-8672	333	7	obtains	obtain	VERB
ap-8672	333	8	solutions	solution	NOUN
ap-8672	333	9	from	from	ADP
ap-8672	333	10	more	more	ADJ
ap-8672	333	11	complex	complex	ADJ
ap-8672	333	12	equations	equation	NOUN
ap-8672	333	13	.	.	PUNCT
ap-8672	334	1	this	this	DET
ap-8672	334	2	distinction	distinction	NOUN
ap-8672	334	3	becomes	become	VERB
ap-8672	334	4	evident	evident	ADJ
ap-8672	334	5	when	when	SCONJ
ap-8672	334	6	considering	consider	VERB
ap-8672	334	7	equations	equation	NOUN
ap-8672	334	8	(	(	PUNCT
ap-8672	334	9	23	23	NUM
ap-8672	334	10	)	)	PUNCT
ap-8672	334	11	to	to	ADP
ap-8672	334	12	(	(	PUNCT
ap-8672	334	13	28	28	NUM
ap-8672	334	14	)	)	PUNCT
ap-8672	334	15	for	for	ADP
ap-8672	334	16	the	the	DET
ap-8672	334	17	present	present	ADJ
ap-8672	334	18	approach	approach	NOUN
ap-8672	334	19	and	and	CCONJ
ap-8672	334	20	equations	equation	NOUN
ap-8672	334	21	(	(	PUNCT
ap-8672	334	22	29	29	NUM
ap-8672	334	23	)	)	PUNCT
ap-8672	334	24	for	for	ADP
ap-8672	334	25	paul	paul	PROPN
ap-8672	334	26	’s	’s	PART
ap-8672	334	27	method	method	NOUN
ap-8672	334	28	.	.	PUNCT
ap-8672	335	1	figure	figure	NOUN
ap-8672	335	2	11	11	NUM
ap-8672	335	3	provides	provide	VERB
ap-8672	335	4	information	information	NOUN
ap-8672	335	5	on	on	ADP
ap-8672	335	6	the	the	DET
ap-8672	335	7	errors	error	NOUN
ap-8672	335	8	in	in	ADP
ap-8672	335	9	position	position	NOUN
ap-8672	335	10	for	for	ADP
ap-8672	335	11	each	each	DET
ap-8672	335	12	point	point	NOUN
ap-8672	335	13	(	(	PUNCT
ap-8672	335	14	defined	define	VERB
ap-8672	335	15	by	by	ADP
ap-8672	335	16	its	its	PRON
ap-8672	335	17	coordinates	coordinate	NOUN
ap-8672	335	18	in	in	ADP
ap-8672	335	19	the	the	DET
ap-8672	335	20	cartesian	cartesian	ADJ
ap-8672	335	21	coordinate	coordinate	NOUN
ap-8672	335	22	system	system	NOUN
ap-8672	335	23	:	:	PUNCT
ap-8672	335	24	x	x	X
ap-8672	335	25	,	,	PUNCT
ap-8672	335	26	y	y	PROPN
ap-8672	335	27	,	,	PUNCT
ap-8672	335	28	z	z	NOUN
ap-8672	335	29	)	)	PUNCT
ap-8672	335	30	of	of	ADP
ap-8672	335	31	the	the	DET
ap-8672	335	32	end	end	NOUN
ap-8672	335	33	-	-	PUNCT
ap-8672	335	34	effector	effector	NOUN
ap-8672	335	35	.	.	PUNCT
ap-8672	336	1	by	by	ADP
ap-8672	336	2	using	use	VERB
ap-8672	336	3	the	the	DET
ap-8672	336	4	results	result	NOUN
ap-8672	336	5	of	of	ADP
ap-8672	336	6	the	the	DET
ap-8672	336	7	end	end	NOUN
ap-8672	336	8	-	-	PUNCT
ap-8672	336	9	effector	effector	NOUN
ap-8672	336	10	configurations	configuration	NOUN
ap-8672	336	11	within	within	ADP
ap-8672	336	12	the	the	DET
ap-8672	336	13	work	work	NOUN
ap-8672	336	14	space	space	NOUN
ap-8672	336	15	that	that	PRON
ap-8672	336	16	are	be	AUX
ap-8672	336	17	generated	generate	VERB
ap-8672	336	18	through	through	ADP
ap-8672	336	19	the	the	DET
ap-8672	336	20	fk	fk	PROPN
ap-8672	336	21	equations	equation	NOUN
ap-8672	336	22	for	for	ADP
ap-8672	336	23	both	both	DET
ap-8672	336	24	methods	method	NOUN
ap-8672	336	25	(	(	PUNCT
ap-8672	336	26	paul	paul	PROPN
ap-8672	336	27	’s	’s	PART
ap-8672	336	28	method	method	NOUN
ap-8672	336	29	and	and	CCONJ
ap-8672	336	30	the	the	DET
ap-8672	336	31	current	current	ADJ
ap-8672	336	32	approach	approach	NOUN
ap-8672	336	33	)	)	PUNCT
ap-8672	336	34	and	and	CCONJ
ap-8672	336	35	by	by	ADP
ap-8672	336	36	calculating	calculate	VERB
ap-8672	336	37	the	the	DET
ap-8672	336	38	corresponding	correspond	VERB
ap-8672	336	39	errors	error	NOUN
ap-8672	336	40	in	in	ADP
ap-8672	336	41	the	the	DET
ap-8672	336	42	coordinate	coordinate	NOUN
ap-8672	336	43	position	position	NOUN
ap-8672	336	44	of	of	ADP
ap-8672	336	45	the	the	DET
ap-8672	336	46	end	end	NOUN
ap-8672	336	47	-	-	PUNCT
ap-8672	336	48	effector	effector	NOUN
ap-8672	336	49	(	(	PUNCT
ap-8672	336	50	xerror	xerror	PROPN
ap-8672	336	51	,	,	PUNCT
ap-8672	336	52	yerror	yerror	NOUN
ap-8672	336	53	,	,	PUNCT
ap-8672	336	54	zerror	zerror	NOUN
ap-8672	336	55	)	)	PUNCT
ap-8672	336	56	during	during	ADP
ap-8672	336	57	the	the	DET
ap-8672	336	58	time	time	NOUN
ap-8672	336	59	for	for	ADP
ap-8672	336	60	all	all	DET
ap-8672	336	61	paths	path	NOUN
ap-8672	336	62	,	,	PUNCT
ap-8672	336	63	as	as	SCONJ
ap-8672	336	64	shown	show	VERB
ap-8672	336	65	in	in	ADP
ap-8672	336	66	figure	figure	NOUN
ap-8672	336	67	11	11	NUM
ap-8672	336	68	.	.	PUNCT
ap-8672	337	1	we	we	PRON
ap-8672	337	2	find	find	VERB
ap-8672	337	3	that	that	SCONJ
ap-8672	337	4	the	the	DET
ap-8672	337	5	errors	error	NOUN
ap-8672	337	6	are	be	AUX
ap-8672	337	7	exceptionally	exceptionally	ADV
ap-8672	337	8	negligible	negligible	ADJ
ap-8672	337	9	,	,	PUNCT
ap-8672	337	10	with	with	ADP
ap-8672	337	11	the	the	DET
ap-8672	337	12	largest	large	ADJ
ap-8672	337	13	error	error	NOUN
ap-8672	337	14	value	value	NOUN
ap-8672	337	15	estimated	estimate	VERB
ap-8672	337	16	to	to	PART
ap-8672	337	17	be	be	AUX
ap-8672	337	18	in	in	ADP
ap-8672	337	19	the	the	DET
ap-8672	337	20	order	order	NOUN
ap-8672	337	21	of	of	ADP
ap-8672	337	22	1×10−15	1×10−15	NUM
ap-8672	337	23	m.	m.	NOUN
ap-8672	337	24	(	(	PUNCT
ap-8672	337	25	a	a	NOUN
ap-8672	337	26	)	)	PUNCT
ap-8672	337	27	.	.	PUNCT
ap-8672	338	1	x	x	PUNCT
ap-8672	338	2	position	position	NOUN
ap-8672	338	3	error	error	NOUN
ap-8672	338	4	.	.	PUNCT
ap-8672	339	1	(	(	PUNCT
ap-8672	339	2	b	b	NOUN
ap-8672	339	3	)	)	PUNCT
ap-8672	339	4	.	.	PUNCT
ap-8672	340	1	y	y	PROPN
ap-8672	340	2	position	position	NOUN
ap-8672	340	3	error	error	NOUN
ap-8672	340	4	.	.	PUNCT
ap-8672	341	1	(	(	PUNCT
ap-8672	341	2	c	c	NOUN
ap-8672	341	3	)	)	PUNCT
ap-8672	341	4	.	.	PUNCT
ap-8672	342	1	z	z	NOUN
ap-8672	342	2	position	position	NOUN
ap-8672	342	3	error	error	NOUN
ap-8672	342	4	.	.	PUNCT
ap-8672	343	1	figure	figure	NOUN
ap-8672	343	2	11	11	NUM
ap-8672	343	3	.	.	PUNCT
ap-8672	344	1	comparison	comparison	NOUN
ap-8672	344	2	of	of	ADP
ap-8672	344	3	end	end	NOUN
ap-8672	344	4	-	-	PUNCT
ap-8672	344	5	effector	effector	NOUN
ap-8672	344	6	position	position	NOUN
ap-8672	344	7	between	between	ADP
ap-8672	344	8	paul	paul	PROPN
ap-8672	344	9	’s	’s	PART
ap-8672	344	10	method	method	NOUN
ap-8672	344	11	and	and	CCONJ
ap-8672	344	12	current	current	ADJ
ap-8672	344	13	approach	approach	NOUN
ap-8672	344	14	.	.	PUNCT
ap-8672	345	1	consequently	consequently	ADV
ap-8672	345	2	,	,	PUNCT
ap-8672	345	3	it	it	PRON
ap-8672	345	4	is	be	AUX
ap-8672	345	5	evident	evident	ADJ
ap-8672	345	6	that	that	SCONJ
ap-8672	345	7	the	the	DET
ap-8672	345	8	current	current	ADJ
ap-8672	345	9	approach	approach	NOUN
ap-8672	345	10	has	have	VERB
ap-8672	345	11	significant	significant	ADJ
ap-8672	345	12	accuracy	accuracy	NOUN
ap-8672	345	13	and	and	CCONJ
ap-8672	345	14	advantage	advantage	NOUN
ap-8672	345	15	in	in	ADP
ap-8672	345	16	obtaining	obtain	VERB
ap-8672	345	17	the	the	DET
ap-8672	345	18	solutions	solution	NOUN
ap-8672	345	19	to	to	ADP
ap-8672	345	20	the	the	DET
ap-8672	345	21	ik	ik	PROPN
ap-8672	345	22	problem	problem	NOUN
ap-8672	345	23	.	.	PUNCT
ap-8672	346	1	the	the	DET
ap-8672	346	2	elapsed	elapse	VERB
ap-8672	346	3	time	time	NOUN
ap-8672	346	4	in	in	ADP
ap-8672	346	5	matlab	matlab	PROPN
ap-8672	346	6	was	be	AUX
ap-8672	346	7	also	also	ADV
ap-8672	346	8	taken	take	VERB
ap-8672	346	9	into	into	ADP
ap-8672	346	10	account	account	NOUN
ap-8672	346	11	for	for	ADP
ap-8672	346	12	both	both	DET
ap-8672	346	13	methods	method	NOUN
ap-8672	346	14	as	as	SCONJ
ap-8672	346	15	shown	show	VERB
ap-8672	346	16	in	in	ADP
ap-8672	346	17	figure	figure	NOUN
ap-8672	346	18	12	12	NUM
ap-8672	346	19	.	.	PUNCT
ap-8672	347	1	from	from	ADP
ap-8672	347	2	figure	figure	NOUN
ap-8672	347	3	12	12	NUM
ap-8672	347	4	,	,	PUNCT
ap-8672	347	5	we	we	PRON
ap-8672	347	6	can	can	AUX
ap-8672	347	7	see	see	VERB
ap-8672	347	8	the	the	DET
ap-8672	347	9	time	time	NOUN
ap-8672	347	10	elapsed	elapse	VERB
ap-8672	347	11	by	by	ADP
ap-8672	347	12	the	the	DET
ap-8672	347	13	two	two	NUM
ap-8672	347	14	methods	method	NOUN
ap-8672	347	15	separately	separately	ADV
ap-8672	347	16	in	in	ADP
ap-8672	347	17	each	each	DET
ap-8672	347	18	portion	portion	NOUN
ap-8672	347	19	of	of	ADP
ap-8672	347	20	the	the	DET
ap-8672	347	21	trajectory	trajectory	NOUN
ap-8672	347	22	,	,	PUNCT
ap-8672	347	23	and	and	CCONJ
ap-8672	347	24	we	we	PRON
ap-8672	347	25	can	can	AUX
ap-8672	347	26	also	also	ADV
ap-8672	347	27	deduce	deduce	VERB
ap-8672	347	28	the	the	DET
ap-8672	347	29	total	total	ADJ
ap-8672	347	30	time	time	NOUN
ap-8672	347	31	elapsed	elapse	VERB
ap-8672	347	32	during	during	ADP
ap-8672	347	33	all	all	DET
ap-8672	347	34	the	the	DET
ap-8672	347	35	robot	robot	NOUN
ap-8672	347	36	’s	’s	PART
ap-8672	347	37	movements	movement	NOUN
ap-8672	347	38	.	.	PUNCT
ap-8672	348	1	the	the	DET
ap-8672	348	2	total	total	ADJ
ap-8672	348	3	elapsed	elapse	VERB
ap-8672	348	4	time	time	NOUN
ap-8672	348	5	in	in	ADP
ap-8672	348	6	paul	paul	PROPN
ap-8672	348	7	’s	’s	PART
ap-8672	348	8	method	method	NOUN
ap-8672	348	9	and	and	CCONJ
ap-8672	348	10	the	the	DET
ap-8672	348	11	vectorial	vectorial	ADJ
ap-8672	348	12	approach	approach	NOUN
ap-8672	348	13	is	be	AUX
ap-8672	348	14	1.59	1.59	NUM
ap-8672	348	15	s	s	NOUN
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ap-8672	348	21	.	.	PUNCT
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ap-8672	349	2	these	these	DET
ap-8672	349	3	results	result	NOUN
ap-8672	349	4	,	,	PUNCT
ap-8672	349	5	it	it	PRON
ap-8672	349	6	can	can	AUX
ap-8672	349	7	be	be	AUX
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ap-8672	349	10	paul	paul	PROPN
ap-8672	349	11	’s	’s	PART
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ap-8672	349	14	slightly	slightly	ADV
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ap-8672	349	17	the	the	DET
ap-8672	349	18	vectorial	vectorial	ADJ
ap-8672	349	19	method	method	NOUN
ap-8672	349	20	.	.	PUNCT
ap-8672	350	1	this	this	DET
ap-8672	350	2	339	339	NUM
ap-8672	350	3	n.	n.	NOUN
ap-8672	350	4	hadidi	hadidi	PROPN
ap-8672	350	5	,	,	PUNCT
ap-8672	350	6	m.	m.	NOUN
ap-8672	350	7	bouaziz	bouaziz	PROPN
ap-8672	350	8	,	,	PUNCT
ap-8672	350	9	c.	c.	PROPN
ap-8672	350	10	mahfoudi	mahfoudi	PROPN
ap-8672	350	11	,	,	PUNCT
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ap-8672	350	13	zaharuddin	zaharuddin	PROPN
ap-8672	350	14	acta	acta	PROPN
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ap-8672	350	18	05	05	NUM
ap-8672	350	19	49	49	NUM
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ap-8672	350	27	23	23	NUM
ap-8672	350	28	37	37	NUM
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ap-8672	350	32	se	se	X
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ap-8672	350	35	,	,	PUNCT
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ap-8672	350	37	92	92	NUM
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ap-8672	350	40	3	3	NUM
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ap-8672	350	42	c	c	PROPN
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ap-8672	350	49	8	8	NUM
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ap-8672	350	53	,	,	PUNCT
ap-8672	350	54	18	18	NUM
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ap-8672	350	56	46	46	NUM
ap-8672	350	57	67	67	NUM
ap-8672	350	58	6	6	NUM
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ap-8672	350	60	c	c	PROPN
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ap-8672	350	62	,	,	PUNCT
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ap-8672	350	70	,	,	PUNCT
ap-8672	350	71	14	14	NUM
ap-8672	350	72	63	63	NUM
ap-8672	350	73	08	08	NUM
ap-8672	350	74	59	59	NUM
ap-8672	350	75	2	2	NUM
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ap-8672	350	77	c	c	PROPN
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ap-8672	350	79	,	,	PUNCT
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ap-8672	350	81	37	37	NUM
ap-8672	350	82	23	23	NUM
ap-8672	350	83	90	90	NUM
ap-8672	350	84	1	1	NUM
ap-8672	350	85	se	se	X
ap-8672	350	86	c	c	PROPN
ap-8672	350	87	0	0	PROPN
ap-8672	350	88	,	,	PUNCT
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ap-8672	350	90	29	29	NUM
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ap-8672	350	92	70	70	NUM
ap-8672	350	93	8	8	NUM
ap-8672	350	94	se	se	X
ap-8672	350	95	c	c	PROPN
ap-8672	350	96	0	0	PROPN
ap-8672	350	97	,	,	PUNCT
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ap-8672	350	99	66	66	NUM
ap-8672	350	100	05	05	NUM
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ap-8672	350	102	3	3	NUM
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ap-8672	350	104	c	c	PROPN
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ap-8672	350	112	c	c	PROPN
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ap-8672	350	147	se	se	X
ap-8672	350	148	c	c	PROPN
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ap-8672	350	157	c	c	PROPN
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ap-8672	350	177	,	,	PUNCT
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ap-8672	350	186	,	,	PUNCT
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ap-8672	350	191	3	3	NUM
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ap-8672	350	194	0	0	NUM
ap-8672	350	195	,	,	PUNCT
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ap-8672	350	197	09	09	NUM
ap-8672	350	198	51	51	NUM
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ap-8672	350	207	57	57	NUM
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ap-8672	350	211	c	c	X
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ap-8672	350	213	r	r	PROPN
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ap-8672	350	215	j	j	PROPN
ap-8672	350	216	0	0	NUM
ap-8672	350	217	-1	-1	PROPN
ap-8672	350	218	t	t	PROPN
ap-8672	350	219	r	r	NOUN
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ap-8672	350	221	j	j	PROPN
ap-8672	350	222	1	1	NUM
ap-8672	350	223	-2	-2	NOUN
ap-8672	350	224	t	t	PROPN
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ap-8672	350	227	j	j	NOUN
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ap-8672	350	230	t	t	PROPN
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ap-8672	350	233	j	j	PROPN
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ap-8672	350	236	t	t	PROPN
ap-8672	350	237	r	r	NOUN
ap-8672	350	238	a	a	DET
ap-8672	350	239	j	j	PROPN
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ap-8672	350	242	t	t	NOUN
ap-8672	350	243	r	r	NOUN
ap-8672	350	244	a	a	DET
ap-8672	350	245	j	j	PROPN
ap-8672	350	246	5	5	NUM
ap-8672	350	247	-6	-6	NOUN
ap-8672	350	248	t	t	PROPN
ap-8672	350	249	r	r	NOUN
ap-8672	350	250	a	a	DET
ap-8672	350	251	j	j	PROPN
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ap-8672	350	253	-7	-7	NOUN
ap-8672	350	254	t	t	PROPN
ap-8672	350	255	r	r	NOUN
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ap-8672	350	257	j	j	PROPN
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ap-8672	350	260	t	t	NOUN
ap-8672	350	261	r	r	NOUN
ap-8672	350	262	a	a	DET
ap-8672	350	263	j	j	PROPN
ap-8672	350	264	8	8	NUM
ap-8672	350	265	-9	-9	NOUN
ap-8672	350	266	t	t	PROPN
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ap-8672	350	268	a	a	DET
ap-8672	350	269	j	j	PROPN
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ap-8672	350	271	-1	-1	SYM
ap-8672	350	272	0	0	NUM
ap-8672	351	1	t	t	NOUN
ap-8672	351	2	r	r	NOUN
ap-8672	351	3	a	a	DET
ap-8672	351	4	j	j	PROPN
ap-8672	351	5	1	1	NUM
ap-8672	351	6	0	0	NUM
ap-8672	351	7	-1	-1	SYM
ap-8672	351	8	1	1	NUM
ap-8672	351	9	paul	paul	PROPN
ap-8672	351	10	's	's	PART
ap-8672	351	11	method	method	ADJ
ap-8672	351	12	vectorial	vectorial	ADJ
ap-8672	351	13	approach	approach	NOUN
ap-8672	351	14	figure	figure	NOUN
ap-8672	351	15	12	12	NUM
ap-8672	351	16	.	.	PUNCT
ap-8672	351	17	elapsed	elapse	VERB
ap-8672	351	18	time	time	NOUN
ap-8672	352	1	[	[	X
ap-8672	352	2	sec	sec	X
ap-8672	352	3	]	]	X
ap-8672	352	4	required	require	VERB
ap-8672	352	5	for	for	ADP
ap-8672	352	6	the	the	DET
ap-8672	352	7	robot	robot	NOUN
ap-8672	352	8	’s	’s	PART
ap-8672	352	9	ik	ik	PROPN
ap-8672	352	10	solution	solution	NOUN
ap-8672	352	11	tracking	track	VERB
ap-8672	352	12	the	the	DET
ap-8672	352	13	path	path	NOUN
ap-8672	352	14	in	in	ADP
ap-8672	352	15	matlab	matlab	PROPN
ap-8672	352	16	.	.	PUNCT
ap-8672	352	17	difference	difference	NOUN
ap-8672	352	18	in	in	ADP
ap-8672	352	19	time	time	NOUN
ap-8672	352	20	comes	come	VERB
ap-8672	352	21	from	from	ADP
ap-8672	352	22	the	the	DET
ap-8672	352	23	necessity	necessity	NOUN
ap-8672	352	24	of	of	ADP
ap-8672	352	25	pre	pre	ADJ
ap-8672	352	26	-	-	ADJ
ap-8672	352	27	calculating	calculate	VERB
ap-8672	352	28	specific	specific	ADJ
ap-8672	352	29	geometric	geometric	ADJ
ap-8672	352	30	parameters	parameter	NOUN
ap-8672	352	31	for	for	ADP
ap-8672	352	32	each	each	DET
ap-8672	352	33	situation	situation	NOUN
ap-8672	352	34	of	of	ADP
ap-8672	352	35	the	the	DET
ap-8672	352	36	end	end	NOUN
ap-8672	352	37	-	-	PUNCT
ap-8672	352	38	effector	effector	NOUN
ap-8672	352	39	,	,	PUNCT
ap-8672	352	40	which	which	PRON
ap-8672	352	41	are	be	AUX
ap-8672	352	42	utilised	utilise	VERB
ap-8672	352	43	in	in	ADP
ap-8672	352	44	the	the	DET
ap-8672	352	45	equations	equation	NOUN
ap-8672	352	46	that	that	PRON
ap-8672	352	47	provide	provide	VERB
ap-8672	352	48	the	the	DET
ap-8672	352	49	solutions	solution	NOUN
ap-8672	352	50	for	for	ADP
ap-8672	352	51	the	the	DET
ap-8672	352	52	joints	joint	NOUN
ap-8672	352	53	(	(	PUNCT
ap-8672	352	54	angles	angle	NOUN
ap-8672	352	55	)	)	PUNCT
ap-8672	352	56	of	of	ADP
ap-8672	352	57	the	the	DET
ap-8672	352	58	robot	robot	NOUN
ap-8672	352	59	.	.	PUNCT
ap-8672	353	1	from	from	ADP
ap-8672	353	2	the	the	DET
ap-8672	353	3	simulations	simulation	NOUN
ap-8672	353	4	and	and	CCONJ
ap-8672	353	5	the	the	DET
ap-8672	353	6	experimental	experimental	ADJ
ap-8672	353	7	results	result	NOUN
ap-8672	353	8	,	,	PUNCT
ap-8672	353	9	we	we	PRON
ap-8672	353	10	can	can	AUX
ap-8672	353	11	conclude	conclude	VERB
ap-8672	353	12	that	that	SCONJ
ap-8672	353	13	the	the	DET
ap-8672	353	14	present	present	ADJ
ap-8672	353	15	approach	approach	NOUN
ap-8672	353	16	is	be	AUX
ap-8672	353	17	a	a	DET
ap-8672	353	18	powerful	powerful	ADJ
ap-8672	353	19	asset	asset	NOUN
ap-8672	353	20	for	for	ADP
ap-8672	353	21	a	a	DET
ap-8672	353	22	geometric	geometric	ADJ
ap-8672	353	23	solution	solution	NOUN
ap-8672	353	24	of	of	ADP
ap-8672	353	25	the	the	DET
ap-8672	353	26	inverse	inverse	NOUN
ap-8672	353	27	kinematics	kinematic	NOUN
ap-8672	353	28	problem	problem	NOUN
ap-8672	353	29	.	.	PUNCT
ap-8672	354	1	8	8	X
ap-8672	354	2	.	.	X
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ap-8672	354	4	this	this	DET
ap-8672	354	5	study	study	NOUN
ap-8672	354	6	proposes	propose	VERB
ap-8672	354	7	an	an	DET
ap-8672	354	8	alternative	alternative	ADJ
ap-8672	354	9	approach	approach	NOUN
ap-8672	354	10	to	to	ADP
ap-8672	354	11	solving	solve	VERB
ap-8672	354	12	the	the	DET
ap-8672	354	13	inverse	inverse	NOUN
ap-8672	354	14	kinematics	kinematic	NOUN
ap-8672	354	15	problem	problem	NOUN
ap-8672	354	16	.	.	PUNCT
ap-8672	355	1	the	the	DET
ap-8672	355	2	approach	approach	NOUN
ap-8672	355	3	is	be	AUX
ap-8672	355	4	based	base	VERB
ap-8672	355	5	on	on	ADP
ap-8672	355	6	vector	vector	NOUN
ap-8672	355	7	calculus	calculus	NOUN
ap-8672	355	8	using	use	VERB
ap-8672	355	9	spatial	spatial	ADJ
ap-8672	355	10	geometry	geometry	NOUN
ap-8672	355	11	and	and	CCONJ
ap-8672	355	12	trigonometric	trigonometric	ADJ
ap-8672	355	13	relationships	relationship	NOUN
ap-8672	355	14	.	.	PUNCT
ap-8672	356	1	the	the	DET
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ap-8672	356	4	the	the	DET
ap-8672	356	5	approach	approach	NOUN
ap-8672	356	6	was	be	AUX
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ap-8672	356	8	on	on	ADP
ap-8672	356	9	a	a	DET
ap-8672	356	10	6	6	NUM
ap-8672	356	11	-	-	PUNCT
ap-8672	356	12	dof	dof	NOUN
ap-8672	356	13	robot	robot	NOUN
ap-8672	356	14	.	.	PUNCT
ap-8672	357	1	by	by	ADP
ap-8672	357	2	utilising	utilise	VERB
ap-8672	357	3	the	the	DET
ap-8672	357	4	geometrical	geometrical	ADJ
ap-8672	357	5	lengths	length	NOUN
ap-8672	357	6	of	of	ADP
ap-8672	357	7	the	the	DET
ap-8672	357	8	robot	robot	NOUN
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ap-8672	357	10	the	the	DET
ap-8672	357	11	given	give	VERB
ap-8672	357	12	matrix	matrix	NOUN
ap-8672	357	13	of	of	ADP
ap-8672	357	14	the	the	DET
ap-8672	357	15	desired	desire	VERB
ap-8672	357	16	position	position	NOUN
ap-8672	357	17	along	along	ADP
ap-8672	357	18	with	with	ADP
ap-8672	357	19	certain	certain	ADJ
ap-8672	357	20	geometrical	geometrical	ADJ
ap-8672	357	21	relationships	relationship	NOUN
ap-8672	357	22	,	,	PUNCT
ap-8672	357	23	all	all	DET
ap-8672	357	24	the	the	DET
ap-8672	357	25	joint	joint	ADJ
ap-8672	357	26	angles	angle	NOUN
ap-8672	357	27	were	be	AUX
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ap-8672	357	29	.	.	PUNCT
ap-8672	358	1	a	a	DET
ap-8672	358	2	major	major	ADJ
ap-8672	358	3	advantage	advantage	NOUN
ap-8672	358	4	of	of	ADP
ap-8672	358	5	the	the	DET
ap-8672	358	6	proposed	propose	VERB
ap-8672	358	7	approach	approach	NOUN
ap-8672	358	8	is	be	AUX
ap-8672	358	9	that	that	SCONJ
ap-8672	358	10	it	it	PRON
ap-8672	358	11	treats	treat	VERB
ap-8672	358	12	the	the	DET
ap-8672	358	13	inverse	inverse	NOUN
ap-8672	358	14	kinematic	kinematic	NOUN
ap-8672	358	15	problem	problem	NOUN
ap-8672	358	16	separately	separately	ADV
ap-8672	358	17	for	for	ADP
ap-8672	358	18	each	each	DET
ap-8672	358	19	joint	joint	ADJ
ap-8672	358	20	angle	angle	NOUN
ap-8672	358	21	,	,	PUNCT
ap-8672	358	22	and	and	CCONJ
ap-8672	358	23	the	the	DET
ap-8672	358	24	resulting	result	VERB
ap-8672	358	25	equations	equation	NOUN
ap-8672	358	26	have	have	VERB
ap-8672	358	27	a	a	DET
ap-8672	358	28	linear	linear	ADJ
ap-8672	358	29	form	form	NOUN
ap-8672	358	30	,	,	PUNCT
ap-8672	358	31	which	which	PRON
ap-8672	358	32	simplifies	simplify	VERB
ap-8672	358	33	the	the	DET
ap-8672	358	34	mathematical	mathematical	ADJ
ap-8672	358	35	model	model	NOUN
ap-8672	358	36	.	.	PUNCT
ap-8672	359	1	experimental	experimental	ADJ
ap-8672	359	2	studies	study	NOUN
ap-8672	359	3	were	be	AUX
ap-8672	359	4	carried	carry	VERB
ap-8672	359	5	out	out	ADP
ap-8672	359	6	on	on	ADP
ap-8672	359	7	a	a	DET
ap-8672	359	8	designed	design	VERB
ap-8672	359	9	and	and	CCONJ
ap-8672	359	10	manufactured	manufacture	VERB
ap-8672	359	11	robot	robot	NOUN
ap-8672	359	12	.	.	PUNCT
ap-8672	360	1	in	in	ADP
ap-8672	360	2	addition	addition	NOUN
ap-8672	360	3	,	,	PUNCT
ap-8672	360	4	simulations	simulation	NOUN
ap-8672	360	5	were	be	AUX
ap-8672	360	6	performed	perform	VERB
ap-8672	360	7	to	to	PART
ap-8672	360	8	test	test	VERB
ap-8672	360	9	and	and	CCONJ
ap-8672	360	10	validate	validate	VERB
ap-8672	360	11	the	the	DET
ap-8672	360	12	effectiveness	effectiveness	NOUN
ap-8672	360	13	and	and	CCONJ
ap-8672	360	14	correctness	correctness	NOUN
ap-8672	360	15	of	of	ADP
ap-8672	360	16	the	the	DET
ap-8672	360	17	approach	approach	NOUN
ap-8672	360	18	.	.	PUNCT
ap-8672	361	1	the	the	DET
ap-8672	361	2	joint	joint	ADJ
ap-8672	361	3	angles	angle	NOUN
ap-8672	361	4	were	be	AUX
ap-8672	361	5	obtained	obtain	VERB
ap-8672	361	6	and	and	CCONJ
ap-8672	361	7	utilised	utilise	VERB
ap-8672	361	8	for	for	ADP
ap-8672	361	9	various	various	ADJ
ap-8672	361	10	desired	desire	VERB
ap-8672	361	11	trajectories	trajectory	NOUN
ap-8672	361	12	.	.	PUNCT
ap-8672	362	1	in	in	ADP
ap-8672	362	2	both	both	DET
ap-8672	362	3	scenarios	scenario	NOUN
ap-8672	362	4	(	(	PUNCT
ap-8672	362	5	experimental	experimental	ADJ
ap-8672	362	6	and	and	CCONJ
ap-8672	362	7	simulation	simulation	NOUN
ap-8672	362	8	)	)	PUNCT
ap-8672	362	9	,	,	PUNCT
ap-8672	362	10	the	the	DET
ap-8672	362	11	end	end	NOUN
ap-8672	362	12	-	-	PUNCT
ap-8672	362	13	effector	effector	NOUN
ap-8672	362	14	successfully	successfully	ADV
ap-8672	362	15	followed	follow	VERB
ap-8672	362	16	the	the	DET
ap-8672	362	17	desired	desire	VERB
ap-8672	362	18	trajectories	trajectory	NOUN
ap-8672	362	19	,	,	PUNCT
ap-8672	362	20	confirming	confirm	VERB
ap-8672	362	21	the	the	DET
ap-8672	362	22	accuracy	accuracy	NOUN
ap-8672	362	23	of	of	ADP
ap-8672	362	24	the	the	DET
ap-8672	362	25	suggested	suggest	VERB
ap-8672	362	26	approach	approach	NOUN
ap-8672	362	27	.	.	PUNCT
ap-8672	363	1	given	give	VERB
ap-8672	363	2	these	these	DET
ap-8672	363	3	advantages	advantage	NOUN
ap-8672	363	4	,	,	PUNCT
ap-8672	363	5	the	the	DET
ap-8672	363	6	approach	approach	NOUN
ap-8672	363	7	developed	develop	VERB
ap-8672	363	8	in	in	ADP
ap-8672	363	9	this	this	DET
ap-8672	363	10	work	work	NOUN
ap-8672	363	11	for	for	ADP
ap-8672	363	12	solving	solve	VERB
ap-8672	363	13	the	the	DET
ap-8672	363	14	inverse	inverse	NOUN
ap-8672	363	15	kinematics	kinematic	NOUN
ap-8672	363	16	problem	problem	NOUN
ap-8672	363	17	represents	represent	VERB
ap-8672	363	18	an	an	DET
ap-8672	363	19	alternative	alternative	ADJ
ap-8672	363	20	solution	solution	NOUN
ap-8672	363	21	that	that	PRON
ap-8672	363	22	could	could	AUX
ap-8672	363	23	find	find	VERB
ap-8672	363	24	widespread	widespread	ADJ
ap-8672	363	25	use	use	NOUN
ap-8672	363	26	in	in	ADP
ap-8672	363	27	various	various	ADJ
ap-8672	363	28	robotic	robotic	ADJ
ap-8672	363	29	structures	structure	NOUN
ap-8672	363	30	.	.	PUNCT
ap-8672	364	1	list	list	NOUN
ap-8672	364	2	of	of	ADP
ap-8672	364	3	symbols	symbol	NOUN
ap-8672	364	4	dh	dh	PROPN
ap-8672	364	5	denavit	denavit	PROPN
ap-8672	365	1	hartemberg	hartemberg	PROPN
ap-8672	365	2	convention	convention	PROPN
ap-8672	365	3	f	f	PROPN
ap-8672	365	4	k	k	PROPN
ap-8672	365	5	forward	forward	PROPN
ap-8672	365	6	kinematics	kinematic	NOUN
ap-8672	365	7	ik	ik	PROPN
ap-8672	365	8	inverse	inverse	PROPN
ap-8672	365	9	kinematics	kinematic	NOUN
ap-8672	365	10	dof	dof	NOUN
ap-8672	365	11	degrees	degree	NOUN
ap-8672	365	12	of	of	ADP
ap-8672	365	13	freedom	freedom	NOUN
ap-8672	365	14	la	la	PROPN
ap-8672	365	15	,	,	PUNCT
ap-8672	365	16	lf	lf	PROPN
ap-8672	365	17	andlh	andlh	ADJ
ap-8672	365	18	geometrical	geometrical	ADJ
ap-8672	365	19	lengths	length	NOUN
ap-8672	365	20	of	of	ADP
ap-8672	365	21	the	the	DET
ap-8672	365	22	robot	robot	NOUN
ap-8672	365	23	,	,	PUNCT
ap-8672	365	24	namely	namely	ADV
ap-8672	365	25	:	:	PUNCT
ap-8672	365	26	arm	arm	NOUN
ap-8672	365	27	,	,	PUNCT
ap-8672	365	28	forearm	forearm	NOUN
ap-8672	365	29	and	and	CCONJ
ap-8672	365	30	hand	hand	NOUN
ap-8672	366	1	[	[	X
ap-8672	366	2	m	m	X
ap-8672	366	3	]	]	X
ap-8672	366	4	fi(i	fi(i	X
ap-8672	367	1	=	=	NOUN
ap-8672	367	2	1	1	NUM
ap-8672	367	3	,	,	PUNCT
ap-8672	367	4	.	.	PUNCT
ap-8672	367	5	.	.	PUNCT
ap-8672	368	1	.	.	PUNCT
ap-8672	369	1	,	,	PUNCT
ap-8672	369	2	7	7	X
ap-8672	369	3	)	)	PUNCT
ap-8672	369	4	reference	reference	NOUN
ap-8672	369	5	frame	frame	NOUN
ap-8672	369	6	t	t	NOUN
ap-8672	369	7	=	=	PUNCT
ap-8672	370	1	[	[	X
ap-8672	370	2	s	s	X
ap-8672	370	3	n	n	PRON
ap-8672	370	4	a	a	DET
ap-8672	370	5	p	p	X
ap-8672	370	6	]	]	X
ap-8672	370	7	matrix	matrix	NOUN
ap-8672	370	8	(	(	PUNCT
ap-8672	370	9	4×4	4×4	NUM
ap-8672	370	10	)	)	PUNCT
ap-8672	370	11	of	of	ADP
ap-8672	370	12	the	the	DET
ap-8672	370	13	desired	desire	VERB
ap-8672	370	14	orientation	orientation	NOUN
ap-8672	370	15	and	and	CCONJ
ap-8672	370	16	position	position	NOUN
ap-8672	370	17	of	of	ADP
ap-8672	370	18	the	the	DET
ap-8672	370	19	end	end	NOUN
ap-8672	370	20	-	-	PUNCT
ap-8672	370	21	effector	effector	NOUN
ap-8672	370	22	−−→	−−→	PROPN
ap-8672	370	23	opw	opw	PROPN
ap-8672	370	24	=	=	X
ap-8672	370	25	(	(	PUNCT
ap-8672	370	26	pwx	pwx	PROPN
ap-8672	370	27	,	,	PUNCT
ap-8672	370	28	pwy	pwy	VERB
ap-8672	370	29	,	,	PUNCT
ap-8672	370	30	pwz)t	pwz)t	PROPN
ap-8672	370	31	vector	vector	NOUN
ap-8672	370	32	of	of	ADP
ap-8672	370	33	wrist	wrist	NOUN
ap-8672	370	34	-	-	PUNCT
ap-8672	370	35	position	position	NOUN
ap-8672	370	36	−−→	−−→	NOUN
ap-8672	370	37	opd	opd	NOUN
ap-8672	370	38	=	=	SYM
ap-8672	370	39	(	(	PUNCT
ap-8672	370	40	pdx	pdx	PROPN
ap-8672	370	41	,	,	PUNCT
ap-8672	370	42	pdy	pdy	PROPN
ap-8672	370	43	,	,	PUNCT
ap-8672	370	44	pdz)t	pdz)t	PROPN
ap-8672	370	45	vector	vector	NOUN
ap-8672	370	46	of	of	ADP
ap-8672	370	47	desired	desire	VERB
ap-8672	370	48	position	position	NOUN
ap-8672	370	49	(	(	PUNCT
ap-8672	370	50	end	end	NOUN
ap-8672	370	51	-	-	PUNCT
ap-8672	370	52	effectors	effector	NOUN
ap-8672	370	53	)	)	PUNCT
ap-8672	370	54	−→	−→	ADJ
ap-8672	370	55	vse	vse	NOUN
ap-8672	370	56	vector	vector	NOUN
ap-8672	370	57	defined	define	VERB
ap-8672	370	58	by	by	ADP
ap-8672	370	59	two	two	NUM
ap-8672	370	60	points	point	NOUN
ap-8672	370	61	(	(	PUNCT
ap-8672	370	62	shoulder	shoulder	NOUN
ap-8672	370	63	-	-	PUNCT
ap-8672	370	64	elbow	elbow	NOUN
ap-8672	370	65	)	)	PUNCT
ap-8672	370	66	−−→	−−→	PROPN
ap-8672	370	67	vwh	vwh	NOUN
ap-8672	370	68	vector	vector	NOUN
ap-8672	370	69	defined	define	VERB
ap-8672	370	70	by	by	ADP
ap-8672	370	71	two	two	NUM
ap-8672	370	72	points	point	NOUN
ap-8672	370	73	(	(	PUNCT
ap-8672	370	74	wrist	wrist	NOUN
ap-8672	370	75	-	-	PUNCT
ap-8672	370	76	h	h	NOUN
ap-8672	370	77	:	:	PUNCT
ap-8672	370	78	the	the	DET
ap-8672	370	79	nearest	near	ADJ
ap-8672	370	80	point	point	NOUN
ap-8672	370	81	on	on	ADP
ap-8672	370	82	the	the	DET
ap-8672	370	83	q	q	NOUN
ap-8672	370	84	-	-	NOUN
ap-8672	370	85	plane	plane	NOUN
ap-8672	370	86	to	to	PART
ap-8672	370	87	origin	origin	VERB
ap-8672	370	88	)	)	PUNCT
ap-8672	371	1	−→nseand−−→nwh	−→nseand−−→nwh	PROPN
ap-8672	371	2	normalised	normalise	VERB
ap-8672	371	3	vectors	vector	NOUN
ap-8672	371	4	of	of	ADP
ap-8672	371	5	−→	−→	ADJ
ap-8672	371	6	vse	vse	NOUN
ap-8672	371	7	and	and	CCONJ
ap-8672	371	8	−−→	−−→	PROPN
ap-8672	371	9	vwh	vwh	NOUN
ap-8672	371	10	,	,	PUNCT
ap-8672	371	11	respectively	respectively	ADV
ap-8672	371	12	340	340	NUM
ap-8672	371	13	vol	vol	NOUN
ap-8672	371	14	.	.	PUNCT
ap-8672	372	1	63	63	NUM
ap-8672	372	2	no	no	NOUN
ap-8672	372	3	.	.	PUNCT
ap-8672	373	1	5/2023	5/2023	NUM
ap-8672	373	2	geometric	geometric	ADJ
ap-8672	373	3	approach	approach	NOUN
ap-8672	373	4	to	to	ADP
ap-8672	373	5	solving	solve	VERB
ap-8672	373	6	inverse	inverse	ADJ
ap-8672	373	7	kinematics	kinematic	NOUN
ap-8672	373	8	of	of	ADP
ap-8672	373	9	six	six	NUM
ap-8672	373	10	dof	dof	NOUN
ap-8672	373	11	robot	robot	NOUN
ap-8672	373	12	∆(ps	∆(ps	NOUN
ap-8672	373	13	,	,	PUNCT
ap-8672	373	14	ph	ph	VERB
ap-8672	373	15	,	,	PUNCT
ap-8672	373	16	e	e	NOUN
ap-8672	373	17	)	)	PUNCT
ap-8672	373	18	triangle	triangle	NOUN
ap-8672	373	19	of	of	ADP
ap-8672	373	20	three	three	NUM
ap-8672	373	21	points	point	NOUN
ap-8672	373	22	q	q	NOUN
ap-8672	373	23	−	−	PROPN
ap-8672	373	24	plane	plane	NOUN
ap-8672	373	25	plane	plane	NOUN
ap-8672	373	26	of	of	ADP
ap-8672	373	27	normal	normal	ADJ
ap-8672	373	28	vector	vector	NOUN
ap-8672	373	29	−→nq	−→nq	PROPN
ap-8672	373	30	det[−→a6	det[−→a6	NOUN
ap-8672	373	31	−−→nwh	−−→nwh	AUX
ap-8672	373	32	−→	−→	NOUN
ap-8672	373	33	s6	s6	PROPN
ap-8672	373	34	]	]	PUNCT
ap-8672	373	35	determinant	determinant	NOUN
ap-8672	373	36	of	of	ADP
ap-8672	373	37	three	three	NUM
ap-8672	373	38	vectors	vector	NOUN
ap-8672	373	39	(	(	PUNCT
ap-8672	373	40	pe	pe	INTJ
ap-8672	373	41	,	,	PUNCT
ap-8672	373	42	p̂w	p̂w	ADV
ap-8672	373	43	,	,	PUNCT
ap-8672	373	44	ph	ph	ADJ
ap-8672	373	45	)	)	PUNCT
ap-8672	373	46	angle	angle	NOUN
ap-8672	373	47	by	by	ADP
ap-8672	373	48	three	three	NUM
ap-8672	373	49	points	point	NOUN
ap-8672	373	50	in	in	ADP
ap-8672	373	51	which	which	PRON
ap-8672	373	52	the	the	DET
ap-8672	373	53	midpoint	midpoint	NOUN
ap-8672	373	54	is	be	AUX
ap-8672	373	55	its	its	PRON
ap-8672	373	56	vertex	vertex	NOUN
ap-8672	373	57	siandcifori	siandcifori	NOUN
ap-8672	373	58	=	=	PUNCT
ap-8672	373	59	1	1	NUM
ap-8672	373	60	,	,	PUNCT
ap-8672	373	61	.	.	PUNCT
ap-8672	373	62	.	.	PUNCT
ap-8672	373	63	.	.	PUNCT
ap-8672	374	1	,	,	PUNCT
ap-8672	374	2	6	6	NUM
ap-8672	374	3	sin(θi	sin(θi	NUM
ap-8672	374	4	)	)	PUNCT
ap-8672	374	5	and	and	CCONJ
ap-8672	374	6	cos(θi	cos(θi	NUM
ap-8672	374	7	)	)	PUNCT
ap-8672	374	8	,	,	PUNCT
ap-8672	374	9	respectively	respectively	ADV
ap-8672	374	10	−→	−→	ADJ
ap-8672	374	11	u	u	NOUN
ap-8672	374	12	.	.	PUNCT
ap-8672	375	1	−→	−→	ADJ
ap-8672	375	2	v	v	NOUN
ap-8672	375	3	dot	dot	NOUN
ap-8672	375	4	product	product	NOUN
ap-8672	375	5	of	of	ADP
ap-8672	375	6	vectors	vector	NOUN
ap-8672	375	7	−→	−→	VERB
ap-8672	375	8	u	u	NOUN
ap-8672	375	9	and	and	CCONJ
ap-8672	375	10	−→	−→	NOUN
ap-8672	375	11	v	v	NOUN
ap-8672	375	12	−→	−→	NOUN
ap-8672	376	1	u	u	NOUN
ap-8672	376	2	∧	∧	PROPN
ap-8672	376	3	−→	−→	NOUN
ap-8672	376	4	v	v	NUM
ap-8672	376	5	cross	cross	NOUN
ap-8672	376	6	product	product	NOUN
ap-8672	376	7	of	of	ADP
ap-8672	376	8	vectors	vector	NOUN
ap-8672	376	9	−→	−→	VERB
ap-8672	376	10	u	u	NOUN
ap-8672	376	11	and	and	CCONJ
ap-8672	376	12	−→	−→	NOUN
ap-8672	376	13	v	v	ADP
ap-8672	376	14	references	reference	NOUN
ap-8672	376	15	[	[	X
ap-8672	376	16	1	1	NUM
ap-8672	376	17	]	]	PUNCT
ap-8672	376	18	h.	h.	PROPN
ap-8672	376	19	ren	ren	PROPN
ap-8672	376	20	,	,	PUNCT
ap-8672	376	21	p.	p.	PROPN
ap-8672	376	22	ben	ben	PROPN
ap-8672	376	23	-	-	PUNCT
ap-8672	376	24	tzvi	tzvi	ADJ
ap-8672	376	25	.	.	PUNCT
ap-8672	377	1	learning	learn	VERB
ap-8672	377	2	inverse	inverse	ADJ
ap-8672	377	3	kinematics	kinematic	NOUN
ap-8672	377	4	and	and	CCONJ
ap-8672	377	5	dynamics	dynamic	NOUN
ap-8672	377	6	of	of	ADP
ap-8672	377	7	a	a	DET
ap-8672	377	8	robotic	robotic	ADJ
ap-8672	377	9	manipulator	manipulator	NOUN
ap-8672	377	10	using	use	VERB
ap-8672	377	11	generative	generative	ADJ
ap-8672	377	12	adversarial	adversarial	ADJ
ap-8672	377	13	networks	network	NOUN
ap-8672	377	14	.	.	PUNCT
ap-8672	378	1	robotics	robotic	NOUN
ap-8672	378	2	and	and	CCONJ
ap-8672	378	3	autonomous	autonomous	ADJ
ap-8672	378	4	systems	system	NOUN
ap-8672	378	5	124(8):379–386	124(8):379–386	NUM
ap-8672	378	6	,	,	PUNCT
ap-8672	378	7	2020	2020	NUM
ap-8672	378	8	.	.	PUNCT
ap-8672	379	1	https://doi.org/10.1016/j.robot.2019.103386	https://doi.org/10.1016/j.robot.2019.103386	VERB
ap-8672	379	2	[	[	PUNCT
ap-8672	379	3	2	2	NUM
ap-8672	379	4	]	]	PUNCT
ap-8672	379	5	m.	m.	NOUN
ap-8672	379	6	alebooyeh	alebooyeh	PROPN
ap-8672	379	7	,	,	PUNCT
ap-8672	379	8	r.	r.	PROPN
ap-8672	379	9	j.	j.	PROPN
ap-8672	379	10	urbanic	urbanic	PROPN
ap-8672	379	11	.	.	PUNCT
ap-8672	379	12	neural	neural	ADJ
ap-8672	379	13	network	network	NOUN
ap-8672	379	14	model	model	NOUN
ap-8672	379	15	for	for	ADP
ap-8672	379	16	identifying	identify	VERB
ap-8672	379	17	workspace	workspace	NOUN
ap-8672	379	18	,	,	PUNCT
ap-8672	379	19	forward	forward	ADV
ap-8672	379	20	and	and	CCONJ
ap-8672	379	21	inverse	inverse	ADJ
ap-8672	379	22	kinematics	kinematic	NOUN
ap-8672	379	23	of	of	ADP
ap-8672	379	24	the	the	DET
ap-8672	379	25	7	7	NUM
ap-8672	379	26	-	-	PUNCT
ap-8672	379	27	dof	dof	NOUN
ap-8672	379	28	yumi	yumi	PROPN
ap-8672	379	29	14000	14000	NUM
ap-8672	379	30	abb	abb	PROPN
ap-8672	379	31	collaborative	collaborative	PROPN
ap-8672	379	32	robot	robot	NOUN
ap-8672	379	33	.	.	PUNCT
ap-8672	380	1	ifac	ifac	NOUN
ap-8672	380	2	-	-	PUNCT
ap-8672	380	3	papersonline	papersonline	NOUN
ap-8672	380	4	52(10):176–181	52(10):176–181	NUM
ap-8672	380	5	,	,	PUNCT
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ap-8672	380	7	.	.	PUNCT
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ap-8672	382	3	]	]	PUNCT
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ap-8672	382	13	,	,	PUNCT
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ap-8672	383	2	novel	novel	ADJ
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ap-8672	383	7	6	6	NUM
ap-8672	383	8	-	-	PUNCT
ap-8672	383	9	dof	dof	NOUN
ap-8672	383	10	robots	robot	NOUN
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ap-8672	383	12	non	non	ADJ
ap-8672	383	13	-	-	ADJ
ap-8672	383	14	spherical	spherical	ADJ
ap-8672	383	15	wrist	wrist	NOUN
ap-8672	383	16	.	.	PUNCT
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ap-8672	384	3	machine	machine	NOUN
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ap-8672	384	6	,	,	PUNCT
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ap-8672	384	8	.	.	PUNCT
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ap-8672	385	3	4	4	NUM
ap-8672	385	4	]	]	PUNCT
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ap-8672	385	7	.	.	PUNCT
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ap-8672	385	22	manipulators	manipulator	NOUN
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ap-8672	385	25	wrist	wrist	NOUN
ap-8672	385	26	.	.	PUNCT
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ap-8672	385	28	soft	soft	ADJ
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ap-8672	385	31	,	,	PUNCT
ap-8672	385	32	2020	2020	NUM
ap-8672	385	33	.	.	PUNCT
ap-8672	386	1	https://doi.org/10.1016/j.asoc.2020.106074	https://doi.org/10.1016/j.asoc.2020.106074	PROPN
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ap-8672	386	3	5	5	X
ap-8672	386	4	]	]	PUNCT
ap-8672	386	5	z.	z.	PROPN
ap-8672	386	6	liao	liao	PROPN
ap-8672	386	7	,	,	PUNCT
ap-8672	386	8	g.	g.	PROPN
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ap-8672	386	11	f.	f.	PROPN
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ap-8672	387	8	6r	6r	NUM
ap-8672	387	9	robot	robot	NOUN
ap-8672	387	10	manipulator	manipulator	NOUN
ap-8672	387	11	with	with	ADP
ap-8672	387	12	offset	offset	ADJ
ap-8672	387	13	joint	joint	NOUN
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ap-8672	387	15	on	on	ADP
ap-8672	387	16	screw	screw	PROPN
ap-8672	387	17	theory	theory	NOUN
ap-8672	387	18	.	.	PUNCT
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ap-8672	388	2	journal	journal	NOUN
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ap-8672	388	4	advance	advance	NOUN
ap-8672	388	5	robotic	robotic	ADJ
ap-8672	388	6	systems	system	NOUN
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ap-8672	388	8	,	,	PUNCT
ap-8672	388	9	2020	2020	NUM
ap-8672	388	10	.	.	PUNCT
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ap-8672	390	2	6	6	NUM
ap-8672	390	3	]	]	PUNCT
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ap-8672	390	5	s.	s.	PROPN
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ap-8672	390	9	s.	s.	PROPN
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ap-8672	390	19	.	.	PUNCT
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ap-8672	391	2	analytical	analytical	ADJ
ap-8672	391	3	and	and	CCONJ
ap-8672	391	4	a	a	DET
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ap-8672	391	7	model	model	NOUN
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ap-8672	391	9	solving	solve	VERB
ap-8672	391	10	the	the	DET
ap-8672	391	11	inverse	inverse	NOUN
ap-8672	391	12	kinematic	kinematic	NOUN
ap-8672	391	13	problem	problem	NOUN
ap-8672	391	14	of	of	ADP
ap-8672	391	15	an	an	DET
ap-8672	391	16	industrial	industrial	ADJ
ap-8672	391	17	parallel	parallel	NOUN
ap-8672	391	18	robot	robot	NOUN
ap-8672	391	19	.	.	PUNCT
ap-8672	392	1	computers	computer	NOUN
ap-8672	392	2	&	&	CCONJ
ap-8672	392	3	industrial	industrial	ADJ
ap-8672	392	4	engineering	engineering	PROPN
ap-8672	392	5	151:106682	151:106682	NUM
ap-8672	392	6	,	,	PUNCT
ap-8672	392	7	2021	2021	NUM
ap-8672	392	8	.	.	PUNCT
ap-8672	393	1	https://doi.org/10.1016/j.cie.2020.106682	https://doi.org/10.1016/j.cie.2020.106682	PROPN
ap-8672	394	1	[	[	X
ap-8672	394	2	7	7	X
ap-8672	394	3	]	]	X
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ap-8672	394	9	,	,	PUNCT
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ap-8672	394	12	,	,	PUNCT
ap-8672	394	13	et	et	PROPN
ap-8672	394	14	al	al	PROPN
ap-8672	394	15	.	.	PUNCT
ap-8672	395	1	forward	forward	PROPN
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ap-8672	395	3	inverse	inverse	ADJ
ap-8672	395	4	kinematics	kinematic	NOUN
ap-8672	395	5	of	of	ADP
ap-8672	395	6	a	a	DET
ap-8672	395	7	5	5	NUM
ap-8672	395	8	-	-	PUNCT
ap-8672	395	9	dof	dof	ADJ
ap-8672	395	10	hybrid	hybrid	NOUN
ap-8672	395	11	robot	robot	NOUN
ap-8672	395	12	for	for	ADP
ap-8672	395	13	composite	composite	ADJ
ap-8672	395	14	material	material	NOUN
ap-8672	395	15	machining	machining	NOUN
ap-8672	395	16	.	.	PUNCT
ap-8672	396	1	robotics	robotic	NOUN
ap-8672	396	2	and	and	CCONJ
ap-8672	396	3	computer	computer	NOUN
ap-8672	396	4	-	-	PUNCT
ap-8672	396	5	integrated	integrate	VERB
ap-8672	396	6	manufacturing	manufacturing	NOUN
ap-8672	396	7	65(1):101961	65(1):101961	NUM
ap-8672	396	8	,	,	PUNCT
ap-8672	396	9	2020	2020	NUM
ap-8672	396	10	.	.	PUNCT
ap-8672	397	1	https://doi.org/10.1016/j.rcim.2020.101961	https://doi.org/10.1016/j.rcim.2020.101961	ADJ
ap-8672	397	2	[	[	X
ap-8672	397	3	8	8	NUM
ap-8672	397	4	]	]	X
ap-8672	397	5	o.	o.	NOUN
ap-8672	397	6	m.	m.	NOUN
ap-8672	397	7	omisore	omisore	PROPN
ap-8672	397	8	,	,	PUNCT
ap-8672	397	9	s.	s.	PROPN
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ap-8672	397	14	,	,	PUNCT
ap-8672	397	15	et	et	PROPN
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ap-8672	397	19	-	-	PUNCT
ap-8672	397	20	learnt	learn	VERB
ap-8672	397	21	damped	damp	VERB
ap-8672	397	22	least	least	ADJ
ap-8672	397	23	-	-	PUNCT
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ap-8672	397	25	(	(	PUNCT
ap-8672	397	26	dl	dl	NOUN
ap-8672	397	27	-	-	PUNCT
ap-8672	397	28	dls	dls	NOUN
ap-8672	397	29	)	)	PUNCT
ap-8672	397	30	method	method	NOUN
ap-8672	397	31	for	for	ADP
ap-8672	397	32	inverse	inverse	ADJ
ap-8672	397	33	kinematics	kinematic	NOUN
ap-8672	397	34	of	of	ADP
ap-8672	397	35	snake	snake	NOUN
ap-8672	397	36	-	-	PUNCT
ap-8672	397	37	like	like	ADJ
ap-8672	397	38	robots	robot	NOUN
ap-8672	397	39	.	.	PUNCT
ap-8672	398	1	neural	neural	ADJ
ap-8672	398	2	networks	network	NOUN
ap-8672	398	3	107(2):34–47	107(2):34–47	NUM
ap-8672	398	4	,	,	PUNCT
ap-8672	398	5	2020	2020	NUM
ap-8672	398	6	.	.	PUNCT
ap-8672	399	1	https://doi.org/10.1016/j.neunet.2018.06.018	https://doi.org/10.1016/j.neunet.2018.06.018	NOUN
ap-8672	400	1	[	[	X
ap-8672	400	2	9	9	NUM
ap-8672	400	3	]	]	PUNCT
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ap-8672	400	6	,	,	PUNCT
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ap-8672	400	9	,	,	PUNCT
ap-8672	400	10	e.	e.	PROPN
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ap-8672	400	12	,	,	PUNCT
ap-8672	400	13	et	et	PROPN
ap-8672	400	14	al	al	PROPN
ap-8672	400	15	.	.	PUNCT
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ap-8672	400	17	-	-	PUNCT
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ap-8672	400	22	kinematics	kinematic	NOUN
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ap-8672	400	25	mobile	mobile	ADJ
ap-8672	400	26	robots	robot	NOUN
ap-8672	400	27	.	.	PUNCT
ap-8672	401	1	mechanism	mechanism	NOUN
ap-8672	401	2	and	and	CCONJ
ap-8672	401	3	machine	machine	NOUN
ap-8672	401	4	theory	theory	NOUN
ap-8672	401	5	153(6):103988	153(6):103988	NUM
ap-8672	401	6	,	,	PUNCT
ap-8672	401	7	2020	2020	NUM
ap-8672	401	8	.	.	PUNCT
ap-8672	402	1	https://doi.org/10.1016/j.mechmachtheory.2020.103988	https://doi.org/10.1016/j.mechmachtheory.2020.103988	PROPN
ap-8672	402	2	[	[	X
ap-8672	402	3	10	10	NUM
ap-8672	402	4	]	]	PUNCT
ap-8672	402	5	m.	m.	NOUN
ap-8672	402	6	u.	u.	PROPN
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ap-8672	402	10	i.	i.	PROPN
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ap-8672	403	2	of	of	ADP
ap-8672	403	3	an	an	DET
ap-8672	403	4	8dof	8dof	NOUN
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ap-8672	403	7	and	and	CCONJ
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ap-8672	403	10	inverse	inverse	NOUN
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ap-8672	403	13	denavit	denavit	PROPN
ap-8672	403	14	-	-	PUNCT
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ap-8672	403	17	.	.	PUNCT
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ap-8672	404	5	.	.	PUNCT
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ap-8672	406	2	11	11	NUM
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ap-8672	406	4	a.	a.	PROPN
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ap-8672	407	1	a	a	DET
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ap-8672	407	7	methods	method	NOUN
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ap-8672	408	6	,	,	PUNCT
ap-8672	408	7	2018	2018	NUM
ap-8672	408	8	.	.	PUNCT
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ap-8672	410	2	12	12	NUM
ap-8672	410	3	]	]	PUNCT
ap-8672	410	4	s.	s.	PROPN
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ap-8672	410	7	n.	n.	PROPN
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ap-8672	410	10	j.	j.	PROPN
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ap-8672	411	1	a	a	DET
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ap-8672	411	4	data	datum	NOUN
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ap-8672	414	2	13	13	NUM
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ap-8672	414	14	manipulator	manipulator	NOUN
ap-8672	414	15	robot	robot	NOUN
ap-8672	414	16	with	with	ADP
ap-8672	414	17	shoulder	shoulder	NOUN
ap-8672	414	18	offset	offset	NOUN
ap-8672	414	19	based	base	VERB
ap-8672	414	20	on	on	ADP
ap-8672	414	21	geometric	geometric	ADJ
ap-8672	414	22	method	method	NOUN
ap-8672	414	23	mixed	mix	VERB
ap-8672	414	24	with	with	ADP
ap-8672	414	25	analytical	analytical	ADJ
ap-8672	414	26	method	method	NOUN
ap-8672	414	27	algorithm	algorithm	NOUN
ap-8672	414	28	.	.	PUNCT
ap-8672	415	1	in	in	ADP
ap-8672	415	2	ieee	ieee	PROPN
ap-8672	415	3	international	international	PROPN
ap-8672	415	4	conference	conference	NOUN
ap-8672	415	5	on	on	ADP
ap-8672	415	6	cyber	cyber	PROPN
ap-8672	415	7	technology	technology	NOUN
ap-8672	415	8	in	in	ADP
ap-8672	415	9	automation	automation	NOUN
ap-8672	415	10	,	,	PUNCT
ap-8672	415	11	control	control	NOUN
ap-8672	415	12	,	,	PUNCT
ap-8672	415	13	and	and	CCONJ
ap-8672	415	14	intelligent	intelligent	ADJ
ap-8672	415	15	systems	system	NOUN
ap-8672	415	16	(	(	PUNCT
ap-8672	415	17	cyber	cyber	NOUN
ap-8672	415	18	)	)	PUNCT
ap-8672	415	19	,	,	PUNCT
ap-8672	415	20	pp	pp	ADJ
ap-8672	415	21	.	.	PUNCT
ap-8672	416	1	1198–1203	1198–1203	NUM
ap-8672	416	2	.	.	NOUN
ap-8672	416	3	2015	2015	NUM
ap-8672	416	4	.	.	PUNCT
ap-8672	417	1	https://doi.org/10.1109/cyber.2015.7288114	https://doi.org/10.1109/cyber.2015.7288114	PROPN
ap-8672	418	1	[	[	X
ap-8672	418	2	14	14	NUM
ap-8672	418	3	]	]	PUNCT
ap-8672	418	4	a.	a.	NOUN
ap-8672	418	5	aristidou	aristidou	PROPN
ap-8672	418	6	,	,	PUNCT
ap-8672	418	7	j.	j.	PROPN
ap-8672	418	8	lasenby	lasenby	PROPN
ap-8672	418	9	.	.	PUNCT
ap-8672	419	1	fabrik	fabrik	PROPN
ap-8672	419	2	:	:	PUNCT
ap-8672	419	3	a	a	DET
ap-8672	419	4	fast	fast	ADJ
ap-8672	419	5	,	,	PUNCT
ap-8672	419	6	iterative	iterative	NOUN
ap-8672	419	7	solver	solver	ADV
ap-8672	419	8	for	for	ADP
ap-8672	419	9	the	the	DET
ap-8672	419	10	inverse	inverse	NOUN
ap-8672	419	11	kinematics	kinematic	NOUN
ap-8672	419	12	problem	problem	NOUN
ap-8672	419	13	.	.	PUNCT
ap-8672	420	1	graphical	graphical	ADJ
ap-8672	420	2	models	model	NOUN
ap-8672	420	3	73(5):243–260	73(5):243–260	PROPN
ap-8672	420	4	,	,	PUNCT
ap-8672	420	5	2011	2011	NUM
ap-8672	420	6	.	.	PUNCT
ap-8672	421	1	https://doi.org/10.1016/j.gmod.2011.05.003	https://doi.org/10.1016/j.gmod.2011.05.003	X
ap-8672	422	1	[	[	X
ap-8672	422	2	15	15	NUM
ap-8672	422	3	]	]	X
ap-8672	422	4	w.	w.	PROPN
ap-8672	422	5	suleiman	suleiman	PROPN
ap-8672	422	6	,	,	PUNCT
ap-8672	422	7	f.	f.	PROPN
ap-8672	422	8	kanehiro	kanehiro	PROPN
ap-8672	422	9	,	,	PUNCT
ap-8672	422	10	e.	e.	PROPN
ap-8672	422	11	yoshida	yoshida	PROPN
ap-8672	422	12	.	.	PUNCT
ap-8672	423	1	infeasibility	infeasibility	NOUN
ap-8672	423	2	-	-	PUNCT
ap-8672	423	3	free	free	ADJ
ap-8672	423	4	inverse	inverse	NOUN
ap-8672	423	5	kinematics	kinematic	NOUN
ap-8672	423	6	method	method	NOUN
ap-8672	423	7	.	.	PUNCT
ap-8672	424	1	in	in	ADP
ap-8672	424	2	ieee	ieee	NOUN
ap-8672	424	3	/	/	SYM
ap-8672	424	4	sice	sice	X
ap-8672	424	5	international	international	ADJ
ap-8672	424	6	symposium	symposium	NOUN
ap-8672	424	7	on	on	ADP
ap-8672	424	8	system	system	NOUN
ap-8672	424	9	integration	integration	NOUN
ap-8672	424	10	(	(	PUNCT
ap-8672	424	11	sii	sii	PROPN
ap-8672	424	12	)	)	PUNCT
ap-8672	424	13	,	,	PUNCT
ap-8672	424	14	pp	pp	ADJ
ap-8672	424	15	.	.	PUNCT
ap-8672	425	1	307–312	307–312	NUM
ap-8672	425	2	.	.	NOUN
ap-8672	425	3	2015	2015	NUM
ap-8672	425	4	.	.	PUNCT
ap-8672	426	1	https://doi.org/10.1109/sii.2015.7404996	https://doi.org/10.1109/sii.2015.7404996	NOUN
ap-8672	427	1	[	[	X
ap-8672	427	2	16	16	NUM
ap-8672	427	3	]	]	X
ap-8672	427	4	w.	w.	PROPN
ap-8672	427	5	khalil	khalil	PROPN
ap-8672	427	6	,	,	PUNCT
ap-8672	427	7	e.	e.	PROPN
ap-8672	427	8	dombre	dombre	PROPN
ap-8672	427	9	.	.	PUNCT
ap-8672	428	1	transformation	transformation	NOUN
ap-8672	428	2	matrix	matrix	NOUN
ap-8672	428	3	between	between	ADP
ap-8672	428	4	vectors	vector	NOUN
ap-8672	428	5	,	,	PUNCT
ap-8672	428	6	frames	frame	NOUN
ap-8672	428	7	and	and	CCONJ
ap-8672	428	8	screws	screw	NOUN
ap-8672	428	9	.	.	PUNCT
ap-8672	429	1	in	in	ADP
ap-8672	429	2	modeling	modeling	NOUN
ap-8672	429	3	,	,	PUNCT
ap-8672	429	4	identification	identification	NOUN
ap-8672	429	5	and	and	CCONJ
ap-8672	429	6	control	control	NOUN
ap-8672	429	7	of	of	ADP
ap-8672	429	8	robots	robot	NOUN
ap-8672	429	9	,	,	PUNCT
ap-8672	429	10	pp	pp	ADV
ap-8672	429	11	.	.	PUNCT
ap-8672	430	1	13–34	13–34	NUM
ap-8672	430	2	.	.	PUNCT
ap-8672	431	1	butterworth	butterworth	PROPN
ap-8672	431	2	-	-	PUNCT
ap-8672	431	3	heinemann	heinemann	PROPN
ap-8672	431	4	,	,	PUNCT
ap-8672	431	5	london	london	PROPN
ap-8672	431	6	,	,	PUNCT
ap-8672	431	7	uk	uk	PROPN
ap-8672	431	8	,	,	PUNCT
ap-8672	431	9	2002	2002	NUM
ap-8672	431	10	.	.	PUNCT
ap-8672	432	1	https://doi.org/10.1016/b978-190399666-9/50002-6	https://doi.org/10.1016/b978-190399666-9/50002-6	NOUN
ap-8672	432	2	[	[	X
ap-8672	432	3	17	17	NUM
ap-8672	432	4	]	]	PUNCT
ap-8672	432	5	m.	m.	NOUN
ap-8672	432	6	raghavan	raghavan	PROPN
ap-8672	432	7	,	,	PUNCT
ap-8672	432	8	b.	b.	PROPN
ap-8672	432	9	roth	roth	PROPN
ap-8672	432	10	.	.	PUNCT
ap-8672	433	1	inverse	inverse	PROPN
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ap-8672	433	3	of	of	ADP
ap-8672	433	4	the	the	DET
ap-8672	433	5	general	general	ADJ
ap-8672	433	6	6r	6r	NUM
ap-8672	433	7	manipulator	manipulator	NOUN
ap-8672	433	8	and	and	CCONJ
ap-8672	433	9	related	related	ADJ
ap-8672	433	10	linkages	linkage	NOUN
ap-8672	433	11	.	.	PUNCT
ap-8672	434	1	journal	journal	NOUN
ap-8672	434	2	of	of	ADP
ap-8672	434	3	mechanical	mechanical	ADJ
ap-8672	434	4	design	design	NOUN
ap-8672	434	5	115(3):502–508	115(3):502–508	NUM
ap-8672	434	6	,	,	PUNCT
ap-8672	434	7	1993	1993	NUM
ap-8672	434	8	.	.	PUNCT
ap-8672	435	1	https://doi.org/10.1115/1.2919218	https://doi.org/10.1115/1.2919218	PROPN
ap-8672	436	1	[	[	X
ap-8672	436	2	18	18	NUM
ap-8672	436	3	]	]	X
ap-8672	436	4	y.	y.	PROPN
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ap-8672	436	6	,	,	PUNCT
ap-8672	436	7	p.	p.	PROPN
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ap-8672	436	9	,	,	PUNCT
ap-8672	436	10	h.	h.	PROPN
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ap-8672	436	13	et	et	PROPN
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ap-8672	437	1	a	a	DET
ap-8672	437	2	closed	close	VERB
ap-8672	437	3	-	-	PUNCT
ap-8672	437	4	form	form	NOUN
ap-8672	437	5	solution	solution	NOUN
ap-8672	437	6	for	for	ADP
ap-8672	437	7	the	the	DET
ap-8672	437	8	inverse	inverse	NOUN
ap-8672	437	9	kinematics	kinematic	NOUN
ap-8672	437	10	of	of	ADP
ap-8672	437	11	the	the	DET
ap-8672	437	12	2n	2n	NUM
ap-8672	437	13	-	-	PUNCT
ap-8672	437	14	dof	dof	NOUN
ap-8672	437	15	hyper	hyper	ADJ
ap-8672	437	16	-	-	ADJ
ap-8672	437	17	redundant	redundant	ADJ
ap-8672	437	18	manipulator	manipulator	NOUN
ap-8672	437	19	based	base	VERB
ap-8672	437	20	on	on	ADP
ap-8672	437	21	general	general	ADJ
ap-8672	437	22	spherical	spherical	ADJ
ap-8672	437	23	joint	joint	NOUN
ap-8672	437	24	.	.	PUNCT
ap-8672	438	1	applied	apply	VERB
ap-8672	438	2	sciences	science	NOUN
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ap-8672	438	4	,	,	PUNCT
ap-8672	438	5	2021	2021	NUM
ap-8672	438	6	.	.	PUNCT
ap-8672	439	1	https://doi.org/10.3390/app11031277	https://doi.org/10.3390/app11031277	NOUN
ap-8672	440	1	[	[	X
ap-8672	440	2	19	19	NUM
ap-8672	440	3	]	]	PUNCT
ap-8672	440	4	j.	j.	PROPN
ap-8672	440	5	q.	q.	PROPN
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ap-8672	440	7	,	,	PUNCT
ap-8672	440	8	e.	e.	PROPN
ap-8672	440	9	oyama	oyama	PROPN
ap-8672	440	10	,	,	PUNCT
ap-8672	440	11	e.	e.	PROPN
ap-8672	440	12	m.	m.	PROPN
ap-8672	440	13	rosales	rosales	PROPN
ap-8672	440	14	,	,	PUNCT
ap-8672	440	15	h.	h.	PROPN
ap-8672	440	16	hu	hu	PROPN
ap-8672	440	17	.	.	PUNCT
ap-8672	441	1	a	a	DET
ap-8672	441	2	complete	complete	ADJ
ap-8672	441	3	analytical	analytical	ADJ
ap-8672	441	4	solution	solution	NOUN
ap-8672	441	5	to	to	ADP
ap-8672	441	6	the	the	DET
ap-8672	441	7	inverse	inverse	ADJ
ap-8672	441	8	kinematics	kinematic	NOUN
ap-8672	441	9	of	of	ADP
ap-8672	441	10	the	the	DET
ap-8672	441	11	pioneer	pioneer	NOUN
ap-8672	441	12	2	2	NUM
ap-8672	441	13	robotic	robotic	ADJ
ap-8672	441	14	arm	arm	NOUN
ap-8672	441	15	.	.	PUNCT
ap-8672	442	1	journal	journal	PROPN
ap-8672	442	2	robotica	robotica	PROPN
ap-8672	442	3	23(1):123–129	23(1):123–129	PROPN
ap-8672	442	4	,	,	PUNCT
ap-8672	442	5	2005	2005	NUM
ap-8672	442	6	.	.	PUNCT
ap-8672	443	1	https://doi.org/10.1017/s0263574704000529	https://doi.org/10.1017/s0263574704000529	NUM
ap-8672	443	2	341	341	NUM
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ap-8672	443	4	https://doi.org/10.1016/j.ifacol.2019.10.019	https://doi.org/10.1016/j.ifacol.2019.10.019	PROPN
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ap-8672	444	1	https://doi.org/10.1016/j.rcim.2020.101961	https://doi.org/10.1016/j.rcim.2020.101961	PROPN
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ap-8672	444	3	https://doi.org/10.1016/j.mechmachtheory.2020.103988	https://doi.org/10.1016/j.mechmachtheory.2020.103988	PROPN
ap-8672	444	4	https://doi.org/10.1016/j.heliyon.2018.e01053	https://doi.org/10.1016/j.heliyon.2018.e01053	AUX
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ap-8672	444	9	https://doi.org/10.1109/sii.2015.7404996	https://doi.org/10.1109/sii.2015.7404996	NOUN
ap-8672	444	10	https://doi.org/10.1016/b978-190399666-9/50002-6	https://doi.org/10.1016/b978-190399666-9/50002-6	PROPN
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ap-8672	444	13	https://doi.org/10.1017/s0263574704000529	https://doi.org/10.1017/s0263574704000529	NUM
ap-8672	444	14	n.	n.	NOUN
ap-8672	444	15	hadidi	hadidi	PROPN
ap-8672	444	16	,	,	PUNCT
ap-8672	444	17	m.	m.	NOUN
ap-8672	444	18	bouaziz	bouaziz	PROPN
ap-8672	444	19	,	,	PUNCT
ap-8672	444	20	c.	c.	PROPN
ap-8672	444	21	mahfoudi	mahfoudi	PROPN
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ap-8672	444	23	m.	m.	NOUN
ap-8672	444	24	zaharuddin	zaharuddin	PROPN
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ap-8672	444	26	polytechnica	polytechnica	PROPN
ap-8672	444	27	[	[	X
ap-8672	444	28	20	20	NUM
ap-8672	444	29	]	]	PUNCT
ap-8672	444	30	b.	b.	PROPN
ap-8672	444	31	tondu	tondu	PROPN
ap-8672	444	32	.	.	PUNCT
ap-8672	445	1	a	a	DET
ap-8672	445	2	closed	close	VERB
ap-8672	445	3	-	-	PUNCT
ap-8672	445	4	form	form	NOUN
ap-8672	445	5	inverse	inverse	NOUN
ap-8672	445	6	kinematic	kinematic	NOUN
ap-8672	445	7	modelling	modelling	NOUN
ap-8672	445	8	of	of	ADP
ap-8672	445	9	a	a	DET
ap-8672	445	10	7r	7r	NUM
ap-8672	445	11	anthropomorphic	anthropomorphic	ADJ
ap-8672	445	12	upper	upper	ADJ
ap-8672	445	13	limb	limb	NOUN
ap-8672	445	14	based	base	VERB
ap-8672	445	15	on	on	ADP
ap-8672	445	16	a	a	DET
ap-8672	445	17	joint	joint	ADJ
ap-8672	445	18	parametrization	parametrization	NOUN
ap-8672	445	19	.	.	PUNCT
ap-8672	446	1	in	in	ADP
ap-8672	446	2	6th	6th	ADJ
ap-8672	446	3	ieee	ieee	NOUN
ap-8672	446	4	-	-	PUNCT
ap-8672	446	5	ras	ras	X
ap-8672	446	6	international	international	ADJ
ap-8672	446	7	conference	conference	NOUN
ap-8672	446	8	on	on	ADP
ap-8672	446	9	humanoid	humanoid	NOUN
ap-8672	446	10	robots	robot	NOUN
ap-8672	446	11	,	,	PUNCT
ap-8672	446	12	pp	pp	ADP
ap-8672	446	13	.	.	PUNCT
ap-8672	447	1	390–397	390–397	NUM
ap-8672	447	2	.	.	PUNCT
ap-8672	448	1	2006	2006	NUM
ap-8672	448	2	.	.	PUNCT
ap-8672	449	1	https://doi.org/10.1109/ichr.2006.321302	https://doi.org/10.1109/ichr.2006.321302	PROPN
ap-8672	450	1	[	[	X
ap-8672	450	2	21	21	NUM
ap-8672	450	3	]	]	PUNCT
ap-8672	450	4	s.	s.	PROPN
ap-8672	450	5	bertrand	bertrand	PROPN
ap-8672	450	6	,	,	PUNCT
ap-8672	450	7	o.	o.	PROPN
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ap-8672	450	10	f.	f.	PROPN
ap-8672	450	11	b.	b.	PROPN
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ap-8672	450	14	s.	s.	PROPN
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ap-8672	451	1	closed	close	VERB
ap-8672	451	2	-	-	PUNCT
ap-8672	451	3	form	form	NOUN
ap-8672	451	4	solutions	solution	NOUN
ap-8672	451	5	of	of	ADP
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ap-8672	451	9	for	for	ADP
ap-8672	451	10	the	the	DET
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ap-8672	451	12	of	of	ADP
ap-8672	451	13	a	a	DET
ap-8672	451	14	biped	biped	ADJ
ap-8672	451	15	robot	robot	NOUN
ap-8672	451	16	with	with	ADP
ap-8672	451	17	8	8	NUM
ap-8672	451	18	active	active	ADJ
ap-8672	451	19	degrees	degree	NOUN
ap-8672	451	20	of	of	ADP
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ap-8672	451	22	per	per	ADP
ap-8672	451	23	leg	leg	NOUN
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ap-8672	452	1	mechanism	mechanism	NOUN
ap-8672	452	2	and	and	CCONJ
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ap-8672	452	4	theory	theory	NOUN
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ap-8672	452	6	,	,	PUNCT
ap-8672	452	7	2012	2012	NUM
ap-8672	452	8	.	.	PUNCT
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ap-8672	454	2	22	22	NUM
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ap-8672	454	5	sardana	sardana	PROPN
ap-8672	454	6	,	,	PUNCT
ap-8672	454	7	m.	m.	PROPN
ap-8672	454	8	k.	k.	PROPN
ap-8672	454	9	sutar	sutar	PROPN
ap-8672	454	10	,	,	PUNCT
ap-8672	454	11	p.	p.	PROPN
ap-8672	454	12	m.	m.	PROPN
ap-8672	454	13	pathak	pathak	PROPN
ap-8672	454	14	.	.	PUNCT
ap-8672	455	1	a	a	DET
ap-8672	455	2	geometric	geometric	ADJ
ap-8672	455	3	approach	approach	NOUN
ap-8672	455	4	for	for	ADP
ap-8672	455	5	inverse	inverse	ADJ
ap-8672	455	6	kinematics	kinematic	NOUN
ap-8672	455	7	of	of	ADP
ap-8672	455	8	a	a	DET
ap-8672	455	9	4	4	NUM
ap-8672	455	10	-	-	PUNCT
ap-8672	455	11	link	link	NOUN
ap-8672	455	12	redundant	redundant	ADJ
ap-8672	455	13	in	in	ADP
ap-8672	455	14	-	-	PUNCT
ap-8672	455	15	vivo	vivo	NOUN
ap-8672	455	16	robot	robot	NOUN
ap-8672	455	17	for	for	ADP
ap-8672	455	18	biopsy	biopsy	NOUN
ap-8672	455	19	.	.	PUNCT
ap-8672	456	1	robotics	robotic	NOUN
ap-8672	456	2	and	and	CCONJ
ap-8672	456	3	autonomous	autonomous	ADJ
ap-8672	456	4	systems	system	NOUN
ap-8672	456	5	61(12):1306–1313	61(12):1306–1313	NUM
ap-8672	456	6	,	,	PUNCT
ap-8672	456	7	2013	2013	NUM
ap-8672	456	8	.	.	PUNCT
ap-8672	457	1	https://doi.org/10.1016/j.robot.2013.09.001	https://doi.org/10.1016/j.robot.2013.09.001	NOUN
ap-8672	457	2	[	[	X
ap-8672	457	3	23	23	NUM
ap-8672	457	4	]	]	PUNCT
ap-8672	457	5	i.	i.	NOUN
ap-8672	457	6	sancaktar	sancaktar	PROPN
ap-8672	457	7	,	,	PUNCT
ap-8672	457	8	b.	b.	PROPN
ap-8672	457	9	tuna	tuna	PROPN
ap-8672	457	10	,	,	PUNCT
ap-8672	457	11	m.	m.	NOUN
ap-8672	457	12	ulutas	uluta	NOUN
ap-8672	457	13	.	.	PUNCT
ap-8672	458	1	inverse	inverse	NOUN
ap-8672	458	2	kinematics	kinematic	NOUN
ap-8672	458	3	application	application	NOUN
ap-8672	458	4	on	on	ADP
ap-8672	458	5	medical	medical	ADJ
ap-8672	458	6	robot	robot	NOUN
ap-8672	458	7	using	use	VERB
ap-8672	458	8	adapted	adapt	VERB
ap-8672	458	9	pso	pso	NOUN
ap-8672	458	10	method	method	NOUN
ap-8672	458	11	.	.	PUNCT
ap-8672	459	1	engineering	engineering	NOUN
ap-8672	459	2	science	science	NOUN
ap-8672	459	3	and	and	CCONJ
ap-8672	459	4	technology	technology	NOUN
ap-8672	459	5	,	,	PUNCT
ap-8672	459	6	an	an	DET
ap-8672	459	7	international	international	ADJ
ap-8672	459	8	journal	journal	NOUN
ap-8672	459	9	21(5):1006–1010	21(5):1006–1010	NUM
ap-8672	459	10	,	,	PUNCT
ap-8672	459	11	2018	2018	NUM
ap-8672	459	12	.	.	PUNCT
ap-8672	460	1	https://doi.org/10.1016/j.jestch.2018.06.011	https://doi.org/10.1016/j.jestch.2018.06.011	PROPN
ap-8672	460	2	[	[	X
ap-8672	460	3	24	24	NUM
ap-8672	460	4	]	]	X
ap-8672	460	5	l.	l.	PROPN
ap-8672	460	6	sciavicco	sciavicco	PROPN
ap-8672	460	7	,	,	PUNCT
ap-8672	460	8	b.	b.	PROPN
ap-8672	460	9	siciliano	siciliano	PROPN
ap-8672	460	10	.	.	PUNCT
ap-8672	461	1	a	a	DET
ap-8672	461	2	dynamic	dynamic	ADJ
ap-8672	461	3	solution	solution	NOUN
ap-8672	461	4	to	to	ADP
ap-8672	461	5	the	the	DET
ap-8672	461	6	inverse	inverse	NOUN
ap-8672	461	7	kinematic	kinematic	NOUN
ap-8672	461	8	problem	problem	NOUN
ap-8672	461	9	for	for	ADP
ap-8672	461	10	redundant	redundant	ADJ
ap-8672	461	11	manipulators	manipulator	NOUN
ap-8672	461	12	.	.	PUNCT
ap-8672	462	1	in	in	ADP
ap-8672	462	2	ieee	ieee	PROPN
ap-8672	462	3	international	international	ADJ
ap-8672	462	4	conference	conference	NOUN
ap-8672	462	5	on	on	ADP
ap-8672	462	6	robotics	robotic	NOUN
ap-8672	462	7	and	and	CCONJ
ap-8672	462	8	automation	automation	NOUN
ap-8672	462	9	,	,	PUNCT
ap-8672	462	10	vol	vol	NOUN
ap-8672	462	11	.	.	PROPN
ap-8672	462	12	4	4	NUM
ap-8672	462	13	,	,	PUNCT
ap-8672	462	14	pp	pp	ADJ
ap-8672	462	15	.	.	PUNCT
ap-8672	462	16	1081–1087	1081–1087	NUM
ap-8672	462	17	.	.	PUNCT
ap-8672	462	18	1987	1987	NUM
ap-8672	462	19	.	.	PUNCT
ap-8672	463	1	https://doi.org/10.1109/robot.1987.1087921	https://doi.org/10.1109/robot.1987.1087921	NOUN
ap-8672	463	2	[	[	X
ap-8672	463	3	25	25	NUM
ap-8672	463	4	]	]	X
ap-8672	463	5	g.	g.	PROPN
ap-8672	463	6	tevatia	tevatia	PROPN
ap-8672	463	7	,	,	PUNCT
ap-8672	463	8	s.	s.	PROPN
ap-8672	463	9	schaal	schaal	PROPN
ap-8672	463	10	.	.	PUNCT
ap-8672	464	1	inverse	inverse	NOUN
ap-8672	464	2	kinematics	kinematic	NOUN
ap-8672	464	3	for	for	ADP
ap-8672	464	4	humanoid	humanoid	NOUN
ap-8672	464	5	robots	robot	NOUN
ap-8672	464	6	.	.	PUNCT
ap-8672	465	1	in	in	ADP
ap-8672	465	2	ieee	ieee	PROPN
ap-8672	465	3	international	international	ADJ
ap-8672	465	4	conference	conference	NOUN
ap-8672	465	5	on	on	ADP
ap-8672	465	6	robotics	robotic	NOUN
ap-8672	465	7	and	and	CCONJ
ap-8672	465	8	automation	automation	NOUN
ap-8672	465	9	.	.	PUNCT
ap-8672	466	1	symposia	symposia	NOUN
ap-8672	466	2	proceedings	proceeding	NOUN
ap-8672	466	3	(	(	PUNCT
ap-8672	466	4	cat	cat	NOUN
ap-8672	466	5	.	.	PUNCT
ap-8672	467	1	no.00ch37065	no.00ch37065	NOUN
ap-8672	467	2	)	)	PUNCT
ap-8672	467	3	,	,	PUNCT
ap-8672	467	4	vol	vol	NOUN
ap-8672	467	5	.	.	PROPN
ap-8672	467	6	1	1	NUM
ap-8672	467	7	,	,	PUNCT
ap-8672	467	8	pp	pp	ADJ
ap-8672	467	9	.	.	PUNCT
ap-8672	468	1	294–299	294–299	NUM
ap-8672	468	2	.	.	NOUN
ap-8672	468	3	2000	2000	NUM
ap-8672	468	4	.	.	PUNCT
ap-8672	469	1	https://doi.org/10.1109/robot.2000.844073	https://doi.org/10.1109/robot.2000.844073	NOUN
ap-8672	470	1	[	[	X
ap-8672	470	2	26	26	NUM
ap-8672	470	3	]	]	X
ap-8672	470	4	r.	r.	PROPN
ap-8672	470	5	pérez	pérez	PROPN
ap-8672	470	6	-	-	PUNCT
ap-8672	470	7	rodríguez	rodríguez	NOUN
ap-8672	470	8	,	,	PUNCT
ap-8672	470	9	a.	a.	PROPN
ap-8672	470	10	marcano	marcano	PROPN
ap-8672	470	11	-	-	PUNCT
ap-8672	470	12	cedeño	cedeño	PROPN
ap-8672	470	13	,	,	PUNCT
ap-8672	470	14	u.	u.	PROPN
ap-8672	470	15	costa	costa	PROPN
ap-8672	470	16	,	,	PUNCT
ap-8672	470	17	et	et	PROPN
ap-8672	470	18	al	al	PROPN
ap-8672	470	19	.	.	PROPN
ap-8672	470	20	inverse	inverse	PROPN
ap-8672	470	21	kinematics	kinematic	NOUN
ap-8672	470	22	of	of	ADP
ap-8672	470	23	a	a	DET
ap-8672	470	24	6	6	NUM
ap-8672	470	25	dof	dof	NOUN
ap-8672	470	26	human	human	ADJ
ap-8672	470	27	upper	upper	ADJ
ap-8672	470	28	limb	limb	NOUN
ap-8672	470	29	using	use	VERB
ap-8672	470	30	anfis	anfis	PROPN
ap-8672	470	31	and	and	CCONJ
ap-8672	470	32	ann	ann	PROPN
ap-8672	470	33	for	for	ADP
ap-8672	470	34	anticipatory	anticipatory	ADJ
ap-8672	470	35	actuation	actuation	NOUN
ap-8672	470	36	in	in	ADP
ap-8672	470	37	adl	adl	PROPN
ap-8672	470	38	-	-	PUNCT
ap-8672	470	39	based	base	VERB
ap-8672	470	40	physical	physical	ADJ
ap-8672	470	41	neurorehabilitation	neurorehabilitation	NOUN
ap-8672	470	42	.	.	PUNCT
ap-8672	471	1	expert	expert	NOUN
ap-8672	471	2	systems	system	NOUN
ap-8672	471	3	with	with	ADP
ap-8672	471	4	applications	application	NOUN
ap-8672	471	5	39(10):9612–9622	39(10):9612–9622	NUM
ap-8672	471	6	,	,	PUNCT
ap-8672	471	7	2012	2012	NUM
ap-8672	471	8	.	.	PUNCT
ap-8672	472	1	https://doi.org/10.1016/j.eswa.2012.02.143	https://doi.org/10.1016/j.eswa.2012.02.143	NOUN
ap-8672	472	2	[	[	X
ap-8672	472	3	27	27	NUM
ap-8672	472	4	]	]	X
ap-8672	472	5	f.	f.	PROPN
ap-8672	472	6	chapelle	chapelle	PROPN
ap-8672	472	7	,	,	PUNCT
ap-8672	472	8	p.	p.	PROPN
ap-8672	472	9	bidaud	bidaud	NOUN
ap-8672	472	10	.	.	PUNCT
ap-8672	473	1	a	a	DET
ap-8672	473	2	closed	closed	ADJ
ap-8672	473	3	form	form	NOUN
ap-8672	473	4	for	for	ADP
ap-8672	473	5	inverse	inverse	NOUN
ap-8672	473	6	kinematics	kinematic	NOUN
ap-8672	473	7	approximation	approximation	NOUN
ap-8672	473	8	of	of	ADP
ap-8672	473	9	general	general	ADJ
ap-8672	473	10	6r	6r	NUM
ap-8672	473	11	manipulators	manipulator	NOUN
ap-8672	473	12	using	use	VERB
ap-8672	473	13	genetic	genetic	ADJ
ap-8672	473	14	programming	programming	NOUN
ap-8672	473	15	.	.	PUNCT
ap-8672	474	1	in	in	ADP
ap-8672	474	2	ieee	ieee	PROPN
ap-8672	474	3	international	international	ADJ
ap-8672	474	4	conference	conference	NOUN
ap-8672	474	5	on	on	ADP
ap-8672	474	6	robotics	robotic	NOUN
ap-8672	474	7	and	and	CCONJ
ap-8672	474	8	automation	automation	NOUN
ap-8672	474	9	(	(	PUNCT
ap-8672	474	10	cat	cat	NOUN
ap-8672	474	11	.	.	PUNCT
ap-8672	475	1	no.01ch37164	no.01ch37164	PROPN
ap-8672	475	2	)	)	PUNCT
ap-8672	475	3	,	,	PUNCT
ap-8672	475	4	vol	vol	NOUN
ap-8672	475	5	.	.	PROPN
ap-8672	475	6	4	4	NUM
ap-8672	475	7	,	,	PUNCT
ap-8672	475	8	pp	pp	ADJ
ap-8672	475	9	.	.	PUNCT
ap-8672	476	1	3364–3369	3364–3369	NUM
ap-8672	476	2	.	.	PUNCT
ap-8672	477	1	2001	2001	NUM
ap-8672	477	2	.	.	PUNCT
ap-8672	478	1	https://doi.org/10.1109/robot.2001.933137	https://doi.org/10.1109/robot.2001.933137	X
ap-8672	479	1	[	[	X
ap-8672	479	2	28	28	NUM
ap-8672	479	3	]	]	X
ap-8672	479	4	m.	m.	NOUN
ap-8672	479	5	jin	jin	PROPN
ap-8672	479	6	,	,	PUNCT
ap-8672	479	7	l.	l.	PROPN
ap-8672	479	8	qiang	qiang	PROPN
ap-8672	479	9	,	,	PUNCT
ap-8672	479	10	b.	b.	PROPN
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ap-8672	479	12	,	,	PUNCT
ap-8672	479	13	h.	h.	PROPN
ap-8672	479	14	liu	liu	PROPN
ap-8672	479	15	.	.	PUNCT
ap-8672	480	1	an	an	DET
ap-8672	480	2	efficient	efficient	ADJ
ap-8672	480	3	and	and	CCONJ
ap-8672	480	4	accurate	accurate	ADJ
ap-8672	480	5	inverse	inverse	NOUN
ap-8672	480	6	kinematics	kinematic	NOUN
ap-8672	480	7	for	for	ADP
ap-8672	480	8	7	7	NUM
ap-8672	480	9	-	-	PUNCT
ap-8672	480	10	dof	dof	ADJ
ap-8672	480	11	redundant	redundant	ADJ
ap-8672	480	12	manipulators	manipulator	NOUN
ap-8672	480	13	based	base	VERB
ap-8672	480	14	on	on	ADP
ap-8672	480	15	a	a	DET
ap-8672	480	16	hybrid	hybrid	NOUN
ap-8672	480	17	of	of	ADP
ap-8672	480	18	analytical	analytical	ADJ
ap-8672	480	19	and	and	CCONJ
ap-8672	480	20	numerical	numerical	ADJ
ap-8672	480	21	method	method	NOUN
ap-8672	480	22	.	.	PUNCT
ap-8672	481	1	ieee	ieee	NOUN
ap-8672	481	2	access	access	NOUN
ap-8672	481	3	8:16316–16330	8:16316–16330	NUM
ap-8672	481	4	,	,	PUNCT
ap-8672	481	5	2020	2020	NUM
ap-8672	481	6	.	.	PUNCT
ap-8672	482	1	https://doi.org/10.1109/access.2020.2966768	https://doi.org/10.1109/access.2020.2966768	NOUN
ap-8672	482	2	[	[	X
ap-8672	482	3	29	29	NUM
ap-8672	482	4	]	]	PUNCT
ap-8672	482	5	w.	w.	PROPN
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ap-8672	482	7	,	,	PUNCT
ap-8672	482	8	h.	h.	PROPN
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ap-8672	482	12	,	,	PUNCT
ap-8672	482	13	y.	y.	PROPN
ap-8672	482	14	ting	ting	PROPN
ap-8672	482	15	-	-	PUNCT
ap-8672	482	16	li	li	PROPN
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ap-8672	482	18	inverse	inverse	PROPN
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ap-8672	482	20	analysis	analysis	NOUN
ap-8672	482	21	of	of	ADP
ap-8672	482	22	general	general	ADJ
ap-8672	482	23	6r	6r	NUM
ap-8672	482	24	serial	serial	ADJ
ap-8672	482	25	robot	robot	NOUN
ap-8672	482	26	mechanism	mechanism	NOUN
ap-8672	482	27	based	base	VERB
ap-8672	482	28	on	on	ADP
ap-8672	482	29	groebner	groebner	NOUN
ap-8672	482	30	base	base	NOUN
ap-8672	482	31	.	.	PUNCT
ap-8672	483	1	frontiers	frontier	NOUN
ap-8672	483	2	of	of	ADP
ap-8672	483	3	mechanical	mechanical	ADJ
ap-8672	483	4	engineering	engineering	NOUN
ap-8672	483	5	in	in	ADP
ap-8672	483	6	china	china	PROPN
ap-8672	483	7	1:115–124	1:115–124	NUM
ap-8672	483	8	,	,	PUNCT
ap-8672	483	9	2006	2006	NUM
ap-8672	483	10	.	.	PUNCT
ap-8672	484	1	https://doi.org/10.1007/s11465-005-0022-7	https://doi.org/10.1007/s11465-005-0022-7	X
ap-8672	485	1	[	[	X
ap-8672	485	2	30	30	NUM
ap-8672	485	3	]	]	X
ap-8672	485	4	y.	y.	PROPN
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ap-8672	486	1	an	an	DET
ap-8672	486	2	optimization	optimization	NOUN
ap-8672	486	3	method	method	NOUN
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ap-8672	486	5	inverse	inverse	ADJ
ap-8672	486	6	kinematics	kinematic	NOUN
ap-8672	486	7	of	of	ADP
ap-8672	486	8	a	a	DET
ap-8672	486	9	7	7	NUM
ap-8672	486	10	-	-	PUNCT
ap-8672	486	11	dof	dof	ADJ
ap-8672	486	12	redundant	redundant	ADJ
ap-8672	486	13	manipulator	manipulator	NOUN
ap-8672	486	14	.	.	PUNCT
ap-8672	487	1	in	in	ADP
ap-8672	487	2	34th	34th	ADJ
ap-8672	487	3	chinese	chinese	PROPN
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ap-8672	487	5	conference	conference	PROPN
ap-8672	487	6	(	(	PUNCT
ap-8672	487	7	ccc	ccc	PROPN
ap-8672	487	8	)	)	PUNCT
ap-8672	487	9	,	,	PUNCT
ap-8672	487	10	pp	pp	PROPN
ap-8672	487	11	.	.	PUNCT
ap-8672	487	12	4472–4479	4472–4479	NUM
ap-8672	487	13	.	.	PUNCT
ap-8672	487	14	2015	2015	NUM
ap-8672	487	15	.	.	PUNCT
ap-8672	488	1	https://doi.org/10.1109/chicc.2015.7260331	https://doi.org/10.1109/chicc.2015.7260331	PROPN
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ap-8672	489	3	]	]	PUNCT
ap-8672	489	4	b.	b.	PROPN
ap-8672	489	5	ma	ma	PROPN
ap-8672	489	6	,	,	PUNCT
ap-8672	489	7	z.	z.	PROPN
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ap-8672	490	4	analytical	analytical	ADJ
ap-8672	490	5	inverse	inverse	NOUN
ap-8672	490	6	kinematic	kinematic	NOUN
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ap-8672	490	8	for	for	ADP
ap-8672	490	9	7	7	NUM
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ap-8672	490	13	manipulator	manipulator	NOUN
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ap-8672	490	15	arm	arm	NOUN
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ap-8672	490	18	.	.	PUNCT
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ap-8672	491	3	mechanical	mechanical	ADJ
ap-8672	491	4	engineering	engineering	NOUN
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ap-8672	491	6	,	,	PUNCT
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ap-8672	491	8	.	.	PUNCT
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ap-8672	492	2	[	[	X
ap-8672	492	3	32	32	NUM
ap-8672	492	4	]	]	PUNCT
ap-8672	492	5	r.	r.	PROPN
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ap-8672	492	8	p.	p.	PROPN
ap-8672	492	9	vieira	vieira	PROPN
ap-8672	492	10	,	,	PUNCT
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ap-8672	492	13	,	,	PUNCT
ap-8672	492	14	et	et	PROPN
ap-8672	492	15	al	al	PROPN
ap-8672	492	16	.	.	PUNCT
ap-8672	492	17	kinematics	kinematic	NOUN
ap-8672	492	18	and	and	CCONJ
ap-8672	492	19	inverse	inverse	NOUN
ap-8672	492	20	kinematics	kinematic	NOUN
ap-8672	492	21	for	for	ADP
ap-8672	492	22	humanoid	humanoid	PROPN
ap-8672	492	23	robot	robot	PROPN
ap-8672	492	24	hubo2+.gt	hubo2+.gt	NOUN
ap-8672	492	25	-	-	PUNCT
ap-8672	492	26	golem-001	golem-001	NOUN
ap-8672	492	27	.	.	PUNCT
ap-8672	493	1	technical	technical	ADJ
ap-8672	493	2	report	report	PROPN
ap-8672	493	3	,	,	PUNCT
ap-8672	493	4	georgia	georgia	PROPN
ap-8672	493	5	institute	institute	PROPN
ap-8672	493	6	of	of	ADP
ap-8672	493	7	technology	technology	PROPN
ap-8672	493	8	,	,	PUNCT
ap-8672	493	9	2013	2013	NUM
ap-8672	493	10	.	.	PUNCT
ap-8672	494	1	[	[	X
ap-8672	494	2	33	33	NUM
ap-8672	494	3	]	]	PUNCT
ap-8672	494	4	t.	t.	PROPN
ap-8672	494	5	lyche	lyche	PROPN
ap-8672	494	6	.	.	PUNCT
ap-8672	495	1	a	a	DET
ap-8672	495	2	short	short	ADJ
ap-8672	495	3	review	review	NOUN
ap-8672	495	4	of	of	ADP
ap-8672	495	5	linear	linear	PROPN
ap-8672	495	6	algebra	algebra	PROPN
ap-8672	495	7	.	.	PUNCT
ap-8672	496	1	in	in	ADP
ap-8672	496	2	numerical	numerical	PROPN
ap-8672	496	3	linear	linear	PROPN
ap-8672	496	4	algebra	algebra	PROPN
ap-8672	496	5	and	and	CCONJ
ap-8672	496	6	matrix	matrix	NOUN
ap-8672	496	7	factorizations	factorization	NOUN
ap-8672	496	8	,	,	PUNCT
ap-8672	496	9	vol	vol	NOUN
ap-8672	496	10	.	.	PROPN
ap-8672	497	1	22	22	NUM
ap-8672	497	2	,	,	PUNCT
ap-8672	497	3	pp	pp	ADJ
ap-8672	497	4	.	.	PUNCT
ap-8672	498	1	1–24	1–24	PROPN
ap-8672	498	2	.	.	PUNCT
ap-8672	499	1	springer	springer	NOUN
ap-8672	499	2	,	,	PUNCT
ap-8672	499	3	chamonix	chamonix	NOUN
ap-8672	499	4	,	,	PUNCT
ap-8672	499	5	ch	ch	NOUN
ap-8672	499	6	,	,	PUNCT
ap-8672	499	7	2020	2020	NUM
ap-8672	499	8	.	.	PUNCT
ap-8672	500	1	https://doi.org/10.1007/978-3-030-36468-7_1	https://doi.org/10.1007/978-3-030-36468-7_1	PROPN
ap-8672	500	2	342	342	NUM
ap-8672	500	3	https://doi.org/10.1109/ichr.2006.321302	https://doi.org/10.1109/ichr.2006.321302	PROPN
ap-8672	500	4	https://doi.org/10.1016/j.mechmachtheory.2011.10.014	https://doi.org/10.1016/j.mechmachtheory.2011.10.014	PROPN
ap-8672	500	5	https://doi.org/10.1016/j.robot.2013.09.001	https://doi.org/10.1016/j.robot.2013.09.001	VERB
ap-8672	500	6	https://doi.org/10.1016/j.jestch.2018.06.011	https://doi.org/10.1016/j.jestch.2018.06.011	PROPN
ap-8672	500	7	https://doi.org/10.1109/robot.1987.1087921	https://doi.org/10.1109/robot.1987.1087921	PROPN
ap-8672	500	8	https://doi.org/10.1109/robot.2000.844073	https://doi.org/10.1109/robot.2000.844073	PROPN
ap-8672	500	9	https://doi.org/10.1016/j.eswa.2012.02.143	https://doi.org/10.1016/j.eswa.2012.02.143	PROPN
ap-8672	500	10	https://doi.org/10.1109/robot.2001.933137	https://doi.org/10.1109/robot.2001.933137	PROPN
ap-8672	501	1	https://doi.org/10.1109/access.2020.2966768	https://doi.org/10.1109/access.2020.2966768	PROPN
ap-8672	501	2	https://doi.org/10.1007/s11465-005-0022-7	https://doi.org/10.1007/s11465-005-0022-7	NUM
ap-8672	501	3	https://doi.org/10.1109/chicc.2015.7260331	https://doi.org/10.1109/chicc.2015.7260331	PROPN
ap-8672	501	4	https://doi.org/10.1007/s11465-021-0630-x	https://doi.org/10.1007/s11465-021-0630-x	PROPN
ap-8672	501	5	https://doi.org/10.1007/978-3-030-36468-7_1	https://doi.org/10.1007/978-3-030-36468-7_1	ADJ
ap-8672	501	6	vol	vol	NOUN
ap-8672	501	7	.	.	PROPN
ap-8672	501	8	63	63	NUM
ap-8672	501	9	no	no	NOUN
ap-8672	501	10	.	.	PUNCT
ap-8672	502	1	5/2023	5/2023	NUM
ap-8672	502	2	geometric	geometric	ADJ
ap-8672	502	3	approach	approach	NOUN
ap-8672	502	4	to	to	ADP
ap-8672	502	5	solving	solve	VERB
ap-8672	502	6	inverse	inverse	ADJ
ap-8672	502	7	kinematics	kinematic	NOUN
ap-8672	502	8	of	of	ADP
ap-8672	502	9	six	six	NUM
ap-8672	502	10	dof	dof	NOUN
ap-8672	502	11	robot	robot	NOUN
ap-8672	502	12	a.	a.	NOUN
ap-8672	502	13	appendicies	appendicies	PROPN
ap-8672	502	14	a.1	a.1	PROPN
ap-8672	502	15	.	.	PUNCT
ap-8672	503	1	trigonometric	trigonometric	ADJ
ap-8672	503	2	function	function	PROPN
ap-8672	503	3	atan2(y	atan2(y	PROPN
ap-8672	503	4	,	,	PUNCT
ap-8672	503	5	x	x	X
ap-8672	503	6	)	)	PUNCT
ap-8672	503	7	atan2(y	atan2(y	PROPN
ap-8672	503	8	,	,	PUNCT
ap-8672	503	9	x	x	NOUN
ap-8672	503	10	)	)	PUNCT
ap-8672	503	11	,	,	PUNCT
ap-8672	503	12	it	it	PRON
ap-8672	503	13	is	be	AUX
ap-8672	503	14	a	a	DET
ap-8672	503	15	helpful	helpful	ADJ
ap-8672	503	16	trigonometric	trigonometric	ADJ
ap-8672	503	17	function	function	NOUN
ap-8672	503	18	utilized	utilize	VERB
ap-8672	503	19	especially	especially	ADV
ap-8672	503	20	by	by	ADP
ap-8672	503	21	the	the	DET
ap-8672	503	22	most	most	ADJ
ap-8672	503	23	computer	computer	NOUN
ap-8672	503	24	languages	language	NOUN
ap-8672	503	25	.	.	PUNCT
ap-8672	504	1	because	because	SCONJ
ap-8672	504	2	,	,	PUNCT
ap-8672	504	3	it	it	PRON
ap-8672	504	4	is	be	AUX
ap-8672	504	5	summarizing	summarize	VERB
ap-8672	504	6	the	the	DET
ap-8672	504	7	four	four	NUM
ap-8672	504	8	quadrants	quadrant	NOUN
ap-8672	504	9	of	of	ADP
ap-8672	504	10	trigonometric	trigonometric	ADJ
ap-8672	504	11	circle	circle	NOUN
ap-8672	504	12	and	and	CCONJ
ap-8672	504	13	consequently	consequently	ADV
ap-8672	504	14	,	,	PUNCT
ap-8672	504	15	gives	give	VERB
ap-8672	504	16	the	the	DET
ap-8672	504	17	corresponding	correspond	VERB
ap-8672	504	18	angles	angle	NOUN
ap-8672	504	19	of	of	ADP
ap-8672	504	20	any	any	DET
ap-8672	504	21	quadrant	quadrant	NOUN
ap-8672	504	22	.	.	PUNCT
ap-8672	505	1	basically	basically	ADV
ap-8672	505	2	,	,	PUNCT
ap-8672	505	3	it	it	PRON
ap-8672	505	4	is	be	AUX
ap-8672	505	5	works	work	NOUN
ap-8672	505	6	with	with	ADP
ap-8672	505	7	polar	polar	ADJ
ap-8672	505	8	coordinates	coordinate	NOUN
ap-8672	505	9	by	by	ADP
ap-8672	505	10	converting	convert	VERB
ap-8672	505	11	the	the	DET
ap-8672	505	12	cartesian	cartesian	ADJ
ap-8672	505	13	coordinates	coordinate	NOUN
ap-8672	505	14	(	(	PUNCT
ap-8672	505	15	x	x	X
ap-8672	505	16	,	,	PUNCT
ap-8672	505	17	y	y	NOUN
ap-8672	505	18	)	)	PUNCT
ap-8672	505	19	to	to	ADP
ap-8672	505	20	polar	polar	ADJ
ap-8672	505	21	coordinates	coordinate	NOUN
ap-8672	505	22	(	(	PUNCT
ap-8672	505	23	r	r	NOUN
ap-8672	505	24	,	,	PUNCT
ap-8672	505	25	θ	θ	NOUN
ap-8672	505	26	)	)	PUNCT
ap-8672	505	27	which	which	PRON
ap-8672	505	28	mean	mean	VERB
ap-8672	505	29	that	that	SCONJ
ap-8672	505	30	r	r	NOUN
ap-8672	505	31	=	=	PUNCT
ap-8672	505	32	√	√	NUM
ap-8672	505	33	x2	x2	NOUN
ap-8672	506	1	+	+	CCONJ
ap-8672	506	2	y2	y2	PROPN
ap-8672	506	3	and	and	CCONJ
ap-8672	506	4	θ	θ	PROPN
ap-8672	507	1	=	=	SYM
ap-8672	507	2	atan2(y	atan2(y	PROPN
ap-8672	507	3	,	,	PUNCT
ap-8672	507	4	x	x	NOUN
ap-8672	507	5	)	)	PUNCT
ap-8672	507	6	,	,	PUNCT
ap-8672	507	7	x	x	X
ap-8672	507	8	=	=	PUNCT
ap-8672	507	9	r.	r.	PROPN
ap-8672	507	10	cos	cos	PROPN
ap-8672	507	11	θ	θ	PROPN
ap-8672	507	12	and	and	CCONJ
ap-8672	507	13	y	y	PROPN
ap-8672	507	14	=	=	SYM
ap-8672	507	15	r.	r.	PROPN
ap-8672	507	16	sin	sin	PROPN
ap-8672	507	17	θ	θ	PROPN
ap-8672	507	18	.	.	PUNCT
ap-8672	508	1	θ	θ	PROPN
ap-8672	508	2	=	=	SYM
ap-8672	508	3	atan2(y	atan2(y	PROPN
ap-8672	508	4	,	,	PUNCT
ap-8672	508	5	x	x	NOUN
ap-8672	508	6	)	)	PUNCT
ap-8672	508	7	=	=	SYM
ap-8672	508	8			NUM
ap-8672	508	9	atan(y	atan(y	NOUN
ap-8672	508	10	,	,	PUNCT
ap-8672	508	11	x	x	NOUN
ap-8672	508	12	)	)	PUNCT
ap-8672	508	13	if	if	SCONJ
ap-8672	508	14	x	x	PROPN
ap-8672	508	15	>	>	X
ap-8672	508	16	0	0	PUNCT
ap-8672	509	1	atan(y	atan(y	NUM
ap-8672	509	2	/	/	SYM
ap-8672	509	3	x	x	NOUN
ap-8672	509	4	)	)	PUNCT
ap-8672	510	1	+	+	CCONJ
ap-8672	510	2	π	π	X
ap-8672	510	3	if	if	SCONJ
ap-8672	510	4	x	x	PROPN
ap-8672	510	5	<	<	X
ap-8672	510	6	0	0	NUM
ap-8672	510	7	and	and	CCONJ
ap-8672	510	8	y	y	PROPN
ap-8672	510	9	≥	≥	NOUN
ap-8672	510	10	0	0	NUM
ap-8672	511	1	atan(y	atan(y	NUM
ap-8672	511	2	/	/	SYM
ap-8672	511	3	x	x	NOUN
ap-8672	511	4	)	)	PUNCT
ap-8672	511	5	−	−	PROPN
ap-8672	511	6	π	π	NOUN
ap-8672	511	7	if	if	SCONJ
ap-8672	511	8	x	x	PROPN
ap-8672	511	9	<	<	X
ap-8672	511	10	0	0	PUNCT
ap-8672	511	11	and	and	CCONJ
ap-8672	511	12	y	y	PROPN
ap-8672	511	13	<	<	X
ap-8672	511	14	0	0	PROPN
ap-8672	511	15	π/2	π/2	NUM
ap-8672	511	16	if	if	SCONJ
ap-8672	511	17	x	x	PROPN
ap-8672	511	18	=	=	SYM
ap-8672	511	19	0	0	NUM
ap-8672	511	20	and	and	CCONJ
ap-8672	511	21	y	y	PROPN
ap-8672	511	22	>	>	X
ap-8672	511	23	0	0	PUNCT
ap-8672	512	1	−π/2	−π/2	PROPN
ap-8672	512	2	if	if	SCONJ
ap-8672	512	3	x	x	ADP
ap-8672	512	4	=	=	SYM
ap-8672	512	5	0	0	NUM
ap-8672	512	6	and	and	CCONJ
ap-8672	512	7	y	y	ADJ
ap-8672	512	8	<	<	X
ap-8672	512	9	0	0	X
ap-8672	512	10	undefined	undefined	ADJ
ap-8672	512	11	if	if	SCONJ
ap-8672	512	12	x	x	PROPN
ap-8672	512	13	=	=	SYM
ap-8672	512	14	0	0	NUM
ap-8672	512	15	and	and	CCONJ
ap-8672	512	16	y	y	PROPN
ap-8672	512	17	=	=	SYM
ap-8672	512	18	0	0	NUM
ap-8672	513	1	343	343	NUM
ap-8672	513	2	n.	n.	NOUN
ap-8672	513	3	hadidi	hadidi	PROPN
ap-8672	513	4	,	,	PUNCT
ap-8672	513	5	m.	m.	NOUN
ap-8672	513	6	bouaziz	bouaziz	PROPN
ap-8672	513	7	,	,	PUNCT
ap-8672	513	8	c.	c.	PROPN
ap-8672	513	9	mahfoudi	mahfoudi	PROPN
ap-8672	513	10	,	,	PUNCT
ap-8672	513	11	m.	m.	NOUN
ap-8672	513	12	zaharuddin	zaharuddin	PROPN
ap-8672	513	13	acta	acta	PROPN
ap-8672	513	14	polytechnica	polytechnica	PROPN
ap-8672	513	15	a.2	a.2	PROPN
ap-8672	513	16	.	.	PUNCT
ap-8672	514	1	path	path	NOUN
ap-8672	514	2	of	of	ADP
ap-8672	514	3	the	the	DET
ap-8672	514	4	robot	robot	NOUN
ap-8672	514	5	’s	’s	PART
ap-8672	514	6	end	end	NOUN
ap-8672	514	7	-	-	PUNCT
ap-8672	514	8	effector	effector	NOUN
ap-8672	514	9	table	table	NOUN
ap-8672	514	10	below	below	ADV
ap-8672	514	11	contains	contain	VERB
ap-8672	514	12	the	the	DET
ap-8672	514	13	ten	ten	NUM
ap-8672	514	14	parts	part	NOUN
ap-8672	514	15	of	of	ADP
ap-8672	514	16	path	path	NOUN
ap-8672	514	17	that	that	PRON
ap-8672	514	18	tracked	track	VERB
ap-8672	514	19	by	by	ADP
ap-8672	514	20	the	the	DET
ap-8672	514	21	robot	robot	NOUN
ap-8672	514	22	’s	’s	PART
ap-8672	514	23	end	end	NOUN
ap-8672	514	24	-	-	PUNCT
ap-8672	514	25	effector	effector	NOUN
ap-8672	514	26	.	.	PUNCT
ap-8672	515	1	reverse	reverse	PROPN
ap-8672	515	2	path	path	PROPN
ap-8672	515	3	coordinates	coordinate	NOUN
ap-8672	515	4	path	path	PROPN
ap-8672	515	5	coordinates	coordinate	NOUN
ap-8672	515	6	remakes	remake	VERB
ap-8672	515	7	0→1	0→1	PROPN
ap-8672	515	8	pdx	pdx	PROPN
ap-8672	515	9	=	=	PUNCT
ap-8672	515	10	0.0	0.0	NUM
ap-8672	515	11	3→4	3→4	NOUN
ap-8672	515	12	pdx	pdx	PROPN
ap-8672	515	13	=	=	SYM
ap-8672	515	14	0.0	0.0	NUM
ap-8672	515	15	pdz	pdz	NOUN
ap-8672	515	16	increments	increment	NOUN
ap-8672	515	17	pdy	pdy	NOUN
ap-8672	515	18	=	=	PUNCT
ap-8672	516	1	−	−	PROPN
ap-8672	517	1	√	√	NOUN
ap-8672	517	2	0.62	0.62	NUM
ap-8672	517	3	−	−	PROPN
ap-8672	517	4	p	p	NOUN
ap-8672	517	5	2	2	NUM
ap-8672	517	6	dz	dz	PROPN
ap-8672	517	7	10→11	10→11	NUM
ap-8672	517	8	pdy	pdy	NOUN
ap-8672	517	9	=	=	PUNCT
ap-8672	518	1	−	−	PROPN
ap-8672	519	1	√	√	NOUN
ap-8672	519	2	0.62	0.62	NUM
ap-8672	519	3	−	−	PROPN
ap-8672	519	4	p	p	NOUN
ap-8672	519	5	2	2	NUM
ap-8672	519	6	dz	dz	NOUN
ap-8672	519	7	(	(	PUNCT
ap-8672	519	8	decrements	decrement	NOUN
ap-8672	519	9	)	)	PUNCT
ap-8672	519	10	by	by	ADP
ap-8672	519	11	a	a	DET
ap-8672	519	12	constant	constant	ADJ
ap-8672	519	13	pdz	pdz	NOUN
ap-8672	519	14	=	=	NOUN
ap-8672	519	15	0.0	0.0	NUM
ap-8672	519	16	:	:	PUNCT
ap-8672	519	17	0.02	0.02	NUM
ap-8672	519	18	:	:	PUNCT
ap-8672	519	19	0.12	0.12	NUM
ap-8672	519	20	(	(	PUNCT
ap-8672	519	21	1→0	1→0	NOUN
ap-8672	519	22	)	)	PUNCT
ap-8672	519	23	pdz	pdz	NOUN
ap-8672	519	24	=	=	NOUN
ap-8672	519	25	0.12	0.12	NUM
ap-8672	519	26	:	:	PUNCT
ap-8672	520	1	−0.02	−0.02	INTJ
ap-8672	520	2	:	:	PUNCT
ap-8672	520	3	0.0	0.0	NUM
ap-8672	520	4	step	step	NOUN
ap-8672	520	5	of	of	ADP
ap-8672	520	6	0.02	0.02	NUM
ap-8672	520	7	m	m	NOUN
ap-8672	520	8	1→2	1→2	NOUN
ap-8672	520	9	pdx	pdx	NOUN
ap-8672	520	10	=	=	NOUN
ap-8672	520	11	0.0	0.0	NUM
ap-8672	520	12	:	:	PUNCT
ap-8672	520	13	0.02	0.02	NUM
ap-8672	520	14	:	:	PUNCT
ap-8672	521	1	0.4	0.4	NUM
ap-8672	521	2	2→3	2→3	ADJ
ap-8672	521	3	pdx	pdx	PROPN
ap-8672	521	4	=	=	PROPN
ap-8672	521	5	0.4	0.4	NUM
ap-8672	521	6	:	:	PUNCT
ap-8672	522	1	−0.02	−0.02	INTJ
ap-8672	522	2	:	:	PUNCT
ap-8672	522	3	0.0	0.0	NUM
ap-8672	522	4	the	the	DET
ap-8672	522	5	value	value	NOUN
ap-8672	522	6	0.59	0.59	NUM
ap-8672	522	7	m	m	NOUN
ap-8672	522	8	in	in	ADP
ap-8672	522	9	pdy	pdy	INTJ
ap-8672	522	10	pdy	pdy	NOUN
ap-8672	522	11	=	=	PUNCT
ap-8672	522	12	−	−	PROPN
ap-8672	523	1	√	√	NUM
ap-8672	523	2	0.592	0.592	NUM
ap-8672	523	3	−	−	NOUN
ap-8672	523	4	p	p	NOUN
ap-8672	523	5	2	2	NUM
ap-8672	523	6	dx	dx	NOUN
ap-8672	523	7	2→1	2→1	NOUN
ap-8672	524	1	pdy	pdy	NOUN
ap-8672	524	2	=	=	PUNCT
ap-8672	525	1	−	−	PROPN
ap-8672	525	2	√	√	NOUN
ap-8672	525	3	0.592	0.592	NUM
ap-8672	526	1	−	−	NOUN
ap-8672	527	1	p	p	NOUN
ap-8672	527	2	2	2	NUM
ap-8672	527	3	dx	dx	NOUN
ap-8672	527	4	represents	represent	VERB
ap-8672	527	5	the	the	DET
ap-8672	527	6	last	last	ADJ
ap-8672	527	7	value	value	NOUN
ap-8672	527	8	of	of	ADP
ap-8672	527	9	pdz	pdz	NOUN
ap-8672	527	10	=	=	NOUN
ap-8672	527	11	0.12	0.12	NUM
ap-8672	527	12	pdz	pdz	NOUN
ap-8672	527	13	=	=	NOUN
ap-8672	527	14	0.12	0.12	NUM
ap-8672	527	15	path	path	NOUN
ap-8672	527	16	0→1	0→1	PROPN
ap-8672	527	17	4→5	4→5	PROPN
ap-8672	528	1	pdx	pdx	PROPN
ap-8672	528	2	=	=	SYM
ap-8672	528	3	0.6	0.6	NUM
ap-8672	528	4	sin	sin	VERB
ap-8672	528	5	α	α	NOUN
ap-8672	528	6	+	+	CCONJ
ap-8672	528	7	0.6	0.6	NUM
ap-8672	528	8	cos	cos	ADP
ap-8672	528	9	π	π	PROPN
ap-8672	528	10	4	4	NUM
ap-8672	528	11	7→8	7→8	NOUN
ap-8672	528	12	pdx	pdx	PROPN
ap-8672	528	13	=	=	SYM
ap-8672	528	14	0.6	0.6	NUM
ap-8672	528	15	sin	sin	VERB
ap-8672	528	16	α	α	NOUN
ap-8672	528	17	+	+	CCONJ
ap-8672	528	18	0.6	0.6	NUM
ap-8672	528	19	cos	cos	ADP
ap-8672	528	20	π	π	PROPN
ap-8672	528	21	4	4	NUM
ap-8672	528	22	π	π	PROPN
ap-8672	528	23	≤	≤	NUM
ap-8672	528	24	α	α	PRON
ap-8672	528	25	<	<	X
ap-8672	528	26	3π/4	3π/4	NUM
ap-8672	528	27	pdy	pdy	NOUN
ap-8672	528	28	=	=	NOUN
ap-8672	528	29	−0.6	−0.6	PROPN
ap-8672	528	30	cos	cos	ADP
ap-8672	529	1	α	α	PRON
ap-8672	530	1	5→4	5→4	NOUN
ap-8672	531	1	pdy	pdy	VERB
ap-8672	532	1	=	=	NOUN
ap-8672	532	2	−0.6	−0.6	PROPN
ap-8672	532	3	cos	cos	ADP
ap-8672	532	4	α	α	PROPN
ap-8672	532	5	with	with	ADP
ap-8672	532	6	a	a	DET
ap-8672	532	7	step	step	NOUN
ap-8672	532	8	of	of	ADP
ap-8672	532	9	:	:	PUNCT
ap-8672	532	10	pdz	pdz	NOUN
ap-8672	532	11	=	=	SYM
ap-8672	532	12	0.6	0.6	NUM
ap-8672	532	13	sin	sin	VERB
ap-8672	532	14	α	α	NOUN
ap-8672	532	15	+	+	CCONJ
ap-8672	532	16	0.6	0.6	NUM
ap-8672	532	17	sin	sin	NOUN
ap-8672	532	18	π	π	PROPN
ap-8672	532	19	4	4	NUM
ap-8672	532	20	pdz	pdz	NOUN
ap-8672	532	21	=	=	SYM
ap-8672	532	22	0.6	0.6	NUM
ap-8672	532	23	sin	sin	VERB
ap-8672	532	24	α	α	NOUN
ap-8672	532	25	+	+	CCONJ
ap-8672	532	26	0.6	0.6	NUM
ap-8672	532	27	sin	sin	NOUN
ap-8672	532	28	π	π	PROPN
ap-8672	532	29	4	4	NUM
ap-8672	532	30	∆α	∆α	NOUN
ap-8672	532	31	=	=	PUNCT
ap-8672	533	1	π	π	PROPN
ap-8672	533	2	60	60	NUM
ap-8672	533	3	rad	rad	NOUN
ap-8672	533	4	5→6	5→6	NOUN
ap-8672	533	5	pdx	pdx	PROPN
ap-8672	533	6	=	=	PUNCT
ap-8672	533	7	pdx	pdx	PROPN
ap-8672	533	8	+	+	CCONJ
ap-8672	533	9	∆pdx	∆pdx	ADJ
ap-8672	533	10	8→9	8→9	NUM
ap-8672	533	11	pdx	pdx	PROPN
ap-8672	533	12	=	=	PROPN
ap-8672	533	13	pdx	pdx	PROPN
ap-8672	534	1	−	−	PROPN
ap-8672	534	2	∆pdx	∆pdx	PROPN
ap-8672	534	3	pdx	pdx	PROPN
ap-8672	534	4	starts	start	VERB
ap-8672	534	5	from	from	ADP
ap-8672	534	6	last	last	ADJ
ap-8672	534	7	value	value	NOUN
ap-8672	534	8	of	of	ADP
ap-8672	534	9	path	path	NOUN
ap-8672	534	10	4→5	4→5	ADV
ap-8672	534	11	until	until	ADP
ap-8672	534	12	pdx	pdx	PROPN
ap-8672	534	13	=	=	PROPN
ap-8672	534	14	0.3	0.3	NUM
ap-8672	534	15	m.	m.	NOUN
ap-8672	534	16	pdy	pdy	INTJ
ap-8672	534	17	=	=	NOUN
ap-8672	534	18	−0.6	−0.6	PROPN
ap-8672	534	19	cos	cos	PROPN
ap-8672	534	20	α	α	PROPN
ap-8672	534	21	(	(	PUNCT
ap-8672	534	22	6→5	6→5	NOUN
ap-8672	534	23	)	)	PUNCT
ap-8672	535	1	pdy	pdy	NOUN
ap-8672	536	1	=	=	NOUN
ap-8672	536	2	−0.6	−0.6	PROPN
ap-8672	536	3	cos	cos	SCONJ
ap-8672	536	4	α	α	DET
ap-8672	536	5	same	same	ADJ
ap-8672	536	6	thing	thing	NOUN
ap-8672	536	7	to	to	PART
ap-8672	536	8	pdz	pdz	VERB
ap-8672	536	9	.	.	PUNCT
ap-8672	537	1	for	for	ADP
ap-8672	537	2	pdy	pdy	PRON
ap-8672	537	3	:	:	PUNCT
ap-8672	537	4	3π	3π	NOUN
ap-8672	537	5	4	4	NUM
ap-8672	537	6	<	<	X
ap-8672	537	7	α	α	X
ap-8672	537	8	<	<	X
ap-8672	537	9	π/2	π/2	NUM
ap-8672	537	10	pdz	pdz	NOUN
ap-8672	537	11	=	=	SYM
ap-8672	537	12	pdz	pdz	NOUN
ap-8672	537	13	+	+	CCONJ
ap-8672	537	14	∆pdz	∆pdz	NOUN
ap-8672	537	15	pdz	pdz	NOUN
ap-8672	537	16	=	=	SYM
ap-8672	537	17	pdz	pdz	NOUN
ap-8672	537	18	−	−	PROPN
ap-8672	537	19	∆pdz	∆pdz	NOUN
ap-8672	537	20	and	and	CCONJ
ap-8672	537	21	step	step	NOUN
ap-8672	537	22	:	:	PUNCT
ap-8672	537	23	∆α	∆α	NOUN
ap-8672	537	24	=	=	PUNCT
ap-8672	538	1	π	π	PROPN
ap-8672	538	2	60	60	NUM
ap-8672	538	3	rad	rad	PROPN
ap-8672	538	4	9→10	9→10	PROPN
ap-8672	538	5			PROPN
ap-8672	538	6	pcx	pcx	NOUN
ap-8672	538	7	=	=	NOUN
ap-8672	538	8	qox	qox	ADV
ap-8672	538	9	+	+	CCONJ
ap-8672	538	10	r	r	NOUN
ap-8672	538	11	cos(ϕ)sqx	cos(ϕ)sqx	VERB
ap-8672	538	12	+	+	NOUN
ap-8672	538	13	r	r	NOUN
ap-8672	538	14	sin(ϕ)nqx	sin(ϕ)nqx	PROPN
ap-8672	538	15	pcy	pcy	NOUN
ap-8672	538	16	=	=	SYM
ap-8672	538	17	qoy	qoy	NOUN
ap-8672	539	1	+	+	CCONJ
ap-8672	539	2	r	r	NOUN
ap-8672	539	3	cos(ϕ)sqy	cos(ϕ)sqy	PROPN
ap-8672	539	4	+	+	CCONJ
ap-8672	539	5	r	r	NOUN
ap-8672	539	6	sin(ϕ)nqy	sin(ϕ)nqy	NOUN
ap-8672	539	7	pcz	pcz	NOUN
ap-8672	539	8	=	=	PUNCT
ap-8672	539	9	qoz	qoz	NOUN
ap-8672	539	10	+	+	CCONJ
ap-8672	539	11	r	r	NOUN
ap-8672	539	12	cos(ϕ)sqz	cos(ϕ)sqz	NOUN
ap-8672	539	13	+	+	CCONJ
ap-8672	539	14	r	r	NOUN
ap-8672	539	15	sin(ϕ)nqz	sin(ϕ)nqz	NOUN
ap-8672	539	16	circularepath	circularepath	NOUN
ap-8672	539	17	which	which	PRON
ap-8672	539	18	is	be	AUX
ap-8672	539	19	located	locate	VERB
ap-8672	539	20	on	on	ADP
ap-8672	539	21	a	a	DET
ap-8672	539	22	plane	plane	NOUN
ap-8672	539	23	of	of	ADP
ap-8672	539	24	equation	equation	NOUN
ap-8672	539	25	:	:	PUNCT
ap-8672	540	1	0.19x	0.19x	NOUN
ap-8672	540	2	−	−	NOUN
ap-8672	540	3	0.94y	0.94y	PROPN
ap-8672	541	1	+	+	CCONJ
ap-8672	541	2	0.19z−	0.19z−	NUM
ap-8672	541	3	r	r	NOUN
ap-8672	541	4	=	=	PUNCT
ap-8672	541	5	0.12	0.12	NUM
ap-8672	541	6	m	m	NOUN
ap-8672	541	7	:	:	PUNCT
ap-8672	542	1	raidus	raidus	NOUN
ap-8672	542	2	of	of	ADP
ap-8672	542	3	circle	circle	NOUN
ap-8672	542	4	0.365	0.365	NUM
ap-8672	542	5	=	=	SYM
ap-8672	542	6	0	0	NUM
ap-8672	542	7	qo	qo	NOUN
ap-8672	542	8	=	=	SYM
ap-8672	542	9	(	(	PUNCT
ap-8672	542	10	0.12	0.12	NUM
ap-8672	542	11	,	,	PUNCT
ap-8672	542	12	−0.58	−0.58	ADJ
ap-8672	542	13	,	,	PUNCT
ap-8672	542	14	0.12	0.12	NUM
ap-8672	542	15	):	):	PUNCT
ap-8672	542	16	center	center	NOUN
ap-8672	542	17	coordinates	coordinate	NOUN
ap-8672	542	18	of	of	ADP
ap-8672	542	19	circle	circle	NOUN
ap-8672	542	20	and	and	CCONJ
ap-8672	542	21	normal	normal	ADJ
ap-8672	542	22	vector	vector	NOUN
ap-8672	542	23	:	:	PUNCT
ap-8672	542	24	−→	−→	ADJ
ap-8672	542	25	sq	sq	NOUN
ap-8672	542	26	=	=	SYM
ap-8672	542	27	(	(	PUNCT
ap-8672	542	28	0.65	0.65	NUM
ap-8672	542	29	,	,	PUNCT
ap-8672	542	30	0.00	0.00	NUM
ap-8672	542	31	,	,	PUNCT
ap-8672	542	32	−0.65)t	−0.65)t	PROPN
ap-8672	542	33	−→n	−→n	VERB
ap-8672	542	34	(	(	PUNCT
ap-8672	542	35	0.19	0.19	NUM
ap-8672	542	36	,	,	PUNCT
ap-8672	542	37	−0.94	−0.94	ADJ
ap-8672	542	38	,	,	PUNCT
ap-8672	542	39	0.19	0.19	NUM
ap-8672	542	40	)	)	PUNCT
ap-8672	542	41	−→	−→	NOUN
ap-8672	542	42	nq	nq	PROPN
ap-8672	542	43	=	=	SYM
ap-8672	542	44	(	(	PUNCT
ap-8672	542	45	0.65	0.65	NUM
ap-8672	542	46	,	,	PUNCT
ap-8672	542	47	0.23	0.23	NUM
ap-8672	542	48	,	,	PUNCT
ap-8672	542	49	0.65)t	0.65)t	NOUN
ap-8672	542	50	0	0	NUM
ap-8672	542	51	≤	≤	NOUN
ap-8672	542	52	ϕ	ϕ	X
ap-8672	542	53	≤	≤	ADJ
ap-8672	542	54	2π	2π	NOUN
ap-8672	542	55	of	of	ADP
ap-8672	542	56	step	step	NOUN
ap-8672	542	57	−→	−→	NOUN
ap-8672	542	58	sq	sq	NOUN
ap-8672	542	59	=	=	SYM
ap-8672	542	60	(	(	PUNCT
ap-8672	542	61	sqx	sqx	ADJ
ap-8672	542	62	,	,	PUNCT
ap-8672	542	63	sqy	sqy	PROPN
ap-8672	542	64	,	,	PUNCT
ap-8672	542	65	sqz)t	sqz)t	PROPN
ap-8672	542	66	and	and	CCONJ
ap-8672	542	67	−→	−→	NOUN
ap-8672	542	68	nq	nq	NOUN
ap-8672	542	69	=	=	PUNCT
ap-8672	542	70	(	(	PUNCT
ap-8672	542	71	nqx	nqx	PROPN
ap-8672	542	72	,	,	PUNCT
ap-8672	542	73	nqy	nqy	PROPN
ap-8672	542	74	,	,	PUNCT
ap-8672	542	75	nqz)t	nqz)t	PROPN
ap-8672	542	76	are	be	AUX
ap-8672	542	77	the	the	DET
ap-8672	542	78	direction	direction	NOUN
ap-8672	542	79	∆ϕ	∆ϕ	NOUN
ap-8672	542	80	=	=	SYM
ap-8672	542	81	π	π	PROPN
ap-8672	542	82	60	60	NUM
ap-8672	542	83	radcosines	radcosine	NOUN
ap-8672	542	84	of	of	ADP
ap-8672	542	85	the	the	DET
ap-8672	542	86	frame	frame	NOUN
ap-8672	542	87	axes	axis	NOUN
ap-8672	542	88	belong	belong	VERB
ap-8672	542	89	the	the	DET
ap-8672	542	90	c	c	NOUN
ap-8672	542	91	-	-	NOUN
ap-8672	542	92	plane	plane	NOUN
ap-8672	542	93	in	in	ADP
ap-8672	542	94	the	the	DET
ap-8672	542	95	reference	reference	NOUN
ap-8672	542	96	frame	frame	NOUN
ap-8672	542	97	f0	f0	PROPN
ap-8672	542	98	344	344	NUM
ap-8672	542	99	vol	vol	NOUN
ap-8672	542	100	.	.	PUNCT
ap-8672	543	1	63	63	NUM
ap-8672	543	2	no	no	NOUN
ap-8672	543	3	.	.	PUNCT
ap-8672	544	1	5/2023	5/2023	NUM
ap-8672	544	2	geometric	geometric	ADJ
ap-8672	544	3	approach	approach	NOUN
ap-8672	544	4	to	to	ADP
ap-8672	544	5	solving	solve	VERB
ap-8672	544	6	inverse	inverse	ADJ
ap-8672	544	7	kinematics	kinematic	NOUN
ap-8672	544	8	of	of	ADP
ap-8672	544	9	six	six	NUM
ap-8672	544	10	dof	dof	NOUN
ap-8672	544	11	robot	robot	NOUN
ap-8672	544	12	a.3	a.3	PROPN
ap-8672	544	13	.	.	PUNCT
ap-8672	545	1	inverse	inverse	PROPN
ap-8672	545	2	kinematics	kinematic	NOUN
ap-8672	545	3	solutions	solution	NOUN
ap-8672	545	4	using	use	VERB
ap-8672	545	5	paul	paul	PROPN
ap-8672	545	6	’s	’s	PART
ap-8672	545	7	method	method	NOUN
ap-8672	545	8	equation	equation	NOUN
ap-8672	545	9	(	(	PUNCT
ap-8672	545	10	a1	a1	NOUN
ap-8672	545	11	)	)	PUNCT
ap-8672	545	12	represents	represent	VERB
ap-8672	545	13	the	the	DET
ap-8672	545	14	forward	forward	ADJ
ap-8672	545	15	kinematics	kinematic	NOUN
ap-8672	545	16	of	of	ADP
ap-8672	545	17	the	the	DET
ap-8672	545	18	robot	robot	NOUN
ap-8672	545	19	.	.	PUNCT
ap-8672	546	1	it	it	PRON
ap-8672	546	2	is	be	AUX
ap-8672	546	3	a	a	DET
ap-8672	546	4	successive	successive	ADJ
ap-8672	546	5	multiplication	multiplication	NOUN
ap-8672	546	6	of	of	ADP
ap-8672	546	7	differents	different	NOUN
ap-8672	546	8	homogeneous	homogeneous	ADJ
ap-8672	546	9	transformation	transformation	NOUN
ap-8672	546	10	matrices	matrix	NOUN
ap-8672	546	11	.	.	PUNCT
ap-8672	547	1	0t1	0t1	NUM
ap-8672	548	1	1t2	1t2	NUM
ap-8672	548	2	2t3	2t3	NUM
ap-8672	548	3	3t4	3t4	NUM
ap-8672	548	4	4t5	4t5	NUM
ap-8672	548	5	5t6	5t6	NUM
ap-8672	548	6	6t7	6t7	NUM
ap-8672	548	7	=	=	PUNCT
ap-8672	549	1	[	[	X
ap-8672	549	2	s	s	X
ap-8672	549	3	n	n	PRON
ap-8672	549	4	a	a	DET
ap-8672	549	5	p	p	X
ap-8672	549	6	]	]	X
ap-8672	549	7	=	=	SYM
ap-8672	549	8			NOUN
ap-8672	549	9	sx	sx	NOUN
ap-8672	549	10	nx	nx	PROPN
ap-8672	549	11	ax	ax	NOUN
ap-8672	549	12	pdx	pdx	PROPN
ap-8672	549	13	sy	sy	PROPN
ap-8672	549	14	ny	ny	PROPN
ap-8672	550	1	ay	ay	PROPN
ap-8672	550	2	pdy	pdy	INTJ
ap-8672	550	3	sz	sz	PROPN
ap-8672	550	4	nz	nz	PROPN
ap-8672	550	5	az	az	PROPN
ap-8672	550	6	pdz	pdz	NOUN
ap-8672	550	7	0	0	NUM
ap-8672	550	8	0	0	NUM
ap-8672	550	9	0	0	NUM
ap-8672	550	10	1	1	NUM
ap-8672	550	11			NOUN
ap-8672	550	12	.	.	PUNCT
ap-8672	551	1	(	(	PUNCT
ap-8672	551	2	a1	a1	NOUN
ap-8672	551	3	)	)	PUNCT
ap-8672	551	4	calculate	calculate	VERB
ap-8672	551	5	the	the	DET
ap-8672	551	6	inverse	inverse	NOUN
ap-8672	551	7	of	of	ADP
ap-8672	551	8	equation	equation	NOUN
ap-8672	551	9	(	(	PUNCT
ap-8672	551	10	a1	a1	NOUN
ap-8672	551	11	):	):	PUNCT
ap-8672	551	12	7t6	7t6	NUM
ap-8672	551	13	6t5	6t5	NUM
ap-8672	551	14	5t4	5t4	NUM
ap-8672	551	15	4t3	4t3	NUM
ap-8672	551	16	3t2	3t2	NUM
ap-8672	551	17	2t1	2t1	NUM
ap-8672	551	18	1t0	1t0	NUM
ap-8672	551	19	=	=	NOUN
ap-8672	551	20			NOUN
ap-8672	551	21	s1	s1	NOUN
ap-8672	551	22	n1	n1	ADJ
ap-8672	551	23	a1	a1	NOUN
ap-8672	551	24	p1	p1	NOUN
ap-8672	551	25	s2	s2	PROPN
ap-8672	551	26	n2	n2	PROPN
ap-8672	551	27	a2	a2	PROPN
ap-8672	551	28	p2	p2	PROPN
ap-8672	551	29	s3	s3	PROPN
ap-8672	551	30	n3	n3	PROPN
ap-8672	551	31	a3	a3	PROPN
ap-8672	551	32	p3	p3	PROPN
ap-8672	551	33	0	0	NUM
ap-8672	551	34	0	0	NUM
ap-8672	551	35	0	0	NUM
ap-8672	551	36	1	1	NUM
ap-8672	551	37			NOUN
ap-8672	551	38	,	,	PUNCT
ap-8672	551	39	(	(	PUNCT
ap-8672	551	40	a2	a2	PROPN
ap-8672	551	41	)	)	PUNCT
ap-8672	552	1	where	where	SCONJ
ap-8672	552	2	:	:	PUNCT
ap-8672	552	3	s1	s1	NOUN
ap-8672	552	4	=	=	SYM
ap-8672	552	5	(	(	PUNCT
ap-8672	552	6	a2.n3	a2.n3	PROPN
ap-8672	552	7	−	−	PROPN
ap-8672	552	8	a3.n2	a3.n2	NOUN
ap-8672	552	9	)	)	PUNCT
ap-8672	552	10	(	(	PUNCT
ap-8672	552	11	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	552	12	−	−	PROPN
ap-8672	552	13	ax.nz.sy	ax.nz.sy	VERB
ap-8672	552	14	−	−	ADP
ap-8672	553	1	ay.nx.sz	ay.nx.sz	X
ap-8672	554	1	+	+	CCONJ
ap-8672	554	2	ay.nz.sx	ay.nz.sx	X
ap-8672	555	1	+	+	CCONJ
ap-8672	555	2	az.nx.sy	az.nx.sy	PRON
ap-8672	555	3	−	−	PRON
ap-8672	555	4	az.ny.sx	az.ny.sx	NUM
ap-8672	555	5	)	)	PUNCT
ap-8672	555	6	,	,	PUNCT
ap-8672	555	7	s2	s2	PROPN
ap-8672	555	8	=	=	PUNCT
ap-8672	556	1	−(a2.s3	−(a2.s3	PROPN
ap-8672	557	1	−	−	PROPN
ap-8672	557	2	a3.s2	a3.s2	PROPN
ap-8672	557	3	)	)	PUNCT
ap-8672	558	1	(	(	PUNCT
ap-8672	558	2	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	558	3	−	−	PROPN
ap-8672	558	4	ax.nz.sy	ax.nz.sy	VERB
ap-8672	558	5	−	−	ADP
ap-8672	559	1	ay.nx.sz	ay.nx.sz	X
ap-8672	560	1	+	+	CCONJ
ap-8672	560	2	ay.nz.sx	ay.nz.sx	X
ap-8672	561	1	+	+	CCONJ
ap-8672	561	2	az.nx.sy	az.nx.sy	PRON
ap-8672	561	3	−	−	PRON
ap-8672	561	4	az.ny.sx	az.ny.sx	NUM
ap-8672	561	5	)	)	PUNCT
ap-8672	561	6	,	,	PUNCT
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ap-8672	561	8	=	=	SYM
ap-8672	561	9	(	(	PUNCT
ap-8672	561	10	n2.s3	n2.s3	PROPN
ap-8672	561	11	−	−	NOUN
ap-8672	561	12	n3.s2	n3.s2	NUM
ap-8672	561	13	)	)	PUNCT
ap-8672	561	14	(	(	PUNCT
ap-8672	561	15	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	561	16	−	−	PROPN
ap-8672	561	17	ax.nz.sy	ax.nz.sy	VERB
ap-8672	561	18	−	−	ADP
ap-8672	562	1	ay.nx.sz	ay.nx.sz	X
ap-8672	563	1	+	+	CCONJ
ap-8672	563	2	ay.nz.sx	ay.nz.sx	X
ap-8672	564	1	+	+	CCONJ
ap-8672	564	2	az.nx.sy	az.nx.sy	PRON
ap-8672	564	3	−	−	PRON
ap-8672	564	4	az.ny.sx	az.ny.sx	NUM
ap-8672	564	5	)	)	PUNCT
ap-8672	564	6	,	,	PUNCT
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ap-8672	564	8	=	=	SYM
ap-8672	564	9	−(ax.sz	−(ax.sz	PROPN
ap-8672	564	10	−	−	PROPN
ap-8672	564	11	az.sx	az.sx	PROPN
ap-8672	564	12	)	)	PUNCT
ap-8672	564	13	(	(	PUNCT
ap-8672	564	14	ax.ny.sz	ax.ny.sz	ADV
ap-8672	564	15	−	−	PROPN
ap-8672	564	16	ax.nz.sy	ax.nz.sy	VERB
ap-8672	564	17	−	−	ADP
ap-8672	565	1	ay.nx.sz	ay.nx.sz	X
ap-8672	566	1	+	+	CCONJ
ap-8672	566	2	ay.nz.sx	ay.nz.sx	X
ap-8672	567	1	+	+	CCONJ
ap-8672	567	2	az.nx.sy	az.nx.sy	PRON
ap-8672	567	3	−	−	PRON
ap-8672	567	4	az.ny.sx	az.ny.sx	NUM
ap-8672	567	5	)	)	PUNCT
ap-8672	567	6	,	,	PUNCT
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ap-8672	567	8	=	=	SYM
ap-8672	567	9	(	(	PUNCT
ap-8672	567	10	ax.sz	ax.sz	PROPN
ap-8672	567	11	−	−	PROPN
ap-8672	567	12	az.sx	az.sx	PROPN
ap-8672	567	13	)	)	PUNCT
ap-8672	567	14	(	(	PUNCT
ap-8672	567	15	ax.ny.sz	ax.ny.sz	ADV
ap-8672	567	16	−	−	PROPN
ap-8672	567	17	ax.nz.sy	ax.nz.sy	VERB
ap-8672	567	18	−	−	ADP
ap-8672	568	1	ay.nx.sz	ay.nx.sz	X
ap-8672	569	1	+	+	CCONJ
ap-8672	569	2	ay.nz.sx	ay.nz.sx	X
ap-8672	570	1	+	+	CCONJ
ap-8672	570	2	az.nx.sy	az.nx.sy	PRON
ap-8672	570	3	−	−	PRON
ap-8672	570	4	az.ny.sx	az.ny.sx	NUM
ap-8672	570	5	)	)	PUNCT
ap-8672	570	6	,	,	PUNCT
ap-8672	570	7	n3	n3	NOUN
ap-8672	570	8	=	=	PUNCT
ap-8672	570	9	−(nx.sz	−(nx.sz	PROPN
ap-8672	570	10	−	−	PROPN
ap-8672	570	11	nz.sx	nz.sx	NOUN
ap-8672	570	12	)	)	PUNCT
ap-8672	570	13	(	(	PUNCT
ap-8672	570	14	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	570	15	−	−	PROPN
ap-8672	570	16	ax.nz.sy	ax.nz.sy	VERB
ap-8672	570	17	−	−	ADP
ap-8672	571	1	ay.nx.sz	ay.nx.sz	X
ap-8672	572	1	+	+	CCONJ
ap-8672	572	2	ay.nz.sx	ay.nz.sx	X
ap-8672	573	1	+	+	CCONJ
ap-8672	573	2	az.nx.sy	az.nx.sy	PRON
ap-8672	573	3	−	−	PRON
ap-8672	573	4	az.ny.sx	az.ny.sx	NUM
ap-8672	573	5	)	)	PUNCT
ap-8672	573	6	,	,	PUNCT
ap-8672	573	7	a1	a1	NOUN
ap-8672	573	8	=	=	SYM
ap-8672	573	9	(	(	PUNCT
ap-8672	573	10	ax.nz	ax.nz	NOUN
ap-8672	573	11	−	−	PROPN
ap-8672	573	12	az.nx	az.nx	NOUN
ap-8672	573	13	)	)	PUNCT
ap-8672	573	14	(	(	PUNCT
ap-8672	573	15	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	573	16	−	−	PROPN
ap-8672	573	17	ax.nz.sy	ax.nz.sy	VERB
ap-8672	573	18	−	−	ADP
ap-8672	574	1	ay.nx.sz	ay.nx.sz	X
ap-8672	575	1	+	+	CCONJ
ap-8672	575	2	ay.nz.sx	ay.nz.sx	X
ap-8672	576	1	+	+	CCONJ
ap-8672	576	2	az.nx.sy	az.nx.sy	PRON
ap-8672	576	3	−	−	PRON
ap-8672	576	4	az.ny.sx	az.ny.sx	NUM
ap-8672	576	5	)	)	PUNCT
ap-8672	576	6	,	,	PUNCT
ap-8672	576	7	a2	a2	PROPN
ap-8672	576	8	=	=	SYM
ap-8672	576	9	−(ax.sy	−(ax.sy	PROPN
ap-8672	577	1	−	−	PROPN
ap-8672	577	2	ay.sx	ay.sx	NOUN
ap-8672	577	3	)	)	PUNCT
ap-8672	577	4	(	(	PUNCT
ap-8672	577	5	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	577	6	−	−	PROPN
ap-8672	577	7	ax.nz.sy	ax.nz.sy	VERB
ap-8672	577	8	−	−	ADP
ap-8672	578	1	ay.nx.sz	ay.nx.sz	X
ap-8672	579	1	+	+	CCONJ
ap-8672	579	2	ay.nz.sx	ay.nz.sx	X
ap-8672	580	1	+	+	CCONJ
ap-8672	580	2	az.nx.sy	az.nx.sy	PRON
ap-8672	580	3	−	−	PRON
ap-8672	580	4	az.ny.sx	az.ny.sx	NUM
ap-8672	580	5	)	)	PUNCT
ap-8672	580	6	,	,	PUNCT
ap-8672	580	7	a3	a3	NOUN
ap-8672	580	8	=	=	SYM
ap-8672	580	9	(	(	PUNCT
ap-8672	580	10	nx.sz	nx.sz	NOUN
ap-8672	580	11	−	−	PROPN
ap-8672	580	12	nz.sx	nz.sx	NOUN
ap-8672	580	13	)	)	PUNCT
ap-8672	580	14	(	(	PUNCT
ap-8672	580	15	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	580	16	−	−	PROPN
ap-8672	580	17	ax.nz.sy	ax.nz.sy	VERB
ap-8672	580	18	−	−	ADP
ap-8672	581	1	ay.nx.sz	ay.nx.sz	X
ap-8672	582	1	+	+	CCONJ
ap-8672	582	2	ay.nz.sx	ay.nz.sx	X
ap-8672	583	1	+	+	CCONJ
ap-8672	583	2	az.nx.sy	az.nx.sy	PRON
ap-8672	583	3	−	−	PRON
ap-8672	583	4	az.ny.sx	az.ny.sx	NUM
ap-8672	583	5	)	)	PUNCT
ap-8672	583	6	,	,	PUNCT
ap-8672	583	7	p1	p1	NOUN
ap-8672	583	8	=	=	PUNCT
ap-8672	584	1	−(pdx.ay.nz	−(pdx.ay.nz	PRON
ap-8672	584	2	−	−	PROPN
ap-8672	584	3	pdx.az.ny	pdx.az.ny	VERB
ap-8672	584	4	−	−	PROPN
ap-8672	585	1	pdy.ax.nz	pdy.ax.nz	NOUN
ap-8672	586	1	+	+	CCONJ
ap-8672	586	2	pdy.az.nx	pdy.az.nx	PROPN
ap-8672	586	3	+	+	CCONJ
ap-8672	586	4	pdz.ax.ny	pdz.ax.ny	PROPN
ap-8672	586	5	−	−	PROPN
ap-8672	586	6	pdz.ay.nx	pdz.ay.nx	NOUN
ap-8672	586	7	)	)	PUNCT
ap-8672	586	8	(	(	PUNCT
ap-8672	586	9	ax.ny.sz	ax.ny.sz	CCONJ
ap-8672	586	10	−	−	PROPN
ap-8672	586	11	ax.nz.sy	ax.nz.sy	VERB
ap-8672	586	12	−	−	ADP
ap-8672	587	1	ay.nx.sz	ay.nx.sz	X
ap-8672	588	1	+	+	CCONJ
ap-8672	588	2	ay.nz.sx	ay.nz.sx	X
ap-8672	589	1	+	+	CCONJ
ap-8672	589	2	az.nx.sy	az.nx.sy	PRON
ap-8672	589	3	−	−	PRON
ap-8672	589	4	az.ny.sx	az.ny.sx	NUM
ap-8672	589	5	)	)	PUNCT
ap-8672	589	6	,	,	PUNCT
ap-8672	589	7	p2	p2	PROPN
ap-8672	589	8	=	=	SYM
ap-8672	589	9	(	(	PUNCT
ap-8672	589	10	pdx.ay.sz	pdx.ay.sz	ADJ
ap-8672	589	11	−	−	PROPN
ap-8672	589	12	pdx.az.sy	pdx.az.sy	NOUN
ap-8672	589	13	−	−	PROPN
ap-8672	589	14	pdy.ax.sz	pdy.ax.sz	PROPN
ap-8672	589	15	+	+	CCONJ
ap-8672	589	16	pdy.az.sx	pdy.az.sx	ADJ
ap-8672	589	17	+	+	CCONJ
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ap-8672	589	19	−	−	PROPN
ap-8672	589	20	pdz.ay.sx	pdz.ay.sx	NOUN
ap-8672	589	21	)	)	PUNCT
ap-8672	589	22	(	(	PUNCT
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ap-8672	589	24	−	−	PROPN
ap-8672	589	25	ax.nz.sy	ax.nz.sy	VERB
ap-8672	589	26	−	−	ADP
ap-8672	590	1	ay.nx.sz	ay.nx.sz	X
ap-8672	591	1	+	+	CCONJ
ap-8672	591	2	ay.nz.sx	ay.nz.sx	X
ap-8672	592	1	+	+	CCONJ
ap-8672	592	2	az.nx.sy	az.nx.sy	PRON
ap-8672	592	3	−	−	PRON
ap-8672	592	4	az.ny.sx	az.ny.sx	NUM
ap-8672	592	5	)	)	PUNCT
ap-8672	592	6	,	,	PUNCT
ap-8672	592	7	p3	p3	PROPN
ap-8672	592	8	=	=	PUNCT
ap-8672	593	1	−(pdx.ny.sz	−(pdx.ny.sz	ADP
ap-8672	593	2	−	−	NOUN
ap-8672	593	3	pdx.nz.sy	pdx.nz.sy	VERB
ap-8672	593	4	−	−	PROPN
ap-8672	594	1	pdy.nx.sz	pdy.nx.sz	ADJ
ap-8672	594	2	+	+	CCONJ
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ap-8672	594	4	+	+	CCONJ
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ap-8672	594	6	−	−	NOUN
ap-8672	594	7	pdz.ny.sx	pdz.ny.sx	NUM
ap-8672	594	8	)	)	PUNCT
ap-8672	594	9	(	(	PUNCT
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ap-8672	594	11	−	−	PROPN
ap-8672	594	12	ax.nz.sy	ax.nz.sy	VERB
ap-8672	594	13	−	−	ADP
ap-8672	595	1	ay.nx.sz	ay.nx.sz	X
ap-8672	596	1	+	+	CCONJ
ap-8672	596	2	ay.nz.sx	ay.nz.sx	X
ap-8672	597	1	+	+	CCONJ
ap-8672	597	2	az.nx.sy	az.nx.sy	PRON
ap-8672	597	3	−	−	NUM
ap-8672	597	4	az.ny.sx	az.ny.sx	NUM
ap-8672	597	5	)	)	PUNCT
ap-8672	597	6	.	.	PUNCT
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ap-8672	598	2	corresponding	correspond	VERB
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ap-8672	598	8	given	give	VERB
ap-8672	598	9	bellow	bellow	ADJ
ap-8672	598	10	.	.	PUNCT
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ap-8672	599	2	.	.	PUNCT
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ap-8672	600	7	=	=	SYM
ap-8672	600	8	(	(	PUNCT
ap-8672	600	9	p1	p1	NOUN
ap-8672	600	10	+	+	CCONJ
ap-8672	601	1	lh)2	lh)2	PROPN
ap-8672	601	2	+	+	CCONJ
ap-8672	601	3	p	p	NOUN
ap-8672	601	4	2	2	NUM
ap-8672	601	5	2	2	NUM
ap-8672	601	6	+	+	CCONJ
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ap-8672	601	8	2	2	NUM
ap-8672	601	9	3	3	NUM
ap-8672	601	10	−	−	NOUN
ap-8672	601	11	l2	l2	NOUN
ap-8672	601	12	a	a	DET
ap-8672	601	13	−	−	NOUN
ap-8672	601	14	l2	l2	NOUN
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ap-8672	601	17	,	,	PUNCT
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ap-8672	601	22	√	√	PROPN
ap-8672	601	23	1	1	NUM
ap-8672	601	24	−	−	PROPN
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ap-8672	601	28	,	,	PUNCT
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ap-8672	601	30	θ4	θ4	NOUN
ap-8672	601	31	)	)	PUNCT
ap-8672	601	32	.	.	PUNCT
ap-8672	602	1	a.3.2	a.3.2	PROPN
ap-8672	602	2	.	.	PUNCT
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ap-8672	603	2	joint	joint	ADJ
ap-8672	603	3	angle	angle	NOUN
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ap-8672	603	6	θ5	θ5	PROPN
ap-8672	603	7	=	=	SYM
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ap-8672	603	9	la	la	PROPN
ap-8672	603	10	.	.	PUNCT
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ap-8672	603	12	θ4	θ4	PROPN
ap-8672	603	13	,	,	PUNCT
ap-8672	603	14	θ5	θ5	PROPN
ap-8672	603	15	=	=	SYM
ap-8672	603	16	atan2(sin	atan2(sin	PUNCT
ap-8672	603	17	θ5	θ5	PROPN
ap-8672	603	18	,	,	PUNCT
ap-8672	603	19	√	√	PROPN
ap-8672	603	20	1	1	NUM
ap-8672	603	21	−	−	PROPN
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ap-8672	603	23	θ2	θ2	PROPN
ap-8672	603	24	5	5	NUM
ap-8672	603	25	)	)	PUNCT
ap-8672	603	26	.	.	PUNCT
ap-8672	604	1	345	345	NUM
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ap-8672	604	10	,	,	PUNCT
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ap-8672	604	16	.	.	PUNCT
ap-8672	605	1	the	the	DET
ap-8672	605	2	joint	joint	ADJ
ap-8672	605	3	angle	angle	NOUN
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ap-8672	605	7	=	=	SYM
ap-8672	605	8	la	la	PROPN
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ap-8672	605	12	.	.	PUNCT
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ap-8672	606	2	θ5.(lh	θ5.(lh	PROPN
ap-8672	606	3	+	+	CCONJ
ap-8672	606	4	p1	p1	NOUN
ap-8672	606	5	)	)	PUNCT
ap-8672	607	1	+	+	CCONJ
ap-8672	607	2	(	(	PUNCT
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ap-8672	607	4	.	.	PUNCT
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ap-8672	607	7	+	+	CCONJ
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ap-8672	607	13	2	2	NUM
ap-8672	607	14	+	+	CCONJ
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ap-8672	607	17	+	+	CCONJ
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ap-8672	609	1	(	(	PUNCT
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ap-8672	609	6	+	+	CCONJ
ap-8672	609	7	lf	lf	NOUN
ap-8672	609	8	)	)	PUNCT
ap-8672	609	9	(	(	PUNCT
ap-8672	609	10	lh	lh	PROPN
ap-8672	609	11	+	+	NUM
ap-8672	609	12	p1	p1	PROPN
ap-8672	609	13	)	)	PUNCT
ap-8672	609	14	p	p	NOUN
ap-8672	609	15	2	2	NUM
ap-8672	609	16	2	2	NUM
ap-8672	609	17	+	+	CCONJ
ap-8672	609	18	(	(	PUNCT
ap-8672	609	19	p1	p1	NOUN
ap-8672	609	20	+	+	CCONJ
ap-8672	610	1	lh)2	lh)2	PROPN
ap-8672	610	2	.	.	PUNCT
ap-8672	611	1	a.3.4	a.3.4	NOUN
ap-8672	611	2	.	.	PUNCT
ap-8672	612	1	the	the	DET
ap-8672	612	2	joint	joint	ADJ
ap-8672	612	3	angle	angle	NOUN
ap-8672	612	4	θ2	θ2	PROPN
ap-8672	612	5	sin	sin	NOUN
ap-8672	612	6	θ2	θ2	PROPN
ap-8672	612	7	=	=	SYM
ap-8672	612	8	−((−	−((−	PRON
ap-8672	612	9	sin	sin	VERB
ap-8672	612	10	θ6.a1	θ6.a1	X
ap-8672	612	11	−	−	PROPN
ap-8672	613	1	cos	cos	X
ap-8672	613	2	θ6.a2	θ6.a2	PROPN
ap-8672	613	3	)	)	PUNCT
ap-8672	613	4	cos	cos	PROPN
ap-8672	613	5	θ5	θ5	PROPN
ap-8672	613	6	+	+	CCONJ
ap-8672	613	7	sin	sin	PROPN
ap-8672	613	8	θ4	θ4	PROPN
ap-8672	613	9	.	.	PUNCT
ap-8672	614	1	sin	sin	PROPN
ap-8672	614	2	θ5.a3	θ5.a3	PROPN
ap-8672	615	1	+	+	PUNCT
ap-8672	615	2	cos	cos	ADP
ap-8672	615	3	θ4(cos	θ4(cos	PRON
ap-8672	615	4	θ6.a1	θ6.a1	X
ap-8672	615	5	−	−	PROPN
ap-8672	615	6	sin	sin	NOUN
ap-8672	615	7	θ6.a2	θ6.a2	PROPN
ap-8672	615	8	)	)	PUNCT
ap-8672	615	9	)	)	PUNCT
ap-8672	615	10	,	,	PUNCT
ap-8672	615	11	θ2	θ2	PROPN
ap-8672	615	12	=	=	PUNCT
ap-8672	615	13	atan2(sin	atan2(sin	PUNCT
ap-8672	615	14	θ2	θ2	PROPN
ap-8672	615	15	,	,	PUNCT
ap-8672	615	16	√	√	PROPN
ap-8672	615	17	1	1	NUM
ap-8672	615	18	−	−	NOUN
ap-8672	615	19	sin	sin	NOUN
ap-8672	615	20	θ2	θ2	ADP
ap-8672	615	21	2	2	NUM
ap-8672	615	22	)	)	PUNCT
ap-8672	615	23	.	.	PUNCT
ap-8672	616	1	a.3.5	a.3.5	PROPN
ap-8672	616	2	.	.	PUNCT
ap-8672	617	1	the	the	DET
ap-8672	617	2	joint	joint	ADJ
ap-8672	617	3	angle	angle	NOUN
ap-8672	617	4	θ3	θ3	PROPN
ap-8672	617	5	sin	sin	NOUN
ap-8672	617	6	θ3	θ3	NOUN
ap-8672	617	7	=	=	SYM
ap-8672	617	8	cos	cos	ADP
ap-8672	617	9	θ4(cos	θ4(cos	PROPN
ap-8672	617	10	θ5(sin	θ5(sin	PROPN
ap-8672	617	11	θ6.a1	θ6.a1	X
ap-8672	617	12	+	+	CCONJ
ap-8672	617	13	cos	cos	ADP
ap-8672	617	14	θ6.a2	θ6.a2	PROPN
ap-8672	617	15	)	)	PUNCT
ap-8672	617	16	−	−	NOUN
ap-8672	617	17	sin	sin	NOUN
ap-8672	617	18	θ5.a3	θ5.a3	NOUN
ap-8672	617	19	)	)	PUNCT
ap-8672	618	1	+	+	CCONJ
ap-8672	618	2	sin	sin	NOUN
ap-8672	618	3	θ4(cos	θ4(cos	X
ap-8672	618	4	θ6.a1	θ6.a1	X
ap-8672	618	5	−	−	PROPN
ap-8672	618	6	sin	sin	NOUN
ap-8672	618	7	θ6.a2	θ6.a2	PROPN
ap-8672	618	8	)	)	PUNCT
ap-8672	618	9	,	,	PUNCT
ap-8672	618	10	cos	cos	PROPN
ap-8672	618	11	θ3	θ3	PROPN
ap-8672	618	12	=	=	PUNCT
ap-8672	618	13	sin	sin	NOUN
ap-8672	618	14	θ5(sin	θ5(sin	X
ap-8672	618	15	θ6.a1	θ6.a1	X
ap-8672	618	16	+	+	CCONJ
ap-8672	618	17	cos	cos	ADP
ap-8672	618	18	θ6.a2	θ6.a2	PROPN
ap-8672	618	19	)	)	PUNCT
ap-8672	619	1	+	+	CCONJ
ap-8672	619	2	sin	sin	NOUN
ap-8672	619	3	θ5.a3	θ5.a3	NOUN
ap-8672	619	4	,	,	PUNCT
ap-8672	619	5	θ3	θ3	NOUN
ap-8672	619	6	=	=	SYM
ap-8672	619	7	atan2(sin	atan2(sin	PUNCT
ap-8672	619	8	θ3	θ3	PROPN
ap-8672	619	9	,	,	PUNCT
ap-8672	619	10	cos	cos	PROPN
ap-8672	619	11	θ3	θ3	PROPN
ap-8672	619	12	)	)	PUNCT
ap-8672	619	13	.	.	PUNCT
ap-8672	620	1	a.3.6	a.3.6	PROPN
ap-8672	620	2	.	.	PUNCT
ap-8672	621	1	the	the	DET
ap-8672	621	2	joint	joint	ADJ
ap-8672	621	3	angle	angle	NOUN
ap-8672	621	4	θ1	θ1	NOUN
ap-8672	621	5	sin	sin	VERB
ap-8672	621	6	θ1	θ1	NOUN
ap-8672	621	7	=	=	SYM
ap-8672	621	8	sin	sin	VERB
ap-8672	621	9	θ4(−	θ4(−	PROPN
ap-8672	621	10	cos	cos	PROPN
ap-8672	621	11	θ5(sin	θ5(sin	PROPN
ap-8672	621	12	θ6.s1	θ6.s1	PROPN
ap-8672	622	1	+	+	CCONJ
ap-8672	622	2	cos	cos	ADP
ap-8672	622	3	θ6.s2	θ6.s2	NOUN
ap-8672	622	4	)	)	PUNCT
ap-8672	623	1	+	+	CCONJ
ap-8672	623	2	sin	sin	NOUN
ap-8672	623	3	θ5.s3	θ5.s3	PROPN
ap-8672	623	4	)	)	PUNCT
ap-8672	624	1	+	+	CCONJ
ap-8672	624	2	cos	cos	ADP
ap-8672	624	3	θ4(cos	θ4(cos	PROPN
ap-8672	624	4	θ6.s1	θ6.s1	PROPN
ap-8672	624	5	−	−	PROPN
ap-8672	624	6	sin	sin	NOUN
ap-8672	624	7	θ6.s2	θ6.s2	NOUN
ap-8672	624	8	)	)	PUNCT
ap-8672	624	9	,	,	PUNCT
ap-8672	624	10	cos	cos	PROPN
ap-8672	624	11	θ1	θ1	PROPN
ap-8672	624	12	=	=	SYM
ap-8672	624	13	−	−	PROPN
ap-8672	624	14	sin	sin	NOUN
ap-8672	624	15	θ4(−	θ4(−	PROPN
ap-8672	624	16	cos	cos	ADP
ap-8672	624	17	θ5(sin	θ5(sin	PROPN
ap-8672	624	18	θ6.n1	θ6.n1	PROPN
ap-8672	624	19	+	+	PROPN
ap-8672	624	20	cos	cos	ADP
ap-8672	624	21	θ6.n2	θ6.n2	PROPN
ap-8672	624	22	)	)	PUNCT
ap-8672	624	23	+	+	NUM
ap-8672	624	24	sin	sin	NOUN
ap-8672	624	25	θ5.n3	θ5.n3	PROPN
ap-8672	624	26	)	)	PUNCT
ap-8672	625	1	+	+	CCONJ
ap-8672	625	2	cos	cos	ADP
ap-8672	625	3	θ4(cos	θ4(cos	PROPN
ap-8672	625	4	θ6.n1	θ6.n1	PROPN
ap-8672	625	5	−	−	NOUN
ap-8672	625	6	sin	sin	NOUN
ap-8672	625	7	θ6.n2	θ6.n2	PROPN
ap-8672	625	8	)	)	PUNCT
ap-8672	625	9	,	,	PUNCT
ap-8672	625	10	θ1	θ1	PROPN
ap-8672	625	11	=	=	SYM
ap-8672	625	12	atan2(sin	atan2(sin	PUNCT
ap-8672	625	13	θ1	θ1	NOUN
ap-8672	625	14	,	,	PUNCT
ap-8672	625	15	cos	cos	ADJ
ap-8672	625	16	θ1	θ1	NOUN
ap-8672	625	17	)	)	PUNCT
ap-8672	625	18	.	.	PUNCT
ap-8672	626	1	346	346	NUM
ap-8672	626	2	acta	acta	PROPN
ap-8672	626	3	polytechnica	polytechnica	PROPN
ap-8672	626	4	63(5):326–346	63(5):326–346	PROPN
ap-8672	626	5	,	,	PUNCT
ap-8672	626	6	2023	2023	NUM
ap-8672	626	7	1	1	NUM
ap-8672	626	8	introduction	introduction	NOUN
ap-8672	626	9	2	2	NUM
ap-8672	626	10	principle	principle	NOUN
ap-8672	626	11	of	of	ADP
ap-8672	626	12	the	the	DET
ap-8672	626	13	approach	approach	NOUN
ap-8672	626	14	for	for	ADP
ap-8672	626	15	inverse	inverse	ADJ
ap-8672	626	16	kinematics	kinematic	NOUN
ap-8672	626	17	3	3	NUM
ap-8672	626	18	robot	robot	NOUN
ap-8672	626	19	structure	structure	NOUN
ap-8672	626	20	and	and	CCONJ
ap-8672	626	21	geometry	geometry	NOUN
ap-8672	626	22	4	4	NUM
ap-8672	626	23	mathematical	mathematical	ADJ
ap-8672	626	24	modelling	modelling	NOUN
ap-8672	626	25	of	of	ADP
ap-8672	626	26	the	the	DET
ap-8672	626	27	robot	robot	NOUN
ap-8672	626	28	4.1	4.1	NUM
ap-8672	626	29	forward	forward	ADJ
ap-8672	626	30	kinematics	kinematic	NOUN
ap-8672	626	31	4.2	4.2	NUM
ap-8672	626	32	inverse	inverse	NOUN
ap-8672	626	33	kinematics	kinematic	NOUN
ap-8672	626	34	solutions	solution	NOUN
ap-8672	626	35	4.2.1	4.2.1	NUM
ap-8672	626	36	calculate	calculate	VERB
ap-8672	626	37	the	the	DET
ap-8672	626	38	geometric	geometric	ADJ
ap-8672	626	39	entities	entity	NOUN
ap-8672	626	40	of	of	ADP
ap-8672	626	41	the	the	DET
ap-8672	626	42	robot	robot	NOUN
ap-8672	626	43	4.2.2	4.2.2	NUM
ap-8672	626	44	calculate	calculate	VERB
ap-8672	626	45	the	the	DET
ap-8672	626	46	joint	joint	ADJ
ap-8672	626	47	angles	angle	NOUN
ap-8672	626	48	of	of	ADP
ap-8672	626	49	the	the	DET
ap-8672	626	50	robot	robot	NOUN
ap-8672	626	51	5	5	NUM
ap-8672	626	52	simulations	simulation	NOUN
ap-8672	626	53	and	and	CCONJ
ap-8672	626	54	results	result	VERB
ap-8672	626	55	6	6	NUM
ap-8672	626	56	experiments	experiment	NOUN
ap-8672	626	57	7	7	NUM
ap-8672	626	58	comparison	comparison	NOUN
ap-8672	626	59	and	and	CCONJ
ap-8672	626	60	discussion	discussion	NOUN
ap-8672	626	61	8	8	NUM
ap-8672	626	62	conclusion	conclusion	NOUN
ap-8672	626	63	list	list	NOUN
ap-8672	626	64	of	of	ADP
ap-8672	626	65	symbols	symbol	NOUN
ap-8672	626	66	references	reference	VERB
ap-8672	626	67	a	a	DET
ap-8672	626	68	appendicies	appendicie	NOUN
ap-8672	626	69	a.1	a.1	PUNCT
ap-8672	626	70	trigonometric	trigonometric	ADJ
ap-8672	626	71	function	function	NOUN
ap-8672	626	72	atan2(y	atan2(y	PROPN
ap-8672	626	73	,	,	PUNCT
ap-8672	626	74	x	x	NOUN
ap-8672	626	75	)	)	PUNCT
ap-8672	626	76	a.2	a.2	VERB
ap-8672	626	77	path	path	NOUN
ap-8672	626	78	of	of	ADP
ap-8672	626	79	the	the	DET
ap-8672	626	80	robot	robot	NOUN
ap-8672	626	81	's	's	PART
ap-8672	626	82	end	end	NOUN
ap-8672	626	83	-	-	PUNCT
ap-8672	626	84	effector	effector	NOUN
ap-8672	626	85	a.3	a.3	NOUN
ap-8672	626	86	inverse	inverse	NOUN
ap-8672	626	87	kinematics	kinematic	NOUN
ap-8672	626	88	solutions	solution	NOUN
ap-8672	626	89	using	use	VERB
ap-8672	626	90	paul	paul	PROPN
ap-8672	626	91	's	's	PART
ap-8672	626	92	method	method	NOUN
ap-8672	626	93	a.3.1	a.3.1	VERB
ap-8672	626	94	the	the	DET
ap-8672	626	95	joint	joint	ADJ
ap-8672	626	96	angle	angle	NOUN
ap-8672	626	97	4	4	NUM
ap-8672	626	98	a.3.2	a.3.2	NOUN
ap-8672	626	99	the	the	DET
ap-8672	626	100	joint	joint	ADJ
ap-8672	626	101	angle	angle	NOUN
ap-8672	626	102	5	5	NUM
ap-8672	626	103	a.3.3	a.3.3	ADV
ap-8672	626	104	the	the	DET
ap-8672	626	105	joint	joint	ADJ
ap-8672	626	106	angle	angle	NOUN
ap-8672	626	107	6	6	NUM
ap-8672	626	108	a.3.4	a.3.4	NOUN
ap-8672	626	109	the	the	DET
ap-8672	626	110	joint	joint	ADJ
ap-8672	626	111	angle	angle	NOUN
ap-8672	626	112	2	2	NUM
ap-8672	626	113	a.3.5	a.3.5	NOUN
ap-8672	626	114	the	the	DET
ap-8672	626	115	joint	joint	ADJ
ap-8672	626	116	angle	angle	NOUN
ap-8672	626	117	3	3	NUM
ap-8672	626	118	a.3.6	a.3.6	PROPN
ap-8672	626	119	the	the	DET
ap-8672	626	120	joint	joint	ADJ
ap-8672	626	121	angle	angle	NOUN
ap-8672	626	122	1	1	NUM