id	sid	tid	token	lemma	pos
ap-6637	1	1	acta	acta	PROPN
ap-6637	1	2	polytechnica	polytechnica	PROPN
ap-6637	1	3	doi:10.14311	doi:10.14311	PROPN
ap-6637	1	4	/	/	SYM
ap-6637	1	5	ap.2020.60.0313	ap.2020.60.0313	PROPN
ap-6637	1	6	acta	acta	PROPN
ap-6637	1	7	polytechnica	polytechnica	PROPN
ap-6637	1	8	60(4):313–317	60(4):313–317	NOUN
ap-6637	1	9	,	,	PUNCT
ap-6637	1	10	2020	2020	NUM
ap-6637	1	11	©	©	PROPN
ap-6637	1	12	czech	czech	PROPN
ap-6637	1	13	technical	technical	PROPN
ap-6637	1	14	university	university	PROPN
ap-6637	1	15	in	in	ADP
ap-6637	1	16	prague	prague	PROPN
ap-6637	1	17	,	,	PUNCT
ap-6637	1	18	2020	2020	NUM
ap-6637	1	19	available	available	ADJ
ap-6637	1	20	online	online	ADV
ap-6637	1	21	at	at	ADP
ap-6637	1	22	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-6637	1	23	external	external	ADJ
ap-6637	1	24	rolling	rolling	NOUN
ap-6637	1	25	of	of	ADP
ap-6637	1	26	a	a	DET
ap-6637	1	27	polygon	polygon	NOUN
ap-6637	1	28	on	on	ADP
ap-6637	1	29	closed	close	VERB
ap-6637	1	30	curvilinear	curvilinear	PROPN
ap-6637	1	31	profile	profile	PROPN
ap-6637	1	32	tetiana	tetiana	PROPN
ap-6637	1	33	kresan	kresan	PROPN
ap-6637	1	34	,	,	PUNCT
ap-6637	1	35	serhii	serhii	PROPN
ap-6637	1	36	pylypaka	pylypaka	PROPN
ap-6637	1	37	,	,	PUNCT
ap-6637	1	38	zinovii	zinovii	PROPN
ap-6637	1	39	ruzhylo	ruzhylo	PROPN
ap-6637	1	40	,	,	PUNCT
ap-6637	1	41	ivan	ivan	PROPN
ap-6637	1	42	rogovskii	rogovskii	PROPN
ap-6637	1	43	,	,	PUNCT
ap-6637	1	44	oleksandra	oleksandra	PROPN
ap-6637	1	45	trokhaniak∗	trokhaniak∗	PROPN
ap-6637	1	46	national	national	PROPN
ap-6637	1	47	university	university	PROPN
ap-6637	1	48	of	of	ADP
ap-6637	1	49	life	life	NOUN
ap-6637	1	50	and	and	CCONJ
ap-6637	1	51	environmental	environmental	ADJ
ap-6637	1	52	sciences	science	NOUN
ap-6637	1	53	of	of	ADP
ap-6637	1	54	ukraine	ukraine	NOUN
ap-6637	1	55	,	,	PUNCT
ap-6637	1	56	heroiv	heroiv	VERB
ap-6637	1	57	oborony	oborony	NOUN
ap-6637	1	58	str	str	PROPN
ap-6637	1	59	.	.	PUNCT
ap-6637	1	60	,	,	PUNCT
ap-6637	1	61	15	15	NUM
ap-6637	1	62	,	,	PUNCT
ap-6637	1	63	kyiv	kyiv	ADJ
ap-6637	1	64	,	,	PUNCT
ap-6637	1	65	ukraine	ukraine	NOUN
ap-6637	1	66	∗	∗	NOUN
ap-6637	1	67	corresponding	correspond	VERB
ap-6637	1	68	author	author	NOUN
ap-6637	1	69	:	:	PUNCT
ap-6637	1	70	klendii_o@ukr.net	klendii_o@ukr.net	X
ap-6637	2	1	abstract	abstract	ADJ
ap-6637	2	2	.	.	PUNCT
ap-6637	3	1	the	the	DET
ap-6637	3	2	rolling	rolling	NOUN
ap-6637	3	3	of	of	ADP
ap-6637	3	4	a	a	DET
ap-6637	3	5	flat	flat	ADJ
ap-6637	3	6	figure	figure	NOUN
ap-6637	3	7	in	in	ADP
ap-6637	3	8	the	the	DET
ap-6637	3	9	form	form	NOUN
ap-6637	3	10	of	of	ADP
ap-6637	3	11	an	an	DET
ap-6637	3	12	equilateral	equilateral	ADJ
ap-6637	3	13	polygon	polygon	NOUN
ap-6637	3	14	on	on	ADP
ap-6637	3	15	a	a	DET
ap-6637	3	16	curvilinear	curvilinear	ADJ
ap-6637	3	17	profile	profile	NOUN
ap-6637	3	18	is	be	AUX
ap-6637	3	19	considered	consider	VERB
ap-6637	3	20	.	.	PUNCT
ap-6637	4	1	the	the	DET
ap-6637	4	2	profile	profile	NOUN
ap-6637	4	3	is	be	AUX
ap-6637	4	4	periodic	periodic	ADJ
ap-6637	4	5	.	.	PUNCT
ap-6637	5	1	it	it	PRON
ap-6637	5	2	is	be	AUX
ap-6637	5	3	formed	form	VERB
ap-6637	5	4	by	by	ADP
ap-6637	5	5	a	a	DET
ap-6637	5	6	series	series	NOUN
ap-6637	5	7	connection	connection	NOUN
ap-6637	5	8	of	of	ADP
ap-6637	5	9	an	an	DET
ap-6637	5	10	arc	arc	NOUN
ap-6637	5	11	of	of	ADP
ap-6637	5	12	a	a	DET
ap-6637	5	13	symmetrical	symmetrical	ADJ
ap-6637	5	14	curve	curve	NOUN
ap-6637	5	15	.	.	PUNCT
ap-6637	6	1	the	the	DET
ap-6637	6	2	ends	end	NOUN
ap-6637	6	3	of	of	ADP
ap-6637	6	4	the	the	DET
ap-6637	6	5	arc	arc	NOUN
ap-6637	6	6	rely	rely	VERB
ap-6637	6	7	on	on	ADP
ap-6637	6	8	a	a	DET
ap-6637	6	9	circle	circle	NOUN
ap-6637	6	10	of	of	ADP
ap-6637	6	11	a	a	DET
ap-6637	6	12	given	give	VERB
ap-6637	6	13	radius	radius	NOUN
ap-6637	6	14	.	.	PUNCT
ap-6637	7	1	the	the	DET
ap-6637	7	2	equation	equation	NOUN
ap-6637	7	3	of	of	ADP
ap-6637	7	4	the	the	DET
ap-6637	7	5	curve	curve	NOUN
ap-6637	7	6	,	,	PUNCT
ap-6637	7	7	from	from	ADP
ap-6637	7	8	which	which	PRON
ap-6637	7	9	the	the	DET
ap-6637	7	10	curvilinear	curvilinear	NOUN
ap-6637	7	11	profile	profile	NOUN
ap-6637	7	12	is	be	AUX
ap-6637	7	13	constructed	construct	VERB
ap-6637	7	14	,	,	PUNCT
ap-6637	7	15	is	be	AUX
ap-6637	7	16	found	find	VERB
ap-6637	7	17	.	.	PUNCT
ap-6637	8	1	this	this	PRON
ap-6637	8	2	is	be	AUX
ap-6637	8	3	done	do	VERB
ap-6637	8	4	provided	provide	VERB
ap-6637	8	5	that	that	SCONJ
ap-6637	8	6	the	the	DET
ap-6637	8	7	centre	centre	NOUN
ap-6637	8	8	of	of	ADP
ap-6637	8	9	the	the	DET
ap-6637	8	10	polygon	polygon	NOUN
ap-6637	8	11	,	,	PUNCT
ap-6637	8	12	when	when	SCONJ
ap-6637	8	13	it	it	PRON
ap-6637	8	14	rolls	roll	VERB
ap-6637	8	15	in	in	ADP
ap-6637	8	16	profile	profile	NOUN
ap-6637	8	17	,	,	PUNCT
ap-6637	8	18	must	must	AUX
ap-6637	8	19	also	also	ADV
ap-6637	8	20	move	move	VERB
ap-6637	8	21	in	in	ADP
ap-6637	8	22	a	a	DET
ap-6637	8	23	circle	circle	NOUN
ap-6637	8	24	.	.	PUNCT
ap-6637	9	1	rolling	rolling	NOUN
ap-6637	9	2	occurs	occur	VERB
ap-6637	9	3	in	in	ADP
ap-6637	9	4	the	the	DET
ap-6637	9	5	absence	absence	NOUN
ap-6637	9	6	of	of	ADP
ap-6637	9	7	sliding	slide	VERB
ap-6637	9	8	.	.	PUNCT
ap-6637	10	1	therefore	therefore	ADV
ap-6637	10	2	,	,	PUNCT
ap-6637	10	3	the	the	DET
ap-6637	10	4	length	length	NOUN
ap-6637	10	5	of	of	ADP
ap-6637	10	6	the	the	DET
ap-6637	10	7	arc	arc	NOUN
ap-6637	10	8	of	of	ADP
ap-6637	10	9	the	the	DET
ap-6637	10	10	curve	curve	NOUN
ap-6637	10	11	is	be	AUX
ap-6637	10	12	equal	equal	ADJ
ap-6637	10	13	to	to	ADP
ap-6637	10	14	the	the	DET
ap-6637	10	15	length	length	NOUN
ap-6637	10	16	of	of	ADP
ap-6637	10	17	the	the	DET
ap-6637	10	18	side	side	NOUN
ap-6637	10	19	of	of	ADP
ap-6637	10	20	the	the	DET
ap-6637	10	21	polygon	polygon	NOUN
ap-6637	10	22	.	.	PUNCT
ap-6637	11	1	to	to	PART
ap-6637	11	2	find	find	VERB
ap-6637	11	3	the	the	DET
ap-6637	11	4	equations	equation	NOUN
ap-6637	11	5	of	of	ADP
ap-6637	11	6	the	the	DET
ap-6637	11	7	curve	curve	NOUN
ap-6637	11	8	of	of	ADP
ap-6637	11	9	the	the	DET
ap-6637	11	10	profile	profile	NOUN
ap-6637	11	11	,	,	PUNCT
ap-6637	11	12	a	a	DET
ap-6637	11	13	first	first	ADJ
ap-6637	11	14	-	-	PUNCT
ap-6637	11	15	order	order	NOUN
ap-6637	11	16	differential	differential	ADJ
ap-6637	11	17	equation	equation	NOUN
ap-6637	11	18	is	be	AUX
ap-6637	11	19	constructed	construct	VERB
ap-6637	11	20	.	.	PUNCT
ap-6637	12	1	its	its	PRON
ap-6637	12	2	analytical	analytical	ADJ
ap-6637	12	3	solution	solution	NOUN
ap-6637	12	4	is	be	AUX
ap-6637	12	5	obtained	obtain	VERB
ap-6637	12	6	.	.	PUNCT
ap-6637	13	1	the	the	DET
ap-6637	13	2	parametric	parametric	ADJ
ap-6637	13	3	equations	equation	NOUN
ap-6637	13	4	of	of	ADP
ap-6637	13	5	the	the	DET
ap-6637	13	6	curve	curve	NOUN
ap-6637	13	7	are	be	AUX
ap-6637	13	8	obtained	obtain	VERB
ap-6637	13	9	in	in	ADP
ap-6637	13	10	the	the	DET
ap-6637	13	11	polar	polar	ADJ
ap-6637	13	12	coordinate	coordinate	NOUN
ap-6637	13	13	system	system	NOUN
ap-6637	13	14	.	.	PUNCT
ap-6637	14	1	the	the	DET
ap-6637	14	2	limits	limit	NOUN
ap-6637	14	3	of	of	ADP
ap-6637	14	4	the	the	DET
ap-6637	14	5	change	change	NOUN
ap-6637	14	6	of	of	ADP
ap-6637	14	7	an	an	DET
ap-6637	14	8	angular	angular	ADJ
ap-6637	14	9	parameter	parameter	NOUN
ap-6637	14	10	for	for	ADP
ap-6637	14	11	the	the	DET
ap-6637	14	12	construction	construction	NOUN
ap-6637	14	13	of	of	ADP
ap-6637	14	14	a	a	DET
ap-6637	14	15	profile	profile	NOUN
ap-6637	14	16	element	element	NOUN
ap-6637	14	17	are	be	AUX
ap-6637	14	18	found	find	VERB
ap-6637	14	19	.	.	PUNCT
ap-6637	15	1	it	it	PRON
ap-6637	15	2	is	be	AUX
ap-6637	15	3	a	a	DET
ap-6637	15	4	part	part	NOUN
ap-6637	15	5	of	of	ADP
ap-6637	15	6	the	the	DET
ap-6637	15	7	arc	arc	NOUN
ap-6637	15	8	of	of	ADP
ap-6637	15	9	the	the	DET
ap-6637	15	10	curve	curve	NOUN
ap-6637	15	11	.	.	PUNCT
ap-6637	16	1	according	accord	VERB
ap-6637	16	2	to	to	ADP
ap-6637	16	3	the	the	DET
ap-6637	16	4	obtained	obtain	VERB
ap-6637	16	5	equations	equation	NOUN
ap-6637	16	6	,	,	PUNCT
ap-6637	16	7	curvilinear	curvilinear	ADJ
ap-6637	16	8	profiles	profile	NOUN
ap-6637	16	9	with	with	ADP
ap-6637	16	10	different	different	ADJ
ap-6637	16	11	numbers	number	NOUN
ap-6637	16	12	of	of	ADP
ap-6637	16	13	their	their	PRON
ap-6637	16	14	elements	element	NOUN
ap-6637	16	15	are	be	AUX
ap-6637	16	16	constructed	construct	VERB
ap-6637	16	17	.	.	PUNCT
ap-6637	17	1	keywords	keyword	NOUN
ap-6637	17	2	:	:	PUNCT
ap-6637	17	3	equilateral	equilateral	ADJ
ap-6637	17	4	polygon	polygon	NOUN
ap-6637	17	5	,	,	PUNCT
ap-6637	17	6	curvilinear	curvilinear	PROPN
ap-6637	17	7	profile	profile	NOUN
ap-6637	17	8	,	,	PUNCT
ap-6637	17	9	external	external	ADJ
ap-6637	17	10	rolling	rolling	ADJ
ap-6637	17	11	,	,	PUNCT
ap-6637	17	12	differential	differential	ADJ
ap-6637	17	13	equation	equation	NOUN
ap-6637	17	14	,	,	PUNCT
ap-6637	17	15	centroids	centroid	NOUN
ap-6637	17	16	.	.	PUNCT
ap-6637	18	1	1	1	X
ap-6637	18	2	.	.	X
ap-6637	18	3	introduction	introduction	NOUN
ap-6637	18	4	some	some	DET
ap-6637	18	5	flat	flat	ADJ
ap-6637	18	6	figures	figure	NOUN
ap-6637	18	7	,	,	PUNCT
ap-6637	18	8	including	include	VERB
ap-6637	18	9	polygons	polygon	NOUN
ap-6637	18	10	that	that	PRON
ap-6637	18	11	can	can	AUX
ap-6637	18	12	be	be	AUX
ap-6637	18	13	rolled	roll	VERB
ap-6637	18	14	on	on	ADP
ap-6637	18	15	a	a	DET
ap-6637	18	16	curvilinear	curvilinear	ADJ
ap-6637	18	17	periodic	periodic	ADJ
ap-6637	18	18	profile	profile	NOUN
ap-6637	18	19	without	without	ADP
ap-6637	18	20	sliding	slide	VERB
ap-6637	18	21	,	,	PUNCT
ap-6637	18	22	are	be	AUX
ap-6637	18	23	considered	consider	VERB
ap-6637	18	24	in	in	ADP
ap-6637	18	25	[	[	X
ap-6637	18	26	1	1	NUM
ap-6637	18	27	]	]	PUNCT
ap-6637	18	28	.	.	PUNCT
ap-6637	19	1	the	the	DET
ap-6637	19	2	profile	profile	NOUN
ap-6637	19	3	is	be	AUX
ap-6637	19	4	formed	form	VERB
ap-6637	19	5	by	by	ADP
ap-6637	19	6	equal	equal	ADJ
ap-6637	19	7	symmetrical	symmetrical	ADJ
ap-6637	19	8	curvilinear	curvilinear	ADJ
ap-6637	19	9	elements	element	NOUN
ap-6637	19	10	of	of	ADP
ap-6637	19	11	their	their	PRON
ap-6637	19	12	serial	serial	ADJ
ap-6637	19	13	connection	connection	NOUN
ap-6637	19	14	so	so	SCONJ
ap-6637	19	15	that	that	SCONJ
ap-6637	19	16	the	the	DET
ap-6637	19	17	ends	end	NOUN
ap-6637	19	18	of	of	ADP
ap-6637	19	19	the	the	DET
ap-6637	19	20	elements	element	NOUN
ap-6637	19	21	abut	abut	VERB
ap-6637	19	22	on	on	ADP
ap-6637	19	23	a	a	DET
ap-6637	19	24	straight	straight	ADJ
ap-6637	19	25	line	line	NOUN
ap-6637	19	26	.	.	PUNCT
ap-6637	20	1	when	when	SCONJ
ap-6637	20	2	rolling	roll	VERB
ap-6637	20	3	a	a	DET
ap-6637	20	4	polygon	polygon	NOUN
ap-6637	20	5	on	on	ADP
ap-6637	20	6	such	such	ADJ
ap-6637	20	7	profile	profile	NOUN
ap-6637	20	8	,	,	PUNCT
ap-6637	20	9	its	its	PRON
ap-6637	20	10	centre	centre	NOUN
ap-6637	20	11	moves	move	VERB
ap-6637	20	12	in	in	ADP
ap-6637	20	13	a	a	DET
ap-6637	20	14	straight	straight	ADJ
ap-6637	20	15	line	line	NOUN
ap-6637	20	16	.	.	PUNCT
ap-6637	21	1	constructing	construct	VERB
ap-6637	21	2	a	a	DET
ap-6637	21	3	closed	closed	ADJ
ap-6637	21	4	profile	profile	NOUN
ap-6637	21	5	in	in	ADP
ap-6637	21	6	which	which	PRON
ap-6637	21	7	curvilinear	curvilinear	NOUN
ap-6637	21	8	elements	element	NOUN
ap-6637	21	9	touch	touch	VERB
ap-6637	21	10	a	a	DET
ap-6637	21	11	circle	circle	NOUN
ap-6637	21	12	is	be	AUX
ap-6637	21	13	important	important	ADJ
ap-6637	21	14	for	for	ADP
ap-6637	21	15	the	the	DET
ap-6637	21	16	design	design	NOUN
ap-6637	21	17	of	of	ADP
ap-6637	21	18	centroids	centroid	NOUN
ap-6637	21	19	of	of	ADP
ap-6637	21	20	non	non	ADJ
ap-6637	21	21	-	-	ADJ
ap-6637	21	22	circular	circular	ADJ
ap-6637	21	23	wheels	wheel	NOUN
ap-6637	21	24	.	.	PUNCT
ap-6637	22	1	when	when	SCONJ
ap-6637	22	2	rolling	roll	VERB
ap-6637	22	3	a	a	DET
ap-6637	22	4	polygon	polygon	NOUN
ap-6637	22	5	on	on	ADP
ap-6637	22	6	such	such	ADJ
ap-6637	22	7	profile	profile	NOUN
ap-6637	22	8	,	,	PUNCT
ap-6637	22	9	its	its	PRON
ap-6637	22	10	centre	centre	NOUN
ap-6637	22	11	moves	move	VERB
ap-6637	22	12	in	in	ADP
ap-6637	22	13	a	a	DET
ap-6637	22	14	circle	circle	NOUN
ap-6637	22	15	.	.	PUNCT
ap-6637	23	1	if	if	SCONJ
ap-6637	23	2	both	both	DET
ap-6637	23	3	centres	centre	NOUN
ap-6637	23	4	(	(	PUNCT
ap-6637	23	5	centre	centre	NOUN
ap-6637	23	6	of	of	ADP
ap-6637	23	7	the	the	DET
ap-6637	23	8	curvilinear	curvilinear	ADJ
ap-6637	23	9	profile	profile	NOUN
ap-6637	23	10	and	and	CCONJ
ap-6637	23	11	centre	centre	NOUN
ap-6637	23	12	of	of	ADP
ap-6637	23	13	the	the	DET
ap-6637	23	14	polygon	polygon	NOUN
ap-6637	23	15	)	)	PUNCT
ap-6637	23	16	are	be	AUX
ap-6637	23	17	stationary	stationary	ADJ
ap-6637	23	18	,	,	PUNCT
ap-6637	23	19	then	then	ADV
ap-6637	23	20	you	you	PRON
ap-6637	23	21	can	can	AUX
ap-6637	23	22	roll	roll	VERB
ap-6637	23	23	these	these	DET
ap-6637	23	24	figures	figure	NOUN
ap-6637	23	25	while	while	SCONJ
ap-6637	23	26	rotating	rotate	VERB
ap-6637	23	27	around	around	ADP
ap-6637	23	28	their	their	PRON
ap-6637	23	29	centres	centre	NOUN
ap-6637	23	30	.	.	PUNCT
ap-6637	24	1	one	one	NUM
ap-6637	24	2	centroid	centroid	NOUN
ap-6637	24	3	will	will	AUX
ap-6637	24	4	be	be	AUX
ap-6637	24	5	a	a	DET
ap-6637	24	6	polygon	polygon	NOUN
ap-6637	24	7	,	,	PUNCT
ap-6637	24	8	the	the	DET
ap-6637	24	9	other	other	ADJ
ap-6637	24	10	will	will	AUX
ap-6637	24	11	be	be	AUX
ap-6637	24	12	a	a	DET
ap-6637	24	13	closed	closed	ADJ
ap-6637	24	14	profile	profile	NOUN
ap-6637	24	15	.	.	PUNCT
ap-6637	25	1	many	many	ADJ
ap-6637	25	2	works	work	NOUN
ap-6637	25	3	are	be	AUX
ap-6637	25	4	devoted	devote	VERB
ap-6637	25	5	to	to	ADP
ap-6637	25	6	the	the	DET
ap-6637	25	7	study	study	NOUN
ap-6637	25	8	of	of	ADP
ap-6637	25	9	the	the	DET
ap-6637	25	10	rolling	rolling	NOUN
ap-6637	25	11	of	of	ADP
ap-6637	25	12	flat	flat	ADJ
ap-6637	25	13	figures	figure	NOUN
ap-6637	25	14	one	one	NUM
ap-6637	25	15	by	by	ADP
ap-6637	25	16	one	one	NUM
ap-6637	25	17	.	.	PUNCT
ap-6637	26	1	there	there	PRON
ap-6637	26	2	are	be	VERB
ap-6637	26	3	common	common	ADJ
ap-6637	26	4	examples	example	NOUN
ap-6637	26	5	of	of	ADP
ap-6637	26	6	rolling	roll	VERB
ap-6637	26	7	a	a	DET
ap-6637	26	8	straight	straight	ADJ
ap-6637	26	9	line	line	NOUN
ap-6637	26	10	segment	segment	NOUN
ap-6637	26	11	along	along	ADP
ap-6637	26	12	a	a	DET
ap-6637	26	13	curve	curve	NOUN
ap-6637	26	14	and	and	CCONJ
ap-6637	26	15	vice	vice	ADV
ap-6637	26	16	versa	versa	ADV
ap-6637	26	17	rolling	roll	VERB
ap-6637	26	18	a	a	DET
ap-6637	26	19	curvilinear	curvilinear	ADJ
ap-6637	26	20	profile	profile	NOUN
ap-6637	26	21	along	along	ADP
ap-6637	26	22	a	a	DET
ap-6637	26	23	straight	straight	ADJ
ap-6637	26	24	line	line	NOUN
ap-6637	26	25	.	.	PUNCT
ap-6637	27	1	for	for	ADP
ap-6637	27	2	the	the	DET
ap-6637	27	3	first	first	ADJ
ap-6637	27	4	case	case	NOUN
ap-6637	27	5	,	,	PUNCT
ap-6637	27	6	the	the	DET
ap-6637	27	7	rolling	rolling	NOUN
ap-6637	27	8	of	of	ADP
ap-6637	27	9	a	a	DET
ap-6637	27	10	straight	straight	ADJ
ap-6637	27	11	line	line	NOUN
ap-6637	27	12	in	in	ADP
ap-6637	27	13	a	a	DET
ap-6637	27	14	circle	circle	NOUN
ap-6637	27	15	is	be	AUX
ap-6637	27	16	the	the	DET
ap-6637	27	17	classic	classic	ADJ
ap-6637	27	18	one	one	NOUN
ap-6637	27	19	,	,	PUNCT
ap-6637	27	20	as	as	ADP
ap-6637	27	21	a	a	DET
ap-6637	27	22	result	result	NOUN
ap-6637	27	23	of	of	ADP
ap-6637	27	24	which	which	PRON
ap-6637	27	25	the	the	DET
ap-6637	27	26	point	point	NOUN
ap-6637	27	27	of	of	ADP
ap-6637	27	28	the	the	DET
ap-6637	27	29	line	line	NOUN
ap-6637	27	30	describes	describe	VERB
ap-6637	27	31	the	the	DET
ap-6637	27	32	evolvent	evolvent	NOUN
ap-6637	27	33	of	of	ADP
ap-6637	27	34	a	a	DET
ap-6637	27	35	circle	circle	NOUN
ap-6637	27	36	,	,	PUNCT
ap-6637	27	37	and	and	CCONJ
ap-6637	27	38	for	for	ADP
ap-6637	27	39	the	the	DET
ap-6637	27	40	second	second	ADJ
ap-6637	27	41	case	case	NOUN
ap-6637	27	42	,	,	PUNCT
ap-6637	27	43	the	the	DET
ap-6637	27	44	rolling	rolling	NOUN
ap-6637	27	45	of	of	ADP
ap-6637	27	46	a	a	DET
ap-6637	27	47	circle	circle	NOUN
ap-6637	27	48	along	along	ADP
ap-6637	27	49	a	a	DET
ap-6637	27	50	straight	straight	ADJ
ap-6637	27	51	line	line	NOUN
ap-6637	27	52	,	,	PUNCT
ap-6637	27	53	as	as	ADP
ap-6637	27	54	a	a	DET
ap-6637	27	55	result	result	NOUN
ap-6637	27	56	of	of	ADP
ap-6637	27	57	which	which	PRON
ap-6637	27	58	a	a	DET
ap-6637	27	59	circle	circle	NOUN
ap-6637	27	60	point	point	NOUN
ap-6637	27	61	describes	describe	VERB
ap-6637	27	62	a	a	DET
ap-6637	27	63	cycloid	cycloid	NOUN
ap-6637	27	64	[	[	X
ap-6637	27	65	2	2	NUM
ap-6637	27	66	]	]	PUNCT
ap-6637	27	67	.	.	PUNCT
ap-6637	28	1	in	in	ADP
ap-6637	28	2	[	[	X
ap-6637	28	3	3	3	NUM
ap-6637	28	4	]	]	PUNCT
ap-6637	28	5	,	,	PUNCT
ap-6637	28	6	information	information	NOUN
ap-6637	28	7	on	on	ADP
ap-6637	28	8	the	the	DET
ap-6637	28	9	rolling	rolling	NOUN
ap-6637	28	10	of	of	ADP
ap-6637	28	11	second	second	ADJ
ap-6637	28	12	-	-	PUNCT
ap-6637	28	13	order	order	NOUN
ap-6637	28	14	curves	curve	NOUN
ap-6637	28	15	along	along	ADP
ap-6637	28	16	a	a	DET
ap-6637	28	17	straight	straight	ADJ
ap-6637	28	18	line	line	NOUN
ap-6637	28	19	is	be	AUX
ap-6637	28	20	given	give	VERB
ap-6637	28	21	.	.	PUNCT
ap-6637	29	1	the	the	DET
ap-6637	29	2	trajectory	trajectory	NOUN
ap-6637	29	3	of	of	ADP
ap-6637	29	4	focus	focus	NOUN
ap-6637	29	5	in	in	ADP
ap-6637	29	6	such	such	ADJ
ap-6637	29	7	rolling	rolling	NOUN
ap-6637	29	8	is	be	AUX
ap-6637	29	9	known	know	VERB
ap-6637	29	10	curves	curve	NOUN
ap-6637	29	11	.	.	PUNCT
ap-6637	30	1	the	the	DET
ap-6637	30	2	formation	formation	NOUN
ap-6637	30	3	of	of	ADP
ap-6637	30	4	flat	flat	ADJ
ap-6637	30	5	curves	curve	NOUN
ap-6637	30	6	by	by	ADP
ap-6637	30	7	given	give	VERB
ap-6637	30	8	kinematic	kinematic	ADJ
ap-6637	30	9	parameters	parameter	NOUN
ap-6637	30	10	is	be	AUX
ap-6637	30	11	considered	consider	VERB
ap-6637	30	12	in	in	ADP
ap-6637	30	13	[	[	X
ap-6637	30	14	4	4	NUM
ap-6637	30	15	]	]	PUNCT
ap-6637	30	16	.	.	PUNCT
ap-6637	31	1	the	the	DET
ap-6637	31	2	basics	basic	NOUN
ap-6637	31	3	of	of	ADP
ap-6637	31	4	designing	design	VERB
ap-6637	31	5	non	non	ADJ
ap-6637	31	6	-	-	ADJ
ap-6637	31	7	circular	circular	ADJ
ap-6637	31	8	wheels	wheel	NOUN
ap-6637	31	9	for	for	ADP
ap-6637	31	10	gears	gear	NOUN
ap-6637	31	11	are	be	AUX
ap-6637	31	12	given	give	VERB
ap-6637	31	13	in	in	ADP
ap-6637	31	14	[	[	X
ap-6637	31	15	5	5	NUM
ap-6637	31	16	]	]	PUNCT
ap-6637	31	17	.	.	PUNCT
ap-6637	32	1	geometric	geometric	ADJ
ap-6637	32	2	modelling	modelling	NOUN
ap-6637	32	3	of	of	ADP
ap-6637	32	4	a	a	DET
ap-6637	32	5	centroid	centroid	NOUN
ap-6637	32	6	of	of	ADP
ap-6637	32	7	non	non	ADJ
ap-6637	32	8	-	-	ADJ
ap-6637	32	9	circular	circular	ADJ
ap-6637	32	10	wheels	wheel	NOUN
ap-6637	32	11	was	be	AUX
ap-6637	32	12	further	far	ADV
ap-6637	32	13	developed	develop	VERB
ap-6637	32	14	in	in	ADP
ap-6637	32	15	the	the	DET
ap-6637	32	16	works	work	NOUN
ap-6637	33	1	[	[	X
ap-6637	33	2	6–8	6–8	X
ap-6637	33	3	]	]	X
ap-6637	33	4	.	.	PUNCT
ap-6637	34	1	the	the	DET
ap-6637	34	2	use	use	NOUN
ap-6637	34	3	of	of	ADP
ap-6637	34	4	non	non	ADJ
ap-6637	34	5	-	-	ADJ
ap-6637	34	6	circular	circular	ADJ
ap-6637	34	7	wheels	wheel	NOUN
ap-6637	34	8	in	in	ADP
ap-6637	34	9	gears	gear	NOUN
ap-6637	34	10	has	have	AUX
ap-6637	34	11	been	be	AUX
ap-6637	34	12	considered	consider	VERB
ap-6637	34	13	in	in	ADP
ap-6637	34	14	[	[	X
ap-6637	34	15	9–17	9–17	NOUN
ap-6637	34	16	]	]	PUNCT
ap-6637	34	17	,	,	PUNCT
ap-6637	34	18	in	in	ADP
ap-6637	34	19	chain	chain	NOUN
ap-6637	34	20	drives	drive	NOUN
ap-6637	34	21	in	in	ADP
ap-6637	34	22	a	a	DET
ap-6637	34	23	monograph	monograph	NOUN
ap-6637	35	1	[	[	X
ap-6637	35	2	18	18	NUM
ap-6637	35	3	]	]	PUNCT
ap-6637	35	4	.	.	PUNCT
ap-6637	36	1	the	the	DET
ap-6637	36	2	purpose	purpose	NOUN
ap-6637	36	3	of	of	ADP
ap-6637	36	4	the	the	DET
ap-6637	36	5	article	article	NOUN
ap-6637	36	6	is	be	AUX
ap-6637	36	7	to	to	PART
ap-6637	36	8	develop	develop	VERB
ap-6637	36	9	an	an	DET
ap-6637	36	10	analytical	analytical	ADJ
ap-6637	36	11	description	description	NOUN
ap-6637	36	12	of	of	ADP
ap-6637	36	13	a	a	DET
ap-6637	36	14	curvilinear	curvilinear	NOUN
ap-6637	36	15	closed	close	VERB
ap-6637	36	16	profile	profile	NOUN
ap-6637	36	17	,	,	PUNCT
ap-6637	36	18	in	in	ADP
ap-6637	36	19	which	which	PRON
ap-6637	36	20	an	an	DET
ap-6637	36	21	equilateral	equilateral	ADJ
ap-6637	36	22	polygon	polygon	NOUN
ap-6637	36	23	will	will	AUX
ap-6637	36	24	be	be	AUX
ap-6637	36	25	rolled	roll	VERB
ap-6637	36	26	without	without	ADP
ap-6637	36	27	sliding	slide	VERB
ap-6637	36	28	and	and	CCONJ
ap-6637	36	29	its	its	PRON
ap-6637	36	30	centre	centre	NOUN
ap-6637	36	31	will	will	AUX
ap-6637	36	32	move	move	VERB
ap-6637	36	33	in	in	ADP
ap-6637	36	34	a	a	DET
ap-6637	36	35	circle	circle	NOUN
ap-6637	36	36	of	of	ADP
ap-6637	36	37	a	a	DET
ap-6637	36	38	given	give	VERB
ap-6637	36	39	radius	radius	NOUN
ap-6637	36	40	.	.	PUNCT
ap-6637	37	1	2	2	X
ap-6637	37	2	.	.	X
ap-6637	37	3	material	material	NOUN
ap-6637	37	4	and	and	CCONJ
ap-6637	37	5	method	method	NOUN
ap-6637	37	6	consider	consider	VERB
ap-6637	37	7	the	the	DET
ap-6637	37	8	rolling	rolling	NOUN
ap-6637	37	9	of	of	ADP
ap-6637	37	10	a	a	DET
ap-6637	37	11	polygon	polygon	NOUN
ap-6637	37	12	by	by	ADP
ap-6637	37	13	the	the	DET
ap-6637	37	14	example	example	NOUN
ap-6637	37	15	of	of	ADP
ap-6637	37	16	a	a	DET
ap-6637	37	17	square	square	NOUN
ap-6637	37	18	.	.	PUNCT
ap-6637	38	1	we	we	PRON
ap-6637	38	2	need	need	VERB
ap-6637	38	3	to	to	PART
ap-6637	38	4	find	find	VERB
ap-6637	38	5	a	a	DET
ap-6637	38	6	form	form	NOUN
ap-6637	38	7	of	of	ADP
ap-6637	38	8	a	a	DET
ap-6637	38	9	flat	flat	ADJ
ap-6637	38	10	profile	profile	NOUN
ap-6637	38	11	in	in	ADP
ap-6637	38	12	which	which	PRON
ap-6637	38	13	the	the	DET
ap-6637	38	14	square	square	NOUN
ap-6637	38	15	will	will	AUX
ap-6637	38	16	be	be	AUX
ap-6637	38	17	rolled	roll	VERB
ap-6637	38	18	without	without	ADP
ap-6637	38	19	sliding	slide	VERB
ap-6637	38	20	,	,	PUNCT
ap-6637	38	21	and	and	CCONJ
ap-6637	38	22	its	its	PRON
ap-6637	38	23	centre	centre	NOUN
ap-6637	38	24	will	will	AUX
ap-6637	38	25	move	move	VERB
ap-6637	38	26	in	in	ADP
ap-6637	38	27	a	a	DET
ap-6637	38	28	circle	circle	NOUN
ap-6637	38	29	of	of	ADP
ap-6637	38	30	radius	radius	NOUN
ap-6637	38	31	r	r	NOUN
ap-6637	38	32	(	(	PUNCT
ap-6637	38	33	fig	fig	NOUN
ap-6637	38	34	.	.	PUNCT
ap-6637	39	1	1,a	1,a	NUM
ap-6637	39	2	)	)	PUNCT
ap-6637	39	3	.	.	PUNCT
ap-6637	40	1	rolling	roll	VERB
ap-6637	40	2	of	of	ADP
ap-6637	40	3	a	a	DET
ap-6637	40	4	square	square	NOUN
ap-6637	40	5	can	can	AUX
ap-6637	40	6	be	be	AUX
ap-6637	40	7	considered	consider	VERB
ap-6637	40	8	as	as	ADP
ap-6637	40	9	an	an	DET
ap-6637	40	10	example	example	NOUN
ap-6637	40	11	of	of	ADP
ap-6637	40	12	rolling	rolling	NOUN
ap-6637	40	13	of	of	ADP
ap-6637	40	14	a	a	DET
ap-6637	40	15	triangle	triangle	NOUN
ap-6637	40	16	,	,	PUNCT
ap-6637	40	17	the	the	DET
ap-6637	40	18	basis	basis	NOUN
ap-6637	40	19	of	of	ADP
ap-6637	40	20	which	which	PRON
ap-6637	40	21	is	be	AUX
ap-6637	40	22	the	the	DET
ap-6637	40	23	side	side	NOUN
ap-6637	40	24	of	of	ADP
ap-6637	40	25	the	the	DET
ap-6637	40	26	square	square	NOUN
ap-6637	40	27	,	,	PUNCT
ap-6637	40	28	and	and	CCONJ
ap-6637	40	29	the	the	DET
ap-6637	40	30	altitude	altitude	NOUN
ap-6637	40	31	the	the	DET
ap-6637	40	32	distance	distance	NOUN
ap-6637	40	33	ac	ac	ADV
ap-6637	40	34	=	=	NOUN
ap-6637	40	35	a	a	NOUN
ap-6637	40	36	from	from	ADP
ap-6637	40	37	its	its	PRON
ap-6637	40	38	centre	centre	NOUN
ap-6637	40	39	to	to	ADP
ap-6637	40	40	the	the	DET
ap-6637	40	41	side	side	NOUN
ap-6637	40	42	.	.	PUNCT
ap-6637	41	1	in	in	ADP
ap-6637	41	2	the	the	DET
ap-6637	41	3	initial	initial	ADJ
ap-6637	41	4	position	position	NOUN
ap-6637	41	5	,	,	PUNCT
ap-6637	41	6	the	the	DET
ap-6637	41	7	altitude	altitude	NOUN
ap-6637	41	8	of	of	ADP
ap-6637	41	9	the	the	DET
ap-6637	41	10	ac	ac	PROPN
ap-6637	41	11	is	be	AUX
ap-6637	41	12	located	locate	VERB
ap-6637	41	13	on	on	ADP
ap-6637	41	14	the	the	DET
ap-6637	41	15	ox	ox	ADJ
ap-6637	41	16	axis	axis	NOUN
ap-6637	41	17	(	(	PUNCT
ap-6637	41	18	fig	fig	NOUN
ap-6637	41	19	.	.	PUNCT
ap-6637	42	1	1,a	1,a	NUM
ap-6637	42	2	)	)	PUNCT
ap-6637	42	3	.	.	PUNCT
ap-6637	43	1	when	when	SCONJ
ap-6637	43	2	rolling	roll	VERB
ap-6637	43	3	a	a	DET
ap-6637	43	4	square	square	NOUN
ap-6637	43	5	,	,	PUNCT
ap-6637	43	6	its	its	PRON
ap-6637	43	7	centre	centre	NOUN
ap-6637	43	8	moves	move	VERB
ap-6637	43	9	in	in	ADP
ap-6637	43	10	a	a	DET
ap-6637	43	11	circle	circle	NOUN
ap-6637	43	12	of	of	ADP
ap-6637	43	13	a	a	DET
ap-6637	43	14	radius	radius	NOUN
ap-6637	43	15	r	r	NOUN
ap-6637	43	16	,	,	PUNCT
ap-6637	43	17	and	and	CCONJ
ap-6637	43	18	the	the	DET
ap-6637	43	19	side	side	NOUN
ap-6637	43	20	rolls	roll	VERB
ap-6637	43	21	along	along	ADP
ap-6637	43	22	the	the	DET
ap-6637	43	23	curve	curve	NOUN
ap-6637	43	24	,	,	PUNCT
ap-6637	43	25	that	that	PRON
ap-6637	43	26	will	will	AUX
ap-6637	43	27	be	be	AUX
ap-6637	43	28	found	find	VERB
ap-6637	43	29	.	.	PUNCT
ap-6637	44	1	the	the	DET
ap-6637	44	2	moment	moment	NOUN
ap-6637	44	3	comes	come	VERB
ap-6637	44	4	when	when	SCONJ
ap-6637	44	5	the	the	DET
ap-6637	44	6	point	point	NOUN
ap-6637	44	7	of	of	ADP
ap-6637	44	8	contact	contact	NOUN
ap-6637	44	9	of	of	ADP
ap-6637	44	10	the	the	DET
ap-6637	44	11	square	square	NOUN
ap-6637	44	12	with	with	ADP
ap-6637	44	13	the	the	DET
ap-6637	44	14	curve	curve	NOUN
ap-6637	44	15	becomes	become	VERB
ap-6637	44	16	its	its	PRON
ap-6637	44	17	vertex	vertex	NOUN
ap-6637	44	18	.	.	PUNCT
ap-6637	45	1	the	the	DET
ap-6637	45	2	diagonal	diagonal	ADJ
ap-6637	45	3	a’c	a’c	NOUN
ap-6637	45	4	’	'	PUNCT
ap-6637	46	1	in	in	ADP
ap-6637	46	2	this	this	DET
ap-6637	46	3	position	position	NOUN
ap-6637	46	4	passes	pass	VERB
ap-6637	46	5	through	through	ADP
ap-6637	46	6	the	the	DET
ap-6637	46	7	origin	origin	NOUN
ap-6637	46	8	of	of	ADP
ap-6637	46	9	coordinates	coordinate	NOUN
ap-6637	46	10	the	the	DET
ap-6637	46	11	point	point	NOUN
ap-6637	47	1	o.	o.	INTJ
ap-6637	47	2	it	it	PRON
ap-6637	47	3	is	be	AUX
ap-6637	47	4	obvious	obvious	ADJ
ap-6637	47	5	that	that	SCONJ
ap-6637	47	6	the	the	DET
ap-6637	47	7	length	length	NOUN
ap-6637	47	8	s	s	X
ap-6637	47	9	of	of	ADP
ap-6637	47	10	the	the	DET
ap-6637	47	11	arc	arc	NOUN
ap-6637	47	12	aa	aa	NOUN
ap-6637	47	13	’	'	PUNCT
ap-6637	47	14	is	be	AUX
ap-6637	47	15	equal	equal	ADJ
ap-6637	47	16	to	to	ADP
ap-6637	47	17	the	the	DET
ap-6637	47	18	length	length	NOUN
ap-6637	47	19	of	of	ADP
ap-6637	47	20	half	half	NOUN
ap-6637	47	21	of	of	ADP
ap-6637	47	22	the	the	DET
ap-6637	47	23	side	side	NOUN
ap-6637	47	24	of	of	ADP
ap-6637	47	25	the	the	DET
ap-6637	47	26	square	square	ADJ
ap-6637	47	27	(	(	PUNCT
ap-6637	47	28	fig	fig	NOUN
ap-6637	47	29	.	.	PUNCT
ap-6637	48	1	1,a	1,a	NUM
ap-6637	48	2	)	)	PUNCT
ap-6637	48	3	.	.	PUNCT
ap-6637	49	1	when	when	SCONJ
ap-6637	49	2	rolling	roll	VERB
ap-6637	49	3	,	,	PUNCT
ap-6637	49	4	the	the	DET
ap-6637	49	5	side	side	NOUN
ap-6637	49	6	of	of	ADP
ap-6637	49	7	the	the	DET
ap-6637	49	8	square	square	NOUN
ap-6637	49	9	is	be	AUX
ap-6637	49	10	tangent	tangent	NOUN
ap-6637	49	11	to	to	ADP
ap-6637	49	12	the	the	DET
ap-6637	49	13	curve	curve	NOUN
ap-6637	49	14	,	,	PUNCT
ap-6637	49	15	and	and	CCONJ
ap-6637	49	16	in	in	ADP
ap-6637	49	17	the	the	DET
ap-6637	49	18	position	position	NOUN
ap-6637	49	19	where	where	SCONJ
ap-6637	49	20	the	the	DET
ap-6637	49	21	point	point	NOUN
ap-6637	49	22	of	of	ADP
ap-6637	49	23	contact	contact	NOUN
ap-6637	49	24	is	be	AUX
ap-6637	49	25	its	its	PRON
ap-6637	49	26	vertex	vertex	NOUN
ap-6637	49	27	,	,	PUNCT
ap-6637	49	28	both	both	DET
ap-6637	49	29	sides	side	NOUN
ap-6637	49	30	of	of	ADP
ap-6637	49	31	the	the	DET
ap-6637	49	32	square	square	ADJ
ap-6637	49	33	touch	touch	NOUN
ap-6637	49	34	the	the	DET
ap-6637	49	35	curves	curve	NOUN
ap-6637	49	36	.	.	PUNCT
ap-6637	50	1	with	with	ADP
ap-6637	50	2	further	further	ADJ
ap-6637	50	3	rolling	rolling	NOUN
ap-6637	50	4	,	,	PUNCT
ap-6637	50	5	the	the	DET
ap-6637	50	6	process	process	NOUN
ap-6637	50	7	is	be	AUX
ap-6637	50	8	repeated	repeat	VERB
ap-6637	50	9	.	.	PUNCT
ap-6637	51	1	in	in	ADP
ap-6637	51	2	such	such	DET
ap-6637	51	3	a	a	DET
ap-6637	51	4	way	way	NOUN
ap-6637	51	5	that	that	PRON
ap-6637	51	6	a	a	DET
ap-6637	51	7	rectilinear	rectilinear	ADJ
ap-6637	51	8	plane	plane	NOUN
ap-6637	51	9	profile	profile	NOUN
ap-6637	51	10	will	will	AUX
ap-6637	51	11	consist	consist	VERB
ap-6637	51	12	of	of	ADP
ap-6637	51	13	equal	equal	ADJ
ap-6637	51	14	arcs	arc	NOUN
ap-6637	51	15	that	that	PRON
ap-6637	51	16	intersect	intersect	ADJ
ap-6637	51	17	on	on	ADP
ap-6637	51	18	a	a	DET
ap-6637	51	19	circle	circle	NOUN
ap-6637	51	20	of	of	ADP
ap-6637	51	21	radius	radius	NOUN
ap-6637	51	22	ro	ro	PROPN
ap-6637	51	23	at	at	ADP
ap-6637	51	24	right	right	ADJ
ap-6637	51	25	angle	angle	NOUN
ap-6637	51	26	(	(	PUNCT
ap-6637	51	27	fig	fig	NOUN
ap-6637	51	28	.	.	PUNCT
ap-6637	52	1	1,a	1,a	NUM
ap-6637	52	2	)	)	PUNCT
ap-6637	52	3	.	.	PUNCT
ap-6637	53	1	313	313	NUM
ap-6637	53	2	https://doi.org/10.14311/ap.2020.60.0313	https://doi.org/10.14311/ap.2020.60.0313	PROPN
ap-6637	53	3	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-6637	53	4	t.	t.	NOUN
ap-6637	53	5	kresan	kresan	NOUN
ap-6637	53	6	,	,	PUNCT
ap-6637	53	7	s.	s.	PROPN
ap-6637	53	8	pylypaka	pylypaka	PROPN
ap-6637	53	9	,	,	PUNCT
ap-6637	53	10	z.	z.	PROPN
ap-6637	53	11	ruzhylo	ruzhylo	PROPN
ap-6637	53	12	et	et	PROPN
ap-6637	53	13	al	al	PROPN
ap-6637	53	14	.	.	PROPN
ap-6637	53	15	acta	acta	PROPN
ap-6637	53	16	polytechnica	polytechnica	PROPN
ap-6637	53	17	figure	figure	NOUN
ap-6637	53	18	1	1	NUM
ap-6637	53	19	.	.	PUNCT
ap-6637	53	20	graphic	graphic	ADJ
ap-6637	53	21	illustrations	illustration	NOUN
ap-6637	53	22	for	for	ADP
ap-6637	53	23	rolling	roll	VERB
ap-6637	53	24	a	a	DET
ap-6637	53	25	square	square	NOUN
ap-6637	53	26	along	along	ADP
ap-6637	53	27	a	a	DET
ap-6637	53	28	curvilinear	curvilinear	ADJ
ap-6637	53	29	contour	contour	NOUN
ap-6637	53	30	:	:	PUNCT
ap-6637	53	31	a	a	X
ap-6637	53	32	)	)	PUNCT
ap-6637	53	33	schematic	schematic	ADJ
ap-6637	53	34	representation	representation	NOUN
ap-6637	53	35	of	of	ADP
ap-6637	53	36	the	the	DET
ap-6637	53	37	two	two	NUM
ap-6637	53	38	positions	position	NOUN
ap-6637	53	39	of	of	ADP
ap-6637	53	40	the	the	DET
ap-6637	53	41	square	square	NOUN
ap-6637	53	42	when	when	SCONJ
ap-6637	53	43	it	it	PRON
ap-6637	53	44	is	be	AUX
ap-6637	53	45	rolling	roll	VERB
ap-6637	53	46	;	;	PUNCT
ap-6637	53	47	b	b	X
ap-6637	53	48	)	)	PUNCT
ap-6637	53	49	the	the	DET
ap-6637	53	50	current	current	ADJ
ap-6637	53	51	point	point	NOUN
ap-6637	53	52	of	of	ADP
ap-6637	53	53	contact	contact	NOUN
ap-6637	53	54	a	a	PRON
ap-6637	53	55	’	'	PUNCT
ap-6637	53	56	in	in	ADP
ap-6637	53	57	the	the	DET
ap-6637	53	58	polar	polar	ADJ
ap-6637	53	59	coordinate	coordinate	NOUN
ap-6637	53	60	system	system	NOUN
ap-6637	53	61	.	.	PUNCT
ap-6637	54	1	in	in	ADP
ap-6637	54	2	fig	fig	NOUN
ap-6637	54	3	.	.	PUNCT
ap-6637	55	1	1,a	1,a	NUM
ap-6637	55	2	,	,	PUNCT
ap-6637	55	3	it	it	PRON
ap-6637	55	4	is	be	AUX
ap-6637	55	5	shown	show	VERB
ap-6637	55	6	that	that	SCONJ
ap-6637	55	7	in	in	ADP
ap-6637	55	8	the	the	DET
ap-6637	55	9	position	position	NOUN
ap-6637	55	10	when	when	SCONJ
ap-6637	55	11	the	the	DET
ap-6637	55	12	point	point	NOUN
ap-6637	55	13	of	of	ADP
ap-6637	55	14	contact	contact	NOUN
ap-6637	55	15	with	with	ADP
ap-6637	55	16	the	the	DET
ap-6637	55	17	curve	curve	NOUN
ap-6637	55	18	is	be	AUX
ap-6637	55	19	the	the	DET
ap-6637	55	20	vertex	vertex	NOUN
ap-6637	55	21	of	of	ADP
ap-6637	55	22	the	the	DET
ap-6637	55	23	square	square	NOUN
ap-6637	55	24	,	,	PUNCT
ap-6637	55	25	its	its	PRON
ap-6637	55	26	centre	centre	NOUN
ap-6637	55	27	is	be	AUX
ap-6637	55	28	on	on	ADP
ap-6637	55	29	the	the	DET
ap-6637	55	30	radius	radius	NOUN
ap-6637	55	31	-	-	PUNCT
ap-6637	55	32	vector	vector	NOUN
ap-6637	55	33	oc	oc	NOUN
ap-6637	55	34	’	'	PUNCT
ap-6637	55	35	.	.	PUNCT
ap-6637	56	1	this	this	PRON
ap-6637	56	2	applies	apply	VERB
ap-6637	56	3	to	to	ADP
ap-6637	56	4	any	any	DET
ap-6637	56	5	current	current	ADJ
ap-6637	56	6	point	point	NOUN
ap-6637	56	7	of	of	ADP
ap-6637	56	8	contact	contact	NOUN
ap-6637	56	9	of	of	ADP
ap-6637	56	10	the	the	DET
ap-6637	56	11	side	side	NOUN
ap-6637	56	12	of	of	ADP
ap-6637	56	13	the	the	DET
ap-6637	56	14	square	square	NOUN
ap-6637	56	15	with	with	ADP
ap-6637	56	16	the	the	DET
ap-6637	56	17	curve	curve	NOUN
ap-6637	56	18	.	.	PUNCT
ap-6637	57	1	let	let	VERB
ap-6637	57	2	the	the	DET
ap-6637	57	3	triangle	triangle	NOUN
ap-6637	57	4	,	,	PUNCT
ap-6637	57	5	which	which	PRON
ap-6637	57	6	is	be	AUX
ap-6637	57	7	the	the	DET
ap-6637	57	8	fourth	fourth	ADJ
ap-6637	57	9	part	part	NOUN
ap-6637	57	10	of	of	ADP
ap-6637	57	11	the	the	DET
ap-6637	57	12	square	square	NOUN
ap-6637	57	13	,	,	PUNCT
ap-6637	57	14	touch	touch	VERB
ap-6637	57	15	the	the	DET
ap-6637	57	16	curve	curve	NOUN
ap-6637	57	17	at	at	ADP
ap-6637	57	18	the	the	DET
ap-6637	57	19	current	current	ADJ
ap-6637	57	20	point	point	NOUN
ap-6637	57	21	a	a	DET
ap-6637	57	22	’	'	PUNCT
ap-6637	57	23	(	(	PUNCT
ap-6637	57	24	fig	fig	NOUN
ap-6637	57	25	.	.	PUNCT
ap-6637	58	1	1,b	1,b	NUM
ap-6637	58	2	)	)	PUNCT
ap-6637	58	3	.	.	PUNCT
ap-6637	59	1	as	as	SCONJ
ap-6637	59	2	it	it	PRON
ap-6637	59	3	is	be	AUX
ap-6637	59	4	rolling	roll	VERB
ap-6637	59	5	without	without	ADP
ap-6637	59	6	sliding	slide	VERB
ap-6637	59	7	,	,	PUNCT
ap-6637	59	8	the	the	DET
ap-6637	59	9	current	current	ADJ
ap-6637	59	10	point	point	NOUN
ap-6637	59	11	of	of	ADP
ap-6637	59	12	contact	contact	NOUN
ap-6637	59	13	a	a	PRON
ap-6637	59	14	’	'	PUNCT
ap-6637	59	15	can	can	AUX
ap-6637	59	16	be	be	AUX
ap-6637	59	17	considered	consider	VERB
ap-6637	59	18	as	as	ADP
ap-6637	59	19	the	the	DET
ap-6637	59	20	instantaneous	instantaneous	ADJ
ap-6637	59	21	centre	centre	NOUN
ap-6637	59	22	of	of	ADP
ap-6637	59	23	the	the	DET
ap-6637	59	24	rotation	rotation	NOUN
ap-6637	59	25	of	of	ADP
ap-6637	59	26	the	the	DET
ap-6637	59	27	segment	segment	NOUN
ap-6637	59	28	a’c	a’c	NOUN
ap-6637	59	29	’	'	PUNCT
ap-6637	59	30	around	around	ADP
ap-6637	59	31	it	it	PRON
ap-6637	59	32	.	.	PUNCT
ap-6637	60	1	in	in	ADP
ap-6637	60	2	this	this	DET
ap-6637	60	3	case	case	NOUN
ap-6637	60	4	,	,	PUNCT
ap-6637	60	5	the	the	DET
ap-6637	60	6	direction	direction	NOUN
ap-6637	60	7	of	of	ADP
ap-6637	60	8	the	the	DET
ap-6637	60	9	velocity	velocity	NOUN
ap-6637	60	10	of	of	ADP
ap-6637	60	11	the	the	DET
ap-6637	60	12	point	point	NOUN
ap-6637	60	13	c	c	NOUN
ap-6637	60	14	’	'	PUNCT
ap-6637	60	15	must	must	AUX
ap-6637	60	16	be	be	AUX
ap-6637	60	17	perpendicular	perpendicular	ADJ
ap-6637	60	18	to	to	ADP
ap-6637	60	19	the	the	DET
ap-6637	60	20	segment	segment	NOUN
ap-6637	60	21	a’c	a’c	PRON
ap-6637	60	22	’	'	PUNCT
ap-6637	60	23	.	.	PUNCT
ap-6637	61	1	however	however	ADV
ap-6637	61	2	,	,	PUNCT
ap-6637	61	3	on	on	ADP
ap-6637	61	4	condition	condition	NOUN
ap-6637	61	5	that	that	SCONJ
ap-6637	61	6	the	the	DET
ap-6637	61	7	point	point	NOUN
ap-6637	61	8	c	c	NOUN
ap-6637	61	9	’	'	PUNCT
ap-6637	61	10	moves	move	NOUN
ap-6637	61	11	in	in	ADP
ap-6637	61	12	a	a	DET
ap-6637	61	13	circle	circle	NOUN
ap-6637	61	14	of	of	ADP
ap-6637	61	15	a	a	DET
ap-6637	61	16	radius	radius	NOUN
ap-6637	61	17	r	r	NOUN
ap-6637	61	18	,	,	PUNCT
ap-6637	61	19	that	that	ADV
ap-6637	61	20	is	is	ADV
ap-6637	61	21	,	,	PUNCT
ap-6637	61	22	it	it	PRON
ap-6637	61	23	must	must	AUX
ap-6637	61	24	be	be	AUX
ap-6637	61	25	perpendicular	perpendicular	ADJ
ap-6637	61	26	to	to	ADP
ap-6637	61	27	the	the	DET
ap-6637	61	28	radius	radius	NOUN
ap-6637	61	29	-	-	PUNCT
ap-6637	61	30	vector	vector	NOUN
ap-6637	61	31	oc	oc	NOUN
ap-6637	61	32	’	'	PUNCT
ap-6637	61	33	.	.	PUNCT
ap-6637	62	1	thus	thus	ADV
ap-6637	62	2	,	,	PUNCT
ap-6637	62	3	the	the	DET
ap-6637	62	4	centre	centre	NOUN
ap-6637	62	5	of	of	ADP
ap-6637	62	6	the	the	DET
ap-6637	62	7	square	square	ADJ
ap-6637	62	8	c	c	NOUN
ap-6637	62	9	’	'	PUNCT
ap-6637	62	10	(	(	PUNCT
ap-6637	62	11	or	or	CCONJ
ap-6637	62	12	the	the	DET
ap-6637	62	13	vertex	vertex	NOUN
ap-6637	62	14	of	of	ADP
ap-6637	62	15	the	the	DET
ap-6637	62	16	corresponding	corresponding	ADJ
ap-6637	62	17	triangle	triangle	NOUN
ap-6637	62	18	,	,	PUNCT
ap-6637	62	19	whose	whose	DET
ap-6637	62	20	base	base	NOUN
ap-6637	62	21	is	be	AUX
ap-6637	62	22	the	the	DET
ap-6637	62	23	side	side	NOUN
ap-6637	62	24	of	of	ADP
ap-6637	62	25	the	the	DET
ap-6637	62	26	square	square	NOUN
ap-6637	62	27	)	)	PUNCT
ap-6637	62	28	and	and	CCONJ
ap-6637	62	29	the	the	DET
ap-6637	62	30	point	point	NOUN
ap-6637	62	31	of	of	ADP
ap-6637	62	32	contact	contact	NOUN
ap-6637	62	33	of	of	ADP
ap-6637	62	34	the	the	DET
ap-6637	62	35	side	side	NOUN
ap-6637	62	36	of	of	ADP
ap-6637	62	37	square	square	PROPN
ap-6637	62	38	a	a	PRON
ap-6637	62	39	’	'	PUNCT
ap-6637	62	40	are	be	AUX
ap-6637	62	41	located	locate	VERB
ap-6637	62	42	on	on	ADP
ap-6637	62	43	a	a	DET
ap-6637	62	44	common	common	ADJ
ap-6637	62	45	radius	radius	NOUN
ap-6637	62	46	-	-	PUNCT
ap-6637	62	47	vector	vector	NOUN
ap-6637	62	48	that	that	PRON
ap-6637	62	49	starts	start	VERB
ap-6637	62	50	at	at	ADP
ap-6637	62	51	the	the	DET
ap-6637	62	52	origin	origin	NOUN
ap-6637	62	53	.	.	PUNCT
ap-6637	63	1	due	due	ADP
ap-6637	63	2	to	to	ADP
ap-6637	63	3	this	this	PRON
ap-6637	63	4	,	,	PUNCT
ap-6637	63	5	the	the	DET
ap-6637	63	6	equation	equation	NOUN
ap-6637	63	7	of	of	ADP
ap-6637	63	8	the	the	DET
ap-6637	63	9	curve	curve	NOUN
ap-6637	63	10	of	of	ADP
ap-6637	63	11	the	the	DET
ap-6637	63	12	profile	profile	NOUN
ap-6637	63	13	is	be	AUX
ap-6637	63	14	conveniently	conveniently	ADV
ap-6637	63	15	considered	consider	VERB
ap-6637	63	16	in	in	ADP
ap-6637	63	17	the	the	DET
ap-6637	63	18	polar	polar	ADJ
ap-6637	63	19	coordinate	coordinate	NOUN
ap-6637	63	20	system	system	NOUN
ap-6637	63	21	.	.	PUNCT
ap-6637	64	1	denote	denote	VERB
ap-6637	64	2	the	the	DET
ap-6637	64	3	distance	distance	NOUN
ap-6637	64	4	from	from	ADP
ap-6637	64	5	the	the	DET
ap-6637	64	6	origin	origin	NOUN
ap-6637	64	7	of	of	ADP
ap-6637	64	8	coordinates	coordinate	NOUN
ap-6637	64	9	to	to	ADP
ap-6637	64	10	the	the	DET
ap-6637	64	11	point	point	NOUN
ap-6637	64	12	of	of	ADP
ap-6637	64	13	contact	contact	NOUN
ap-6637	64	14	oa’=ρ	oa’=ρ	NOUN
ap-6637	64	15	(	(	PUNCT
ap-6637	64	16	fig	fig	NOUN
ap-6637	64	17	.	.	PUNCT
ap-6637	65	1	1,b	1,b	NUM
ap-6637	65	2	)	)	PUNCT
ap-6637	65	3	,	,	PUNCT
ap-6637	65	4	where	where	SCONJ
ap-6637	65	5	ρ	ρ	PROPN
ap-6637	65	6	is	be	AUX
ap-6637	65	7	a	a	DET
ap-6637	65	8	function	function	NOUN
ap-6637	65	9	of	of	ADP
ap-6637	65	10	the	the	DET
ap-6637	65	11	angle	angle	NOUN
ap-6637	65	12	α	α	NOUN
ap-6637	65	13	:	:	PUNCT
ap-6637	65	14	ρ	ρ	PROPN
ap-6637	65	15	=	=	NOUN
ap-6637	65	16	ρ(α	ρ(α	NOUN
ap-6637	65	17	)	)	PUNCT
ap-6637	65	18	.	.	PUNCT
ap-6637	66	1	the	the	DET
ap-6637	66	2	constant	constant	ADJ
ap-6637	66	3	distance	distance	NOUN
ap-6637	66	4	r	r	NOUN
ap-6637	66	5	is	be	AUX
ap-6637	66	6	the	the	DET
ap-6637	66	7	sum	sum	NOUN
ap-6637	66	8	of	of	ADP
ap-6637	66	9	two	two	NUM
ap-6637	66	10	segments	segment	NOUN
ap-6637	66	11	of	of	ADP
ap-6637	66	12	variable	variable	ADJ
ap-6637	66	13	lengths	length	NOUN
ap-6637	66	14	:	:	PUNCT
ap-6637	66	15	r	r	NOUN
ap-6637	66	16	=	=	SYM
ap-6637	66	17	ρ+a’c	ρ+a’c	NUM
ap-6637	66	18	’	'	PUNCT
ap-6637	66	19	.	.	PUNCT
ap-6637	67	1	the	the	DET
ap-6637	67	2	length	length	NOUN
ap-6637	67	3	of	of	ADP
ap-6637	67	4	the	the	DET
ap-6637	67	5	hypotenuse	hypotenuse	NOUN
ap-6637	67	6	a’c	a’c	NOUN
ap-6637	67	7	’	'	PUNCT
ap-6637	67	8	can	can	AUX
ap-6637	67	9	be	be	AUX
ap-6637	67	10	found	find	VERB
ap-6637	67	11	from	from	ADP
ap-6637	67	12	the	the	DET
ap-6637	67	13	right	right	ADJ
ap-6637	67	14	triangle	triangle	NOUN
ap-6637	67	15	a’c’b	a’c’b	ADV
ap-6637	67	16	.	.	PUNCT
ap-6637	68	1	we	we	PRON
ap-6637	68	2	find	find	VERB
ap-6637	68	3	the	the	DET
ap-6637	68	4	expressions	expression	NOUN
ap-6637	68	5	of	of	ADP
ap-6637	68	6	the	the	DET
ap-6637	68	7	lengths	length	NOUN
ap-6637	68	8	of	of	ADP
ap-6637	68	9	the	the	DET
ap-6637	68	10	legs	leg	NOUN
ap-6637	68	11	a’b	a’b	NOUN
ap-6637	68	12	and	and	CCONJ
ap-6637	68	13	bc	bc	PROPN
ap-6637	68	14	’	'	PUNCT
ap-6637	68	15	for	for	ADP
ap-6637	68	16	the	the	DET
ap-6637	68	17	current	current	ADJ
ap-6637	68	18	tangency	tangency	NOUN
ap-6637	68	19	point	point	NOUN
ap-6637	68	20	a	a	PRON
ap-6637	68	21	’	'	PUNCT
ap-6637	68	22	.	.	PUNCT
ap-6637	69	1	for	for	ADP
ap-6637	69	2	a	a	DET
ap-6637	69	3	better	well	ADJ
ap-6637	69	4	understanding	understanding	NOUN
ap-6637	69	5	of	of	ADP
ap-6637	69	6	the	the	DET
ap-6637	69	7	rolling	rolling	ADJ
ap-6637	69	8	process	process	NOUN
ap-6637	69	9	,	,	PUNCT
ap-6637	69	10	consider	consider	VERB
ap-6637	69	11	the	the	DET
ap-6637	69	12	moving	move	VERB
ap-6637	69	13	coordinate	coordinate	NOUN
ap-6637	69	14	system	system	NOUN
ap-6637	69	15	the	the	DET
ap-6637	69	16	accompanying	accompanying	ADJ
ap-6637	69	17	trihedral	trihedral	NOUN
ap-6637	69	18	of	of	ADP
ap-6637	69	19	the	the	DET
ap-6637	69	20	curve	curve	NOUN
ap-6637	69	21	of	of	ADP
ap-6637	69	22	the	the	DET
ap-6637	69	23	profile	profile	NOUN
ap-6637	69	24	,	,	PUNCT
ap-6637	69	25	in	in	ADP
ap-6637	69	26	which	which	PRON
ap-6637	69	27	the	the	DET
ap-6637	69	28	unit	unit	NOUN
ap-6637	69	29	vector	vector	NOUN
ap-6637	69	30	τ	τ	PROPN
ap-6637	69	31	is	be	AUX
ap-6637	69	32	tangent	tangent	ADJ
ap-6637	69	33	to	to	ADP
ap-6637	69	34	it	it	PRON
ap-6637	69	35	,	,	PUNCT
ap-6637	69	36	the	the	DET
ap-6637	69	37	unit	unit	NOUN
ap-6637	69	38	vector	vector	NOUN
ap-6637	69	39	n	n	PROPN
ap-6637	69	40	is	be	AUX
ap-6637	69	41	perpendicular	perpendicular	ADJ
ap-6637	69	42	,	,	PUNCT
ap-6637	69	43	and	and	CCONJ
ap-6637	69	44	the	the	DET
ap-6637	69	45	unit	unit	NOUN
ap-6637	69	46	vector	vector	NOUN
ap-6637	69	47	of	of	ADP
ap-6637	69	48	the	the	DET
ap-6637	69	49	binormal	binormal	ADJ
ap-6637	69	50	b	b	PROPN
ap-6637	69	51	is	be	AUX
ap-6637	69	52	projected	project	VERB
ap-6637	69	53	to	to	ADP
ap-6637	69	54	a	a	DET
ap-6637	69	55	point	point	NOUN
ap-6637	69	56	.	.	PUNCT
ap-6637	70	1	the	the	DET
ap-6637	70	2	vertex	vertex	NOUN
ap-6637	70	3	of	of	ADP
ap-6637	70	4	the	the	DET
ap-6637	70	5	trihedral	trihedral	NOUN
ap-6637	70	6	is	be	AUX
ap-6637	70	7	point	point	NOUN
ap-6637	70	8	à	à	X
ap-6637	70	9	in	in	ADP
ap-6637	70	10	its	its	PRON
ap-6637	70	11	initial	initial	ADJ
ap-6637	70	12	position	position	NOUN
ap-6637	70	13	,	,	PUNCT
ap-6637	70	14	with	with	ADP
ap-6637	70	15	the	the	DET
ap-6637	70	16	altitude	altitude	NOUN
ap-6637	70	17	ac	ac	ADP
ap-6637	70	18	lying	lie	VERB
ap-6637	70	19	on	on	ADP
ap-6637	70	20	the	the	DET
ap-6637	70	21	ox	ox	ADJ
ap-6637	70	22	axis	axis	NOUN
ap-6637	70	23	(	(	PUNCT
ap-6637	70	24	fig	fig	NOUN
ap-6637	70	25	.	.	PUNCT
ap-6637	71	1	1	1	NUM
ap-6637	71	2	,	,	PUNCT
ap-6637	71	3	a	a	DET
ap-6637	71	4	,	,	PUNCT
ap-6637	71	5	b	b	NOUN
ap-6637	71	6	)	)	PUNCT
ap-6637	71	7	,	,	PUNCT
ap-6637	71	8	which	which	PRON
ap-6637	71	9	coincides	coincide	VERB
ap-6637	71	10	with	with	ADP
ap-6637	71	11	the	the	DET
ap-6637	71	12	unit	unit	NOUN
ap-6637	71	13	normal	normal	ADJ
ap-6637	71	14	vector	vector	NOUN
ap-6637	71	15	n	n	CCONJ
ap-6637	71	16	(	(	PUNCT
ap-6637	71	17	fig	fig	NOUN
ap-6637	71	18	.	.	PUNCT
ap-6637	72	1	1	1	NUM
ap-6637	72	2	,	,	PUNCT
ap-6637	72	3	b	b	NOUN
ap-6637	72	4	)	)	PUNCT
ap-6637	72	5	.	.	PUNCT
ap-6637	73	1	when	when	SCONJ
ap-6637	73	2	rolling	roll	VERB
ap-6637	73	3	the	the	DET
ap-6637	73	4	triangle	triangle	NOUN
ap-6637	73	5	,	,	PUNCT
ap-6637	73	6	the	the	DET
ap-6637	73	7	point	point	NOUN
ap-6637	73	8	of	of	ADP
ap-6637	73	9	contact	contact	NOUN
ap-6637	73	10	a	a	PRON
ap-6637	73	11	’	'	PUNCT
ap-6637	73	12	,	,	PUNCT
ap-6637	73	13	which	which	PRON
ap-6637	73	14	is	be	AUX
ap-6637	73	15	the	the	DET
ap-6637	73	16	vertex	vertex	NOUN
ap-6637	73	17	of	of	ADP
ap-6637	73	18	the	the	DET
ap-6637	73	19	trihedral	trihedral	NOUN
ap-6637	73	20	,	,	PUNCT
ap-6637	73	21	moves	move	NOUN
ap-6637	73	22	along	along	ADP
ap-6637	73	23	the	the	DET
ap-6637	73	24	curve	curve	NOUN
ap-6637	73	25	and	and	CCONJ
ap-6637	73	26	unit	unit	NOUN
ap-6637	73	27	vector	vector	NOUN
ap-6637	73	28	τ	τ	PROPN
ap-6637	73	29	remains	remain	VERB
ap-6637	73	30	tangent	tangent	ADJ
ap-6637	73	31	to	to	ADP
ap-6637	73	32	the	the	DET
ap-6637	73	33	curve	curve	NOUN
ap-6637	73	34	.	.	PUNCT
ap-6637	74	1	in	in	ADP
ap-6637	74	2	the	the	DET
ap-6637	74	3	initial	initial	ADJ
ap-6637	74	4	position	position	NOUN
ap-6637	74	5	τn	τn	ADP
ap-6637	74	6	of	of	ADP
ap-6637	74	7	the	the	DET
ap-6637	74	8	trihedral	trihedral	ADJ
ap-6637	74	9	,	,	PUNCT
ap-6637	74	10	points	point	VERB
ap-6637	74	11	a	a	PRON
ap-6637	74	12	and	and	CCONJ
ap-6637	74	13	b	b	NUM
ap-6637	74	14	coincided	coincide	VERB
ap-6637	74	15	,	,	PUNCT
ap-6637	74	16	and	and	CCONJ
ap-6637	74	17	the	the	DET
ap-6637	74	18	altitude	altitude	NOUN
ap-6637	74	19	a	a	PRON
ap-6637	74	20	of	of	ADP
ap-6637	74	21	the	the	DET
ap-6637	74	22	triangle	triangle	NOUN
ap-6637	74	23	coincided	coincide	VERB
ap-6637	74	24	with	with	ADP
ap-6637	74	25	the	the	DET
ap-6637	74	26	unit	unit	NOUN
ap-6637	74	27	vectorn	vectorn	VERB
ap-6637	74	28	.	.	PUNCT
ap-6637	75	1	when	when	SCONJ
ap-6637	75	2	rolling	roll	VERB
ap-6637	75	3	a	a	DET
ap-6637	75	4	triangle	triangle	NOUN
ap-6637	75	5	along	along	ADP
ap-6637	75	6	the	the	DET
ap-6637	75	7	curve	curve	NOUN
ap-6637	75	8	,	,	PUNCT
ap-6637	75	9	the	the	DET
ap-6637	75	10	trihedral	trihedral	ADJ
ap-6637	75	11	occupies	occupy	VERB
ap-6637	75	12	a	a	DET
ap-6637	75	13	new	new	ADJ
ap-6637	75	14	position	position	NOUN
ap-6637	75	15	τ	τ	X
ap-6637	75	16	′n′	′n′	VERB
ap-6637	75	17	with	with	ADP
ap-6637	75	18	the	the	DET
ap-6637	75	19	vertex	vertex	NOUN
ap-6637	75	20	at	at	ADP
ap-6637	75	21	point	point	NOUN
ap-6637	75	22	a	a	PRON
ap-6637	75	23	’	'	PUNCT
ap-6637	75	24	(	(	PUNCT
ap-6637	75	25	fig	fig	NOUN
ap-6637	75	26	.	.	PUNCT
ap-6637	76	1	1,b	1,b	NUM
ap-6637	76	2	)	)	PUNCT
ap-6637	76	3	.	.	PUNCT
ap-6637	77	1	the	the	DET
ap-6637	77	2	coordinates	coordinate	NOUN
ap-6637	77	3	of	of	ADP
ap-6637	77	4	the	the	DET
ap-6637	77	5	point	point	NOUN
ap-6637	77	6	c	c	NOUN
ap-6637	77	7	’	'	PUNCT
ap-6637	77	8	in	in	ADP
ap-6637	77	9	its	its	PRON
ap-6637	77	10	system	system	NOUN
ap-6637	77	11	are	be	AUX
ap-6637	77	12	as	as	SCONJ
ap-6637	77	13	follows	follow	VERB
ap-6637	77	14	.	.	PUNCT
ap-6637	78	1	the	the	DET
ap-6637	78	2	segment	segment	NOUN
ap-6637	78	3	a’b	a’b	PROPN
ap-6637	78	4	is	be	AUX
ap-6637	78	5	equal	equal	ADJ
ap-6637	78	6	to	to	ADP
ap-6637	78	7	the	the	DET
ap-6637	78	8	length	length	NOUN
ap-6637	78	9	of	of	ADP
ap-6637	78	10	the	the	DET
ap-6637	78	11	arc	arc	NOUN
ap-6637	78	12	aa	aa	NOUN
ap-6637	78	13	’	'	PUNCT
ap-6637	78	14	of	of	ADP
ap-6637	78	15	the	the	DET
ap-6637	78	16	curve	curve	NOUN
ap-6637	78	17	:	:	PUNCT
ap-6637	78	18	aa’=a’b	aa’=a’b	NOUN
ap-6637	79	1	=	=	SYM
ap-6637	79	2	s.	s.	NOUN
ap-6637	79	3	the	the	DET
ap-6637	79	4	altitude	altitude	NOUN
ap-6637	79	5	a	a	PRON
ap-6637	79	6	of	of	ADP
ap-6637	79	7	the	the	DET
ap-6637	79	8	triangle	triangle	NOUN
ap-6637	79	9	when	when	SCONJ
ap-6637	79	10	it	it	PRON
ap-6637	79	11	is	be	AUX
ap-6637	79	12	rolling	roll	VERB
ap-6637	79	13	remains	remain	VERB
ap-6637	79	14	parallel	parallel	ADJ
ap-6637	79	15	to	to	ADP
ap-6637	79	16	the	the	DET
ap-6637	79	17	principal	principal	NOUN
ap-6637	79	18	normaln′	normaln′	NOUN
ap-6637	79	19	.	.	PUNCT
ap-6637	80	1	so	so	ADV
ap-6637	80	2	the	the	DET
ap-6637	80	3	length	length	NOUN
ap-6637	80	4	of	of	ADP
ap-6637	80	5	the	the	DET
ap-6637	80	6	segment	segment	NOUN
ap-6637	80	7	a’c	a’c	PRON
ap-6637	80	8	’	'	PUNCT
ap-6637	80	9	is	be	AUX
ap-6637	80	10	determined	determine	VERB
ap-6637	80	11	by	by	ADP
ap-6637	80	12	the	the	DET
ap-6637	80	13	pythagorean	pythagorean	PROPN
ap-6637	80	14	theorem	theorem	PROPN
ap-6637	80	15	:	:	PUNCT
ap-6637	80	16	a′c	a′c	ADJ
ap-6637	80	17	′	′	NUM
ap-6637	80	18	=	=	PUNCT
ap-6637	80	19	√	√	PROPN
ap-6637	80	20	s2	s2	PROPN
ap-6637	80	21	+	+	NUM
ap-6637	80	22	a2	a2	PROPN
ap-6637	80	23	.	.	PUNCT
ap-6637	81	1	the	the	DET
ap-6637	81	2	expression	expression	NOUN
ap-6637	81	3	r	r	NOUN
ap-6637	81	4	=	=	NOUN
ap-6637	81	5	ρ+a’c	ρ+a’c	NUM
ap-6637	81	6	’	'	PUNCT
ap-6637	81	7	can	can	AUX
ap-6637	81	8	be	be	AUX
ap-6637	81	9	written	write	VERB
ap-6637	81	10	as	as	SCONJ
ap-6637	81	11	follows	follow	VERB
ap-6637	81	12	:	:	PUNCT
ap-6637	81	13	r	r	NOUN
ap-6637	81	14	=	=	SYM
ap-6637	81	15	ρ+	ρ+	NOUN
ap-6637	81	16	√	√	NUM
ap-6637	81	17	s2	s2	PROPN
ap-6637	81	18	+	+	CCONJ
ap-6637	81	19	a2	a2	PROPN
ap-6637	81	20	.	.	PUNCT
ap-6637	82	1	(	(	PUNCT
ap-6637	82	2	1	1	X
ap-6637	82	3	)	)	PUNCT
ap-6637	82	4	let‘s	let‘s	NOUN
ap-6637	82	5	solve	solve	VERB
ap-6637	82	6	equation	equation	NOUN
ap-6637	82	7	(	(	PUNCT
ap-6637	82	8	1	1	NUM
ap-6637	82	9	)	)	PUNCT
ap-6637	82	10	for	for	ADP
ap-6637	82	11	s	s	NOUN
ap-6637	82	12	:	:	PUNCT
ap-6637	82	13	s	s	PART
ap-6637	82	14	=	=	PUNCT
ap-6637	82	15	√	√	INTJ
ap-6637	82	16	(	(	PUNCT
ap-6637	82	17	r	r	NOUN
ap-6637	82	18	−	−	PROPN
ap-6637	82	19	ρ)2	ρ)2	PROPN
ap-6637	82	20	−	−	PROPN
ap-6637	82	21	a2	a2	PROPN
ap-6637	82	22	.	.	PUNCT
ap-6637	83	1	(	(	PUNCT
ap-6637	83	2	2	2	X
ap-6637	83	3	)	)	PUNCT
ap-6637	83	4	let‘s	let‘s	NOUN
ap-6637	83	5	write	write	VERB
ap-6637	83	6	the	the	DET
ap-6637	83	7	parametric	parametric	ADJ
ap-6637	83	8	equations	equation	NOUN
ap-6637	83	9	of	of	ADP
ap-6637	83	10	the	the	DET
ap-6637	83	11	curve	curve	NOUN
ap-6637	83	12	of	of	ADP
ap-6637	83	13	the	the	DET
ap-6637	83	14	profile	profile	NOUN
ap-6637	83	15	in	in	ADP
ap-6637	83	16	the	the	DET
ap-6637	83	17	polar	polar	ADJ
ap-6637	83	18	coordinate	coordinate	NOUN
ap-6637	83	19	system	system	NOUN
ap-6637	83	20	:	:	PUNCT
ap-6637	83	21	x	x	SYM
ap-6637	83	22	=	=	SYM
ap-6637	83	23	ρ	ρ	NUM
ap-6637	83	24	cosα	cosα	NOUN
ap-6637	83	25	;	;	PUNCT
ap-6637	83	26	y	y	PROPN
ap-6637	83	27	=	=	SYM
ap-6637	83	28	ρ	ρ	PROPN
ap-6637	83	29	sinα	sinα	PROPN
ap-6637	83	30	.	.	PUNCT
ap-6637	84	1	(	(	PUNCT
ap-6637	84	2	3	3	X
ap-6637	84	3	)	)	PUNCT
ap-6637	84	4	let‘s	let‘s	NOUN
ap-6637	84	5	find	find	VERB
ap-6637	84	6	the	the	DET
ap-6637	84	7	expression	expression	NOUN
ap-6637	84	8	of	of	ADP
ap-6637	84	9	the	the	DET
ap-6637	84	10	arc	arc	NOUN
ap-6637	84	11	length	length	NOUN
ap-6637	84	12	s	s	PROPN
ap-6637	84	13	of	of	ADP
ap-6637	84	14	the	the	DET
ap-6637	84	15	curve	curve	NOUN
ap-6637	84	16	(	(	PUNCT
ap-6637	84	17	3	3	NUM
ap-6637	84	18	)	)	PUNCT
ap-6637	84	19	.	.	PUNCT
ap-6637	85	1	to	to	PART
ap-6637	85	2	do	do	VERB
ap-6637	85	3	this	this	PRON
ap-6637	85	4	,	,	PUNCT
ap-6637	85	5	we	we	PRON
ap-6637	85	6	define	define	VERB
ap-6637	85	7	its	its	PRON
ap-6637	85	8	first	first	ADJ
ap-6637	85	9	derivatives	derivative	NOUN
ap-6637	85	10	:	:	PUNCT
ap-6637	85	11	x′	x′	X
ap-6637	85	12	=	=	SYM
ap-6637	85	13	ρ′	ρ′	PRON
ap-6637	85	14	cosα−	cosα−	NOUN
ap-6637	85	15	ρ	ρ	PROPN
ap-6637	85	16	sinα	sinα	NOUN
ap-6637	85	17	;	;	PUNCT
ap-6637	85	18	y′	y′	X
ap-6637	85	19	=	=	SYM
ap-6637	85	20	ρ′	ρ′	PROPN
ap-6637	85	21	sinα+	sinα+	NUM
ap-6637	85	22	ρ	ρ	NUM
ap-6637	85	23	cosα	cosα	NOUN
ap-6637	85	24	.	.	PUNCT
ap-6637	86	1	(	(	PUNCT
ap-6637	86	2	4	4	NUM
ap-6637	86	3	)	)	PUNCT
ap-6637	86	4	by	by	ADP
ap-6637	86	5	the	the	DET
ap-6637	86	6	known	know	VERB
ap-6637	86	7	formula	formula	NOUN
ap-6637	86	8	we	we	PRON
ap-6637	86	9	write	write	VERB
ap-6637	86	10	:	:	PUNCT
ap-6637	86	11	ds	ds	PRON
ap-6637	86	12	dα	dα	NOUN
ap-6637	86	13	=	=	PUNCT
ap-6637	86	14	√	√	PROPN
ap-6637	86	15	x′2	x′2	NOUN
ap-6637	87	1	+	+	CCONJ
ap-6637	87	2	y′2	y′2	ADJ
ap-6637	87	3	=	=	SYM
ap-6637	87	4	√	√	PROPN
ap-6637	87	5	ρ2	ρ2	PROPN
ap-6637	87	6	+	+	CCONJ
ap-6637	87	7	ρ′2	ρ′2	ADJ
ap-6637	87	8	.	.	PUNCT
ap-6637	88	1	(	(	PUNCT
ap-6637	88	2	5	5	X
ap-6637	88	3	)	)	PUNCT
ap-6637	88	4	the	the	DET
ap-6637	88	5	derivative	derivative	NOUN
ap-6637	88	6	of	of	ADP
ap-6637	88	7	arc	arc	NOUN
ap-6637	88	8	s	s	PART
ap-6637	88	9	can	can	AUX
ap-6637	88	10	be	be	AUX
ap-6637	88	11	found	find	VERB
ap-6637	88	12	by	by	ADP
ap-6637	88	13	a	a	DET
ap-6637	88	14	differentiation	differentiation	NOUN
ap-6637	88	15	of	of	ADP
ap-6637	88	16	expression	expression	NOUN
ap-6637	88	17	(	(	PUNCT
ap-6637	88	18	2	2	NUM
ap-6637	88	19	):	):	PUNCT
ap-6637	88	20	ds	ds	PRON
ap-6637	88	21	dα	dα	ADJ
ap-6637	88	22	=	=	PUNCT
ap-6637	88	23	−	−	PROPN
ap-6637	88	24	ρ′	ρ′	NUM
ap-6637	88	25	(	(	PUNCT
ap-6637	88	26	r	r	NOUN
ap-6637	88	27	−	−	PROPN
ap-6637	88	28	ρ)√	ρ)√	NOUN
ap-6637	88	29	(	(	PUNCT
ap-6637	88	30	r	r	NOUN
ap-6637	88	31	−	−	PROPN
ap-6637	88	32	ρ)2	ρ)2	PROPN
ap-6637	88	33	−	−	PROPN
ap-6637	88	34	a2	a2	PROPN
ap-6637	88	35	.	.	PUNCT
ap-6637	89	1	(	(	PUNCT
ap-6637	89	2	6	6	X
ap-6637	89	3	)	)	PUNCT
ap-6637	89	4	we	we	PRON
ap-6637	89	5	equate	equate	VERB
ap-6637	89	6	expressions	expression	NOUN
ap-6637	89	7	(	(	PUNCT
ap-6637	89	8	5	5	NUM
ap-6637	89	9	)	)	PUNCT
ap-6637	89	10	and	and	CCONJ
ap-6637	89	11	(	(	PUNCT
ap-6637	89	12	6	6	NUM
ap-6637	89	13	)	)	PUNCT
ap-6637	89	14	and	and	CCONJ
ap-6637	89	15	solve	solve	VERB
ap-6637	89	16	for	for	ADP
ap-6637	89	17	ρ	ρ	NOUN
ap-6637	89	18	’	'	PUNCT
ap-6637	89	19	:	:	PUNCT
ap-6637	89	20	dρ	dρ	ADP
ap-6637	89	21	dα	dα	VERB
ap-6637	90	1	=	=	PUNCT
ap-6637	90	2	ρ	ρ	PROPN
ap-6637	90	3	a	a	PRON
ap-6637	90	4	√	√	PROPN
ap-6637	90	5	(	(	PUNCT
ap-6637	90	6	r	r	NOUN
ap-6637	90	7	−	−	PROPN
ap-6637	90	8	ρ)2	ρ)2	PROPN
ap-6637	90	9	−	−	PROPN
ap-6637	90	10	a2	a2	PROPN
ap-6637	90	11	.	.	PUNCT
ap-6637	91	1	(	(	PUNCT
ap-6637	91	2	7	7	X
ap-6637	91	3	)	)	PUNCT
ap-6637	91	4	314	314	NUM
ap-6637	91	5	vol	vol	NOUN
ap-6637	91	6	.	.	PUNCT
ap-6637	92	1	60	60	NUM
ap-6637	92	2	no	no	INTJ
ap-6637	92	3	.	.	PUNCT
ap-6637	93	1	4/2020	4/2020	NUM
ap-6637	93	2	external	external	ADJ
ap-6637	93	3	rolling	rolling	NOUN
ap-6637	93	4	of	of	ADP
ap-6637	93	5	a	a	DET
ap-6637	93	6	polygon	polygon	NOUN
ap-6637	93	7	on	on	ADP
ap-6637	93	8	closed	close	VERB
ap-6637	93	9	curvilinear	curvilinear	PROPN
ap-6637	93	10	profile	profile	VERB
ap-6637	93	11	the	the	DET
ap-6637	93	12	differential	differential	ADJ
ap-6637	93	13	equation	equation	NOUN
ap-6637	93	14	of	of	ADP
ap-6637	93	15	first	first	ADJ
ap-6637	93	16	order	order	NOUN
ap-6637	93	17	(	(	PUNCT
ap-6637	93	18	7	7	X
ap-6637	93	19	)	)	PUNCT
ap-6637	93	20	is	be	AUX
ap-6637	93	21	obtained	obtain	VERB
ap-6637	93	22	on	on	ADP
ap-6637	93	23	the	the	DET
ap-6637	93	24	basis	basis	NOUN
ap-6637	93	25	of	of	ADP
ap-6637	93	26	the	the	DET
ap-6637	93	27	equality	equality	NOUN
ap-6637	93	28	of	of	ADP
ap-6637	93	29	the	the	DET
ap-6637	93	30	arcs	arcs	NOUN
ap-6637	93	31	of	of	ADP
ap-6637	93	32	the	the	DET
ap-6637	93	33	profile	profile	NOUN
ap-6637	93	34	curve	curve	NOUN
ap-6637	93	35	and	and	CCONJ
ap-6637	93	36	the	the	DET
ap-6637	93	37	side	side	NOUN
ap-6637	93	38	of	of	ADP
ap-6637	93	39	the	the	DET
ap-6637	93	40	square	square	NOUN
ap-6637	93	41	that	that	PRON
ap-6637	93	42	rolls	roll	VERB
ap-6637	93	43	on	on	ADP
ap-6637	93	44	it	it	PRON
ap-6637	93	45	without	without	ADP
ap-6637	93	46	sliding	slide	VERB
ap-6637	93	47	.	.	PUNCT
ap-6637	94	1	the	the	DET
ap-6637	94	2	altitude	altitude	NOUN
ap-6637	94	3	a	a	PRON
ap-6637	94	4	of	of	ADP
ap-6637	94	5	the	the	DET
ap-6637	94	6	triangle	triangle	NOUN
ap-6637	94	7	can	can	AUX
ap-6637	94	8	be	be	AUX
ap-6637	94	9	found	find	VERB
ap-6637	94	10	through	through	ADP
ap-6637	94	11	the	the	DET
ap-6637	94	12	angle	angle	NOUN
ap-6637	94	13	ε	ε	PROPN
ap-6637	94	14	:	:	PUNCT
ap-6637	94	15	a	a	DET
ap-6637	94	16	=	=	X
ap-6637	94	17	r	r	NOUN
ap-6637	94	18	·	·	PUNCT
ap-6637	94	19	cos	cos	PROPN
ap-6637	94	20	ε	ε	PROPN
ap-6637	94	21	,	,	PUNCT
ap-6637	94	22	where	where	SCONJ
ap-6637	94	23	r	r	NOUN
ap-6637	94	24	is	be	AUX
ap-6637	94	25	the	the	DET
ap-6637	94	26	length	length	NOUN
ap-6637	94	27	of	of	ADP
ap-6637	94	28	the	the	DET
ap-6637	94	29	side	side	NOUN
ap-6637	94	30	of	of	ADP
ap-6637	94	31	the	the	DET
ap-6637	94	32	triangle	triangle	NOUN
ap-6637	94	33	that	that	PRON
ap-6637	94	34	is	be	AUX
ap-6637	94	35	equal	equal	ADJ
ap-6637	94	36	to	to	ADP
ap-6637	94	37	the	the	DET
ap-6637	94	38	radius	radius	NOUN
ap-6637	94	39	of	of	ADP
ap-6637	94	40	the	the	DET
ap-6637	94	41	circle	circle	NOUN
ap-6637	94	42	circumscribed	circumscribe	VERB
ap-6637	94	43	about	about	ADP
ap-6637	94	44	the	the	DET
ap-6637	94	45	square	square	NOUN
ap-6637	94	46	.	.	PUNCT
ap-6637	95	1	let	let	VERB
ap-6637	95	2	’s	’s	PRON
ap-6637	95	3	extend	extend	VERB
ap-6637	95	4	this	this	DET
ap-6637	95	5	expression	expression	NOUN
ap-6637	95	6	to	to	ADP
ap-6637	95	7	a	a	DET
ap-6637	95	8	polygon	polygon	NOUN
ap-6637	95	9	with	with	ADP
ap-6637	95	10	an	an	DET
ap-6637	95	11	arbitrary	arbitrary	ADJ
ap-6637	95	12	number	number	NOUN
ap-6637	95	13	of	of	ADP
ap-6637	95	14	sides	side	NOUN
ap-6637	95	15	n.	n.	VERB
ap-6637	95	16	the	the	DET
ap-6637	95	17	angle	angle	NOUN
ap-6637	95	18	ε	ε	PROPN
ap-6637	95	19	,	,	PUNCT
ap-6637	95	20	in	in	ADP
ap-6637	95	21	this	this	DET
ap-6637	95	22	case	case	NOUN
ap-6637	95	23	,	,	PUNCT
ap-6637	95	24	will	will	AUX
ap-6637	95	25	depend	depend	VERB
ap-6637	95	26	on	on	ADP
ap-6637	95	27	the	the	DET
ap-6637	95	28	number	number	NOUN
ap-6637	95	29	of	of	ADP
ap-6637	95	30	sides	side	NOUN
ap-6637	95	31	of	of	ADP
ap-6637	95	32	the	the	DET
ap-6637	95	33	polygon	polygon	NOUN
ap-6637	95	34	:	:	PUNCT
ap-6637	95	35	ε	ε	PROPN
ap-6637	95	36	=	=	SYM
ap-6637	95	37	π	π	PROPN
ap-6637	95	38	/	/	SYM
ap-6637	95	39	n.	n.	NOUN
ap-6637	95	40	the	the	DET
ap-6637	95	41	differential	differential	ADJ
ap-6637	95	42	equation	equation	NOUN
ap-6637	95	43	(	(	PUNCT
ap-6637	95	44	7	7	NUM
ap-6637	95	45	)	)	PUNCT
ap-6637	95	46	for	for	ADP
ap-6637	95	47	a	a	DET
ap-6637	95	48	polygon	polygon	NOUN
ap-6637	95	49	with	with	ADP
ap-6637	95	50	an	an	DET
ap-6637	95	51	arbitrary	arbitrary	ADJ
ap-6637	95	52	number	number	NOUN
ap-6637	95	53	of	of	ADP
ap-6637	95	54	sides	side	NOUN
ap-6637	95	55	n	n	CCONJ
ap-6637	95	56	,	,	PUNCT
ap-6637	95	57	being	be	AUX
ap-6637	95	58	inscribed	inscribe	VERB
ap-6637	95	59	in	in	ADP
ap-6637	95	60	a	a	DET
ap-6637	95	61	circle	circle	NOUN
ap-6637	95	62	of	of	ADP
ap-6637	95	63	radius	radius	NOUN
ap-6637	95	64	r	r	NOUN
ap-6637	95	65	,	,	PUNCT
ap-6637	95	66	will	will	AUX
ap-6637	95	67	be	be	AUX
ap-6637	95	68	written	write	VERB
ap-6637	95	69	:	:	PUNCT
ap-6637	95	70	dρ	dρ	INTJ
ap-6637	95	71	dα	dα	ADJ
ap-6637	95	72	=	=	SYM
ap-6637	95	73	ρ	ρ	PROPN
ap-6637	95	74	r	r	NOUN
ap-6637	95	75	cos	cos	PROPN
ap-6637	95	76	(	(	PUNCT
ap-6637	95	77	π	π	PROPN
ap-6637	95	78	/	/	SYM
ap-6637	95	79	n	n	CCONJ
ap-6637	95	80	)	)	PUNCT
ap-6637	95	81	√	√	PROPN
ap-6637	95	82	(	(	PUNCT
ap-6637	95	83	r	r	NOUN
ap-6637	95	84	−	−	PROPN
ap-6637	95	85	ρ)2	ρ)2	NOUN
ap-6637	95	86	−r2	−r2	PROPN
ap-6637	95	87	cos2	cos2	NOUN
ap-6637	95	88	(	(	PUNCT
ap-6637	95	89	π	π	NOUN
ap-6637	95	90	/	/	SYM
ap-6637	95	91	n	n	CCONJ
ap-6637	95	92	)	)	PUNCT
ap-6637	95	93	.	.	PUNCT
ap-6637	96	1	(	(	PUNCT
ap-6637	96	2	8)	8)	NUM
ap-6637	96	3	differential	differential	NOUN
ap-6637	96	4	equation	equation	NOUN
ap-6637	96	5	(	(	PUNCT
ap-6637	96	6	8)	8)	NUM
ap-6637	96	7	has	have	VERB
ap-6637	96	8	an	an	DET
ap-6637	96	9	analytical	analytical	ADJ
ap-6637	96	10	solution	solution	NOUN
ap-6637	96	11	.	.	PUNCT
ap-6637	97	1	on	on	ADP
ap-6637	97	2	a	a	DET
ap-6637	97	3	condition	condition	NOUN
ap-6637	97	4	that	that	SCONJ
ap-6637	97	5	α=0	α=0	PROPN
ap-6637	97	6	ρ	ρ	NUM
ap-6637	97	7	=	=	SYM
ap-6637	97	8	r	r	VERB
ap-6637	97	9	-	-	PUNCT
ap-6637	97	10	a	a	DET
ap-6637	97	11	=	=	NOUN
ap-6637	97	12	r	r	NOUN
ap-6637	97	13	-	-	PUNCT
ap-6637	97	14	r·cos(π	r·cos(π	NOUN
ap-6637	97	15	/	/	SYM
ap-6637	97	16	n	n	CCONJ
ap-6637	97	17	)	)	PUNCT
ap-6637	97	18	,	,	PUNCT
ap-6637	97	19	we	we	PRON
ap-6637	97	20	find	find	VERB
ap-6637	97	21	the	the	DET
ap-6637	97	22	corresponding	corresponding	ADJ
ap-6637	97	23	value	value	NOUN
ap-6637	97	24	of	of	ADP
ap-6637	97	25	the	the	DET
ap-6637	97	26	constant	constant	NOUN
ap-6637	97	27	of	of	ADP
ap-6637	97	28	integration	integration	NOUN
ap-6637	97	29	.	.	PUNCT
ap-6637	98	1	with	with	ADP
ap-6637	98	2	consideration	consideration	NOUN
ap-6637	98	3	of	of	ADP
ap-6637	98	4	this	this	DET
ap-6637	98	5	constant	constant	ADJ
ap-6637	98	6	,	,	PUNCT
ap-6637	98	7	the	the	DET
ap-6637	98	8	solution	solution	NOUN
ap-6637	98	9	of	of	ADP
ap-6637	98	10	equation	equation	NOUN
ap-6637	98	11	(	(	PUNCT
ap-6637	98	12	8)	8)	NUM
ap-6637	98	13	takes	take	VERB
ap-6637	98	14	the	the	DET
ap-6637	98	15	final	final	ADJ
ap-6637	98	16	form	form	NOUN
ap-6637	98	17	:	:	PUNCT
ap-6637	98	18	ρ	ρ	PROPN
ap-6637	98	19	=	=	SYM
ap-6637	98	20	r2	r2	PROPN
ap-6637	98	21	−r2	−r2	PROPN
ap-6637	98	22	cos2	cos2	PROPN
ap-6637	98	23	(	(	PUNCT
ap-6637	98	24	π	π	NOUN
ap-6637	98	25	/	/	SYM
ap-6637	98	26	n	n	CCONJ
ap-6637	98	27	)	)	PUNCT
ap-6637	98	28	r	r	NOUN
ap-6637	99	1	+	+	NOUN
ap-6637	99	2	r	r	NOUN
ap-6637	99	3	cos	cos	PROPN
ap-6637	99	4	(	(	PUNCT
ap-6637	99	5	π	π	PROPN
ap-6637	99	6	/	/	SYM
ap-6637	99	7	n	n	CCONJ
ap-6637	99	8	)	)	PUNCT
ap-6637	99	9	cosh	cosh	NOUN
ap-6637	99	10	(	(	PUNCT
ap-6637	99	11	α	α	NOUN
ap-6637	99	12	√	√	NOUN
ap-6637	99	13	r2	r2	PROPN
ap-6637	99	14	r2	r2	PROPN
ap-6637	99	15	cos2(π	cos2(π	PROPN
ap-6637	99	16	/	/	SYM
ap-6637	99	17	n	n	CCONJ
ap-6637	99	18	)	)	PUNCT
ap-6637	99	19	−	−	PROPN
ap-6637	99	20	1	1	NUM
ap-6637	99	21	)	)	PUNCT
ap-6637	99	22	.	.	PUNCT
ap-6637	100	1	(	(	PUNCT
ap-6637	100	2	9	9	X
ap-6637	100	3	)	)	PUNCT
ap-6637	100	4	substitution	substitution	NOUN
ap-6637	100	5	(	(	PUNCT
ap-6637	100	6	9	9	NUM
ap-6637	100	7	)	)	PUNCT
ap-6637	100	8	in	in	ADP
ap-6637	100	9	(	(	PUNCT
ap-6637	100	10	3	3	X
ap-6637	100	11	)	)	PUNCT
ap-6637	100	12	will	will	AUX
ap-6637	100	13	give	give	VERB
ap-6637	100	14	parametric	parametric	ADJ
ap-6637	100	15	equations	equation	NOUN
ap-6637	100	16	of	of	ADP
ap-6637	100	17	the	the	DET
ap-6637	100	18	curve	curve	NOUN
ap-6637	100	19	.	.	PUNCT
ap-6637	101	1	we	we	PRON
ap-6637	101	2	need	need	VERB
ap-6637	101	3	a	a	DET
ap-6637	101	4	limited	limited	ADJ
ap-6637	101	5	arc	arc	NOUN
ap-6637	101	6	to	to	PART
ap-6637	101	7	construct	construct	VERB
ap-6637	101	8	a	a	DET
ap-6637	101	9	profile	profile	NOUN
ap-6637	101	10	.	.	PUNCT
ap-6637	102	1	the	the	DET
ap-6637	102	2	magnitude	magnitude	NOUN
ap-6637	102	3	of	of	ADP
ap-6637	102	4	this	this	DET
ap-6637	102	5	arc	arc	NOUN
ap-6637	102	6	is	be	AUX
ap-6637	102	7	due	due	ADJ
ap-6637	102	8	to	to	ADP
ap-6637	102	9	the	the	DET
ap-6637	102	10	minimum	minimum	ADJ
ap-6637	102	11	value	value	NOUN
ap-6637	102	12	of	of	ADP
ap-6637	102	13	the	the	DET
ap-6637	102	14	radius	radius	NOUN
ap-6637	102	15	-	-	PUNCT
ap-6637	102	16	vector	vector	NOUN
ap-6637	102	17	ρ	ρ	NOUN
ap-6637	102	18	=	=	NOUN
ap-6637	102	19	ro	ro	X
ap-6637	102	20	(	(	PUNCT
ap-6637	102	21	fig	fig	NOUN
ap-6637	102	22	.	.	PUNCT
ap-6637	103	1	1a	1a	NOUN
ap-6637	103	2	)	)	PUNCT
ap-6637	103	3	.	.	PUNCT
ap-6637	104	1	inversely	inversely	ADV
ap-6637	104	2	,	,	PUNCT
ap-6637	104	3	ro	ro	X
ap-6637	104	4	=	=	NOUN
ap-6637	104	5	r	r	NOUN
ap-6637	104	6	-	-	PUNCT
ap-6637	104	7	a’c’=r	a’c’=r	ADJ
ap-6637	104	8	-	-	PUNCT
ap-6637	104	9	r.	r.	NOUN
ap-6637	104	10	let‘s	let‘s	PROPN
ap-6637	104	11	substitute	substitute	PROPN
ap-6637	104	12	in	in	ADP
ap-6637	104	13	(	(	PUNCT
ap-6637	104	14	9	9	NUM
ap-6637	104	15	)	)	PUNCT
ap-6637	104	16	ρ	ρ	NOUN
ap-6637	104	17	=	=	NOUN
ap-6637	104	18	rr	rr	NOUN
ap-6637	104	19	and	and	CCONJ
ap-6637	104	20	solve	solve	VERB
ap-6637	104	21	for	for	ADP
ap-6637	104	22	α	α	NOUN
ap-6637	104	23	:	:	PUNCT
ap-6637	104	24	α0	α0	PROPN
ap-6637	104	25	=	=	SYM
ap-6637	104	26	±	±	PROPN
ap-6637	104	27	r	r	NOUN
ap-6637	104	28	cos	cos	PROPN
ap-6637	104	29	(	(	PUNCT
ap-6637	104	30	π	π	PROPN
ap-6637	104	31	/	/	SYM
ap-6637	104	32	n)√	n)√	PROPN
ap-6637	104	33	r2	r2	PROPN
ap-6637	104	34	−r2	−r2	PROPN
ap-6637	104	35	cos2	cos2	PROPN
ap-6637	104	36	(	(	PUNCT
ap-6637	104	37	π	π	PROPN
ap-6637	104	38	/	/	SYM
ap-6637	104	39	n	n	CCONJ
ap-6637	104	40	)	)	PUNCT
ap-6637	104	41	arc	arc	NOUN
ap-6637	104	42	cosh	cosh	NOUN
ap-6637	104	43	(	(	PUNCT
ap-6637	104	44	r	r	NOUN
ap-6637	104	45	−r	−r	ADJ
ap-6637	104	46	cos2	cos2	NOUN
ap-6637	104	47	(	(	PUNCT
ap-6637	104	48	π	π	PROPN
ap-6637	104	49	/	/	SYM
ap-6637	104	50	n	n	CCONJ
ap-6637	104	51	)	)	PUNCT
ap-6637	104	52	(	(	PUNCT
ap-6637	104	53	r	r	NOUN
ap-6637	104	54	−r	−r	NOUN
ap-6637	104	55	)	)	PUNCT
ap-6637	105	1	cos	cos	PROPN
ap-6637	105	2	(	(	PUNCT
ap-6637	105	3	π	π	PROPN
ap-6637	105	4	/	/	SYM
ap-6637	105	5	n	n	CCONJ
ap-6637	105	6	)	)	PUNCT
ap-6637	105	7	)	)	PUNCT
ap-6637	105	8	.	.	PUNCT
ap-6637	106	1	(	(	PUNCT
ap-6637	106	2	10	10	NUM
ap-6637	106	3	)	)	PUNCT
ap-6637	106	4	the	the	DET
ap-6637	106	5	wanted	wanted	ADJ
ap-6637	106	6	arc	arc	NOUN
ap-6637	106	7	of	of	ADP
ap-6637	106	8	the	the	DET
ap-6637	106	9	curve	curve	NOUN
ap-6637	106	10	at	at	ADP
ap-6637	106	11	given	give	VERB
ap-6637	106	12	values	value	NOUN
ap-6637	106	13	of	of	ADP
ap-6637	106	14	r	r	NOUN
ap-6637	106	15	,	,	PUNCT
ap-6637	106	16	r	r	NOUN
ap-6637	106	17	and	and	CCONJ
ap-6637	106	18	n	n	PROPN
ap-6637	106	19	is	be	AUX
ap-6637	106	20	constructed	construct	VERB
ap-6637	106	21	according	accord	VERB
ap-6637	106	22	to	to	ADP
ap-6637	106	23	equations	equation	NOUN
ap-6637	106	24	(	(	PUNCT
ap-6637	106	25	3	3	X
ap-6637	106	26	)	)	PUNCT
ap-6637	106	27	taking	take	VERB
ap-6637	106	28	into	into	ADP
ap-6637	106	29	account	account	NOUN
ap-6637	106	30	(	(	PUNCT
ap-6637	106	31	9	9	NUM
ap-6637	106	32	)	)	PUNCT
ap-6637	106	33	when	when	SCONJ
ap-6637	106	34	the	the	DET
ap-6637	106	35	angle	angle	NOUN
ap-6637	106	36	α	α	NOUN
ap-6637	106	37	changes	change	NOUN
ap-6637	106	38	within	within	ADP
ap-6637	106	39	α=	α=	PROPN
ap-6637	106	40	–	–	PUNCT
ap-6637	106	41	αî	αî	NOUN
ap-6637	106	42	.	.	PUNCT
ap-6637	106	43	.	.	PUNCT
ap-6637	107	1	.αî	.αî	PROPN
ap-6637	107	2	.	.	PUNCT
ap-6637	108	1	however	however	ADV
ap-6637	108	2	,	,	PUNCT
ap-6637	108	3	in	in	ADP
ap-6637	108	4	this	this	DET
ap-6637	108	5	case	case	NOUN
ap-6637	108	6	,	,	PUNCT
ap-6637	108	7	we	we	PRON
ap-6637	108	8	will	will	AUX
ap-6637	108	9	not	not	PART
ap-6637	108	10	be	be	AUX
ap-6637	108	11	able	able	ADJ
ap-6637	108	12	to	to	PART
ap-6637	108	13	place	place	VERB
ap-6637	108	14	the	the	DET
ap-6637	108	15	required	require	VERB
ap-6637	108	16	number	number	NOUN
ap-6637	108	17	of	of	ADP
ap-6637	108	18	arcs	arc	NOUN
ap-6637	108	19	so	so	SCONJ
ap-6637	108	20	that	that	SCONJ
ap-6637	108	21	a	a	DET
ap-6637	108	22	closed	closed	ADJ
ap-6637	108	23	profile	profile	NOUN
ap-6637	108	24	is	be	AUX
ap-6637	108	25	obtained	obtain	VERB
ap-6637	108	26	.	.	PUNCT
ap-6637	109	1	if	if	SCONJ
ap-6637	109	2	we	we	PRON
ap-6637	109	3	want	want	VERB
ap-6637	109	4	to	to	PART
ap-6637	109	5	construct	construct	VERB
ap-6637	109	6	a	a	DET
ap-6637	109	7	profile	profile	NOUN
ap-6637	109	8	of	of	ADP
ap-6637	109	9	four	four	NUM
ap-6637	109	10	arcs	arc	NOUN
ap-6637	109	11	,	,	PUNCT
ap-6637	109	12	then	then	ADV
ap-6637	109	13	the	the	DET
ap-6637	109	14	angle	angle	NOUN
ap-6637	109	15	αî=±π/4	αî=±π/4	PROPN
ap-6637	109	16	(	(	PUNCT
ap-6637	109	17	this	this	DET
ap-6637	109	18	case	case	NOUN
ap-6637	109	19	is	be	AUX
ap-6637	109	20	shown	show	VERB
ap-6637	109	21	in	in	ADP
ap-6637	109	22	fig	fig	NOUN
ap-6637	109	23	.	.	PUNCT
ap-6637	110	1	1,a	1,a	NUM
ap-6637	110	2	)	)	PUNCT
ap-6637	110	3	.	.	PUNCT
ap-6637	111	1	the	the	DET
ap-6637	111	2	measure	measure	NOUN
ap-6637	111	3	of	of	ADP
ap-6637	111	4	the	the	DET
ap-6637	111	5	angle	angle	NOUN
ap-6637	111	6	αo	αo	NOUN
ap-6637	111	7	is	be	AUX
ap-6637	111	8	determined	determine	VERB
ap-6637	111	9	by	by	ADP
ap-6637	111	10	dividing	divide	VERB
ap-6637	111	11	the	the	DET
ap-6637	111	12	number	number	NOUN
ap-6637	111	13	π	π	NOUN
ap-6637	111	14	by	by	ADP
ap-6637	111	15	the	the	DET
ap-6637	111	16	number	number	NOUN
ap-6637	111	17	of	of	ADP
ap-6637	111	18	arcs	arc	NOUN
ap-6637	111	19	.	.	PUNCT
ap-6637	112	1	hence	hence	ADV
ap-6637	112	2	,	,	PUNCT
ap-6637	112	3	for	for	ADP
ap-6637	112	4	a	a	DET
ap-6637	112	5	given	give	VERB
ap-6637	112	6	number	number	NOUN
ap-6637	112	7	of	of	ADP
ap-6637	112	8	arcs	arc	NOUN
ap-6637	112	9	of	of	ADP
ap-6637	112	10	a	a	DET
ap-6637	112	11	profile	profile	NOUN
ap-6637	112	12	and	and	CCONJ
ap-6637	112	13	the	the	DET
ap-6637	112	14	number	number	NOUN
ap-6637	112	15	of	of	ADP
ap-6637	112	16	sides	side	NOUN
ap-6637	112	17	of	of	ADP
ap-6637	112	18	a	a	DET
ap-6637	112	19	polygon	polygon	NOUN
ap-6637	112	20	of	of	ADP
ap-6637	112	21	two	two	NUM
ap-6637	112	22	radii	radii	NOUN
ap-6637	112	23	r	r	NOUN
ap-6637	112	24	and	and	CCONJ
ap-6637	112	25	r	r	NOUN
ap-6637	112	26	,	,	PUNCT
ap-6637	112	27	we	we	PRON
ap-6637	112	28	can	can	AUX
ap-6637	112	29	only	only	ADV
ap-6637	112	30	specify	specify	VERB
ap-6637	112	31	one	one	NUM
ap-6637	112	32	of	of	ADP
ap-6637	112	33	them	they	PRON
ap-6637	112	34	,	,	PUNCT
ap-6637	112	35	since	since	SCONJ
ap-6637	112	36	the	the	DET
ap-6637	112	37	angle	angle	NOUN
ap-6637	112	38	αî	αî	X
ap-6637	112	39	will	will	AUX
ap-6637	112	40	also	also	ADV
ap-6637	112	41	be	be	AUX
ap-6637	112	42	given	give	VERB
ap-6637	112	43	.	.	PUNCT
ap-6637	113	1	equation	equation	NOUN
ap-6637	113	2	(	(	PUNCT
ap-6637	113	3	10	10	NUM
ap-6637	113	4	)	)	PUNCT
ap-6637	113	5	can	can	AUX
ap-6637	113	6	not	not	PART
ap-6637	113	7	be	be	AUX
ap-6637	113	8	solved	solve	VERB
ap-6637	113	9	with	with	ADP
ap-6637	113	10	respect	respect	NOUN
ap-6637	113	11	to	to	ADP
ap-6637	113	12	one	one	NUM
ap-6637	113	13	of	of	ADP
ap-6637	113	14	the	the	DET
ap-6637	113	15	radii	radii	NOUN
ap-6637	113	16	r	r	NOUN
ap-6637	113	17	or	or	CCONJ
ap-6637	113	18	r	r	NOUN
ap-6637	113	19	,	,	PUNCT
ap-6637	113	20	so	so	ADV
ap-6637	113	21	numerical	numerical	ADJ
ap-6637	113	22	techniques	technique	NOUN
ap-6637	113	23	must	must	AUX
ap-6637	113	24	be	be	AUX
ap-6637	113	25	used	use	VERB
ap-6637	113	26	.	.	PUNCT
ap-6637	114	1	3	3	X
ap-6637	114	2	.	.	X
ap-6637	114	3	result	result	VERB
ap-6637	114	4	it	it	PRON
ap-6637	114	5	should	should	AUX
ap-6637	114	6	be	be	AUX
ap-6637	114	7	noted	note	VERB
ap-6637	114	8	that	that	SCONJ
ap-6637	114	9	the	the	DET
ap-6637	114	10	curvilinear	curvilinear	NOUN
ap-6637	114	11	profile	profile	NOUN
ap-6637	114	12	can	can	AUX
ap-6637	114	13	consist	consist	VERB
ap-6637	114	14	of	of	ADP
ap-6637	114	15	one	one	NUM
ap-6637	114	16	arc	arc	NOUN
ap-6637	114	17	.	.	PUNCT
ap-6637	115	1	if	if	SCONJ
ap-6637	115	2	the	the	DET
ap-6637	115	3	polygon	polygon	NOUN
ap-6637	115	4	is	be	AUX
ap-6637	115	5	a	a	DET
ap-6637	115	6	square	square	NOUN
ap-6637	115	7	,	,	PUNCT
ap-6637	115	8	then	then	ADV
ap-6637	115	9	at	at	ADP
ap-6637	115	10	αi	αi	X
ap-6637	115	11	=	=	SYM
ap-6637	115	12	±π	±π	PROPN
ap-6637	115	13	,	,	PUNCT
ap-6637	115	14	n	n	NOUN
ap-6637	115	15	=	=	SYM
ap-6637	115	16	4	4	NUM
ap-6637	115	17	,	,	PUNCT
ap-6637	115	18	r	r	NOUN
ap-6637	115	19	=	=	SYM
ap-6637	115	20	100	100	NUM
ap-6637	115	21	,	,	PUNCT
ap-6637	115	22	we	we	PRON
ap-6637	115	23	find	find	VERB
ap-6637	115	24	:	:	PUNCT
ap-6637	115	25	r	r	NOUN
ap-6637	115	26	=	=	SYM
ap-6637	115	27	95.28	95.28	NUM
ap-6637	115	28	.	.	PUNCT
ap-6637	116	1	in	in	ADP
ap-6637	116	2	fig	fig	NOUN
ap-6637	116	3	.	.	PUNCT
ap-6637	117	1	2	2	NUM
ap-6637	117	2	,	,	PUNCT
ap-6637	117	3	we	we	PRON
ap-6637	117	4	can	can	AUX
ap-6637	117	5	see	see	VERB
ap-6637	117	6	a	a	DET
ap-6637	117	7	curvilinear	curvilinear	ADJ
ap-6637	117	8	profile	profile	NOUN
ap-6637	117	9	and	and	CCONJ
ap-6637	117	10	a	a	DET
ap-6637	117	11	square	square	NOUN
ap-6637	117	12	in	in	ADP
ap-6637	117	13	figure	figure	NOUN
ap-6637	117	14	2	2	NUM
ap-6637	117	15	.	.	PUNCT
ap-6637	117	16	curvilinear	curvilinear	PROPN
ap-6637	117	17	profile	profile	NOUN
ap-6637	117	18	,	,	PUNCT
ap-6637	117	19	with	with	ADP
ap-6637	117	20	complete	complete	ADJ
ap-6637	117	21	rolling	rolling	NOUN
ap-6637	117	22	during	during	ADP
ap-6637	117	23	which	which	PRON
ap-6637	117	24	the	the	DET
ap-6637	117	25	square	square	NOUN
ap-6637	117	26	makes	make	VERB
ap-6637	117	27	quarter	quarter	NOUN
ap-6637	117	28	of	of	ADP
ap-6637	117	29	a	a	DET
ap-6637	117	30	turn	turn	NOUN
ap-6637	117	31	.	.	PUNCT
ap-6637	118	1	two	two	NUM
ap-6637	118	2	positions	position	NOUN
ap-6637	118	3	on	on	ADP
ap-6637	118	4	opposite	opposite	ADJ
ap-6637	118	5	sides	side	NOUN
ap-6637	118	6	.	.	PUNCT
ap-6637	119	1	when	when	SCONJ
ap-6637	119	2	the	the	DET
ap-6637	119	3	profile	profile	NOUN
ap-6637	119	4	is	be	AUX
ap-6637	119	5	completely	completely	ADV
ap-6637	119	6	rolled	roll	VERB
ap-6637	119	7	,	,	PUNCT
ap-6637	119	8	only	only	ADV
ap-6637	119	9	one	one	NUM
ap-6637	119	10	side	side	NOUN
ap-6637	119	11	of	of	ADP
ap-6637	119	12	the	the	DET
ap-6637	119	13	square	square	ADJ
ap-6637	119	14	contacts	contact	NOUN
ap-6637	119	15	it	it	PRON
ap-6637	119	16	,	,	PUNCT
ap-6637	119	17	that	that	ADV
ap-6637	119	18	is	is	ADV
ap-6637	119	19	,	,	PUNCT
ap-6637	119	20	the	the	DET
ap-6637	119	21	square	square	NOUN
ap-6637	119	22	makes	make	VERB
ap-6637	119	23	quarter	quarter	NOUN
ap-6637	119	24	of	of	ADP
ap-6637	119	25	a	a	DET
ap-6637	119	26	turn	turn	NOUN
ap-6637	119	27	.	.	PUNCT
ap-6637	120	1	if	if	SCONJ
ap-6637	120	2	a	a	DET
ap-6637	120	3	curvilinear	curvilinear	NOUN
ap-6637	120	4	profile	profile	NOUN
ap-6637	120	5	consists	consist	VERB
ap-6637	120	6	of	of	ADP
ap-6637	120	7	four	four	NUM
ap-6637	120	8	elements	element	NOUN
ap-6637	120	9	,	,	PUNCT
ap-6637	120	10	then	then	ADV
ap-6637	120	11	the	the	DET
ap-6637	120	12	square	square	NOUN
ap-6637	120	13	during	during	ADP
ap-6637	120	14	one	one	NUM
ap-6637	120	15	complete	complete	ADJ
ap-6637	120	16	rolling	rolling	NOUN
ap-6637	120	17	of	of	ADP
ap-6637	120	18	the	the	DET
ap-6637	120	19	profile	profile	NOUN
ap-6637	120	20	makes	make	VERB
ap-6637	120	21	one	one	NUM
ap-6637	120	22	turn	turn	NOUN
ap-6637	120	23	.	.	PUNCT
ap-6637	121	1	repeating	repeat	VERB
ap-6637	121	2	the	the	DET
ap-6637	121	3	calculation	calculation	NOUN
ap-6637	121	4	at	at	ADP
ap-6637	121	5	αi	αi	NOUN
ap-6637	121	6	=	=	SYM
ap-6637	121	7	±π/4	±π/4	PROPN
ap-6637	121	8	,	,	PUNCT
ap-6637	121	9	n	n	NOUN
ap-6637	121	10	=	=	SYM
ap-6637	121	11	4	4	NUM
ap-6637	121	12	,	,	PUNCT
ap-6637	121	13	r	r	NOUN
ap-6637	121	14	=	=	SYM
ap-6637	121	15	100	100	NUM
ap-6637	121	16	,	,	PUNCT
ap-6637	121	17	we	we	PRON
ap-6637	121	18	find	find	VERB
ap-6637	121	19	:	:	PUNCT
ap-6637	121	20	r	r	NOUN
ap-6637	121	21	=	=	SYM
ap-6637	121	22	62.27	62.27	NUM
ap-6637	121	23	.	.	PUNCT
ap-6637	122	1	in	in	ADP
ap-6637	122	2	fig	fig	NOUN
ap-6637	122	3	.	.	PUNCT
ap-6637	123	1	3	3	NUM
ap-6637	123	2	,	,	PUNCT
ap-6637	123	3	we	we	PRON
ap-6637	123	4	can	can	AUX
ap-6637	123	5	see	see	VERB
ap-6637	123	6	a	a	DET
ap-6637	123	7	curvilinear	curvilinear	ADJ
ap-6637	123	8	profile	profile	NOUN
ap-6637	123	9	of	of	ADP
ap-6637	123	10	four	four	NUM
ap-6637	123	11	elements	element	NOUN
ap-6637	123	12	and	and	CCONJ
ap-6637	123	13	a	a	DET
ap-6637	123	14	set	set	NOUN
ap-6637	123	15	of	of	ADP
ap-6637	123	16	positions	position	NOUN
ap-6637	123	17	of	of	ADP
ap-6637	123	18	a	a	DET
ap-6637	123	19	square	square	NOUN
ap-6637	123	20	when	when	SCONJ
ap-6637	123	21	it	it	PRON
ap-6637	123	22	is	be	AUX
ap-6637	123	23	rolled	roll	VERB
ap-6637	123	24	along	along	ADP
ap-6637	123	25	one	one	NUM
ap-6637	123	26	of	of	ADP
ap-6637	123	27	the	the	DET
ap-6637	123	28	elements	element	NOUN
ap-6637	123	29	.	.	PUNCT
ap-6637	124	1	sequential	sequential	ADJ
ap-6637	124	2	movement	movement	NOUN
ap-6637	124	3	of	of	ADP
ap-6637	124	4	the	the	DET
ap-6637	124	5	centre	centre	NOUN
ap-6637	124	6	of	of	ADP
ap-6637	124	7	the	the	DET
ap-6637	124	8	square	square	NOUN
ap-6637	124	9	when	when	SCONJ
ap-6637	124	10	it	it	PRON
ap-6637	124	11	is	be	AUX
ap-6637	124	12	rolled	roll	VERB
ap-6637	124	13	is	be	AUX
ap-6637	124	14	shown	show	VERB
ap-6637	124	15	by	by	ADP
ap-6637	124	16	circles	circle	NOUN
ap-6637	124	17	.	.	PUNCT
ap-6637	125	1	in	in	ADP
ap-6637	125	2	the	the	DET
ap-6637	125	3	extreme	extreme	ADJ
ap-6637	125	4	positions	position	NOUN
ap-6637	125	5	of	of	ADP
ap-6637	125	6	a	a	DET
ap-6637	125	7	square	square	NOUN
ap-6637	125	8	,	,	PUNCT
ap-6637	125	9	when	when	SCONJ
ap-6637	125	10	its	its	PRON
ap-6637	125	11	vertices	vertex	NOUN
ap-6637	125	12	are	be	AUX
ap-6637	125	13	points	point	NOUN
ap-6637	125	14	of	of	ADP
ap-6637	125	15	contact	contact	NOUN
ap-6637	125	16	with	with	ADP
ap-6637	125	17	the	the	DET
ap-6637	125	18	profile	profile	NOUN
ap-6637	125	19	,	,	PUNCT
ap-6637	125	20	the	the	DET
ap-6637	125	21	sides	side	NOUN
ap-6637	125	22	of	of	ADP
ap-6637	125	23	the	the	DET
ap-6637	125	24	square	square	NOUN
ap-6637	125	25	are	be	AUX
ap-6637	125	26	depicted	depict	VERB
ap-6637	125	27	thickened	thicken	VERB
ap-6637	125	28	.	.	PUNCT
ap-6637	126	1	it	it	PRON
ap-6637	126	2	should	should	AUX
ap-6637	126	3	be	be	AUX
ap-6637	126	4	noted	note	VERB
ap-6637	126	5	that	that	SCONJ
ap-6637	126	6	for	for	ADP
ap-6637	126	7	the	the	DET
ap-6637	126	8	physical	physical	ADJ
ap-6637	126	9	rolling	rolling	NOUN
ap-6637	126	10	of	of	ADP
ap-6637	126	11	a	a	DET
ap-6637	126	12	polygon	polygon	NOUN
ap-6637	126	13	along	along	ADP
ap-6637	126	14	a	a	DET
ap-6637	126	15	curvilinear	curvilinear	NOUN
ap-6637	126	16	profile	profile	NOUN
ap-6637	126	17	,	,	PUNCT
ap-6637	126	18	there	there	PRON
ap-6637	126	19	is	be	VERB
ap-6637	126	20	a	a	DET
ap-6637	126	21	limit	limit	NOUN
ap-6637	126	22	on	on	ADP
ap-6637	126	23	the	the	DET
ap-6637	126	24	number	number	NOUN
ap-6637	126	25	of	of	ADP
ap-6637	126	26	its	its	PRON
ap-6637	126	27	sides	side	NOUN
ap-6637	126	28	.	.	PUNCT
ap-6637	127	1	the	the	DET
ap-6637	127	2	number	number	NOUN
ap-6637	127	3	of	of	ADP
ap-6637	127	4	sides	side	NOUN
ap-6637	127	5	of	of	ADP
ap-6637	127	6	a	a	DET
ap-6637	127	7	polygon	polygon	NOUN
ap-6637	127	8	can	can	AUX
ap-6637	127	9	not	not	PART
ap-6637	127	10	be	be	AUX
ap-6637	127	11	less	less	ADJ
ap-6637	127	12	than	than	ADP
ap-6637	127	13	four	four	NUM
ap-6637	127	14	.	.	PUNCT
ap-6637	128	1	this	this	PRON
ap-6637	128	2	is	be	AUX
ap-6637	128	3	explained	explain	VERB
ap-6637	128	4	as	as	SCONJ
ap-6637	128	5	follows	follow	VERB
ap-6637	128	6	.	.	PUNCT
ap-6637	129	1	when	when	SCONJ
ap-6637	129	2	rolling	roll	VERB
ap-6637	129	3	a	a	DET
ap-6637	129	4	polygon	polygon	NOUN
ap-6637	129	5	,	,	PUNCT
ap-6637	129	6	its	its	PRON
ap-6637	129	7	vertex	vertex	NOUN
ap-6637	129	8	describes	describe	VERB
ap-6637	129	9	a	a	DET
ap-6637	129	10	known	know	VERB
ap-6637	129	11	curve	curve	NOUN
ap-6637	129	12	evolvent	evolvent	NOUN
ap-6637	129	13	.	.	PUNCT
ap-6637	130	1	its	its	PRON
ap-6637	130	2	property	property	NOUN
ap-6637	130	3	is	be	AUX
ap-6637	130	4	that	that	SCONJ
ap-6637	130	5	at	at	ADP
ap-6637	130	6	the	the	DET
ap-6637	130	7	moment	moment	NOUN
ap-6637	130	8	of	of	ADP
ap-6637	130	9	detachment	detachment	NOUN
ap-6637	130	10	from	from	ADP
ap-6637	130	11	the	the	DET
ap-6637	130	12	curve	curve	NOUN
ap-6637	130	13	,	,	PUNCT
ap-6637	130	14	the	the	DET
ap-6637	130	15	point	point	NOUN
ap-6637	130	16	of	of	ADP
ap-6637	130	17	the	the	DET
ap-6637	130	18	straight	straight	NOUN
ap-6637	130	19	that	that	PRON
ap-6637	130	20	rolls	roll	VERB
ap-6637	130	21	on	on	ADP
ap-6637	130	22	it	it	PRON
ap-6637	130	23	(	(	PUNCT
ap-6637	130	24	in	in	ADP
ap-6637	130	25	our	our	PRON
ap-6637	130	26	case	case	NOUN
ap-6637	130	27	the	the	DET
ap-6637	130	28	end	end	NOUN
ap-6637	130	29	of	of	ADP
ap-6637	130	30	the	the	DET
ap-6637	130	31	side	side	NOUN
ap-6637	130	32	of	of	ADP
ap-6637	130	33	the	the	DET
ap-6637	130	34	square	square	NOUN
ap-6637	130	35	)	)	PUNCT
ap-6637	130	36	moves	move	VERB
ap-6637	130	37	perpendicular	perpendicular	ADJ
ap-6637	130	38	to	to	ADP
ap-6637	130	39	it	it	PRON
ap-6637	130	40	.	.	PUNCT
ap-6637	131	1	this	this	PRON
ap-6637	131	2	can	can	AUX
ap-6637	131	3	be	be	AUX
ap-6637	131	4	seen	see	VERB
ap-6637	131	5	from	from	ADP
ap-6637	131	6	the	the	DET
ap-6637	131	7	enlarged	enlarge	VERB
ap-6637	131	8	fragment	fragment	NOUN
ap-6637	131	9	in	in	ADP
ap-6637	131	10	fig	fig	NOUN
ap-6637	131	11	.	.	PUNCT
ap-6637	132	1	3	3	NUM
ap-6637	132	2	,	,	PUNCT
ap-6637	132	3	b.	b.	NOUN
ap-6637	132	4	if	if	SCONJ
ap-6637	132	5	the	the	DET
ap-6637	132	6	polygon	polygon	NOUN
ap-6637	132	7	was	be	AUX
ap-6637	132	8	a	a	DET
ap-6637	132	9	triangle	triangle	NOUN
ap-6637	132	10	,	,	PUNCT
ap-6637	132	11	then	then	ADV
ap-6637	132	12	the	the	DET
ap-6637	132	13	angle	angle	NOUN
ap-6637	132	14	between	between	ADP
ap-6637	132	15	neighbouring	neighbouring	ADJ
ap-6637	132	16	elements	element	NOUN
ap-6637	132	17	would	would	AUX
ap-6637	132	18	be	be	AUX
ap-6637	132	19	60	60	NUM
ap-6637	132	20	◦	◦	NOUN
ap-6637	132	21	and	and	CCONJ
ap-6637	132	22	physical	physical	ADJ
ap-6637	132	23	rolling	rolling	NOUN
ap-6637	132	24	would	would	AUX
ap-6637	132	25	be	be	AUX
ap-6637	132	26	impossible	impossible	ADJ
ap-6637	132	27	.	.	PUNCT
ap-6637	133	1	the	the	DET
ap-6637	133	2	considered	consider	VERB
ap-6637	133	3	approach	approach	NOUN
ap-6637	133	4	allows	allow	VERB
ap-6637	133	5	constructing	construct	VERB
ap-6637	133	6	a	a	DET
ap-6637	133	7	curvilinear	curvilinear	ADJ
ap-6637	133	8	profile	profile	NOUN
ap-6637	133	9	that	that	PRON
ap-6637	133	10	would	would	AUX
ap-6637	133	11	provide	provide	VERB
ap-6637	133	12	the	the	DET
ap-6637	133	13	required	require	VERB
ap-6637	133	14	number	number	NOUN
ap-6637	133	15	of	of	ADP
ap-6637	133	16	revolutions	revolution	NOUN
ap-6637	133	17	of	of	ADP
ap-6637	133	18	the	the	DET
ap-6637	133	19	polygon	polygon	NOUN
ap-6637	133	20	at	at	ADP
ap-6637	133	21	complete	complete	ADJ
ap-6637	133	22	rolling	rolling	NOUN
ap-6637	133	23	along	along	ADP
ap-6637	133	24	the	the	DET
ap-6637	133	25	profile	profile	NOUN
ap-6637	133	26	.	.	PUNCT
ap-6637	134	1	it	it	PRON
ap-6637	134	2	is	be	AUX
ap-6637	134	3	determined	determine	VERB
ap-6637	134	4	by	by	ADP
ap-6637	134	5	the	the	DET
ap-6637	134	6	ratio	ratio	NOUN
ap-6637	134	7	of	of	ADP
ap-6637	134	8	the	the	DET
ap-6637	134	9	number	number	NOUN
ap-6637	134	10	of	of	ADP
ap-6637	134	11	profile	profile	NOUN
ap-6637	134	12	elements	element	NOUN
ap-6637	134	13	to	to	ADP
ap-6637	134	14	the	the	DET
ap-6637	134	15	number	number	NOUN
ap-6637	134	16	of	of	ADP
ap-6637	134	17	sides	side	NOUN
ap-6637	134	18	of	of	ADP
ap-6637	134	19	the	the	DET
ap-6637	134	20	polygon	polygon	NOUN
ap-6637	134	21	.	.	PUNCT
ap-6637	135	1	in	in	ADP
ap-6637	135	2	fig	fig	NOUN
ap-6637	135	3	.	.	PUNCT
ap-6637	136	1	4,a	4,a	NUM
ap-6637	136	2	,	,	PUNCT
ap-6637	136	3	a	a	DET
ap-6637	136	4	profile	profile	NOUN
ap-6637	136	5	consisting	consist	VERB
ap-6637	136	6	of	of	ADP
ap-6637	136	7	8	8	NUM
ap-6637	136	8	elements	element	NOUN
ap-6637	136	9	is	be	AUX
ap-6637	136	10	constructed	construct	VERB
ap-6637	136	11	.	.	PUNCT
ap-6637	137	1	at	at	ADP
ap-6637	137	2	r	r	NOUN
ap-6637	137	3	=	=	SYM
ap-6637	137	4	100	100	NUM
ap-6637	137	5	,	,	PUNCT
ap-6637	137	6	the	the	DET
ap-6637	137	7	radius	radius	NOUN
ap-6637	137	8	of	of	ADP
ap-6637	137	9	the	the	DET
ap-6637	137	10	circumscribed	circumscribed	ADJ
ap-6637	137	11	circle	circle	NOUN
ap-6637	137	12	is	be	AUX
ap-6637	137	13	r	r	NOUN
ap-6637	137	14	=	=	SYM
ap-6637	137	15	41.76	41.76	NUM
ap-6637	137	16	.	.	PUNCT
ap-6637	138	1	when	when	SCONJ
ap-6637	138	2	completely	completely	ADV
ap-6637	138	3	rolling	roll	VERB
ap-6637	138	4	along	along	ADP
ap-6637	138	5	the	the	DET
ap-6637	138	6	profile	profile	NOUN
ap-6637	138	7	,	,	PUNCT
ap-6637	138	8	the	the	DET
ap-6637	138	9	square	square	NOUN
ap-6637	138	10	makes	make	VERB
ap-6637	138	11	2	2	NUM
ap-6637	138	12	turns	turn	NOUN
ap-6637	138	13	.	.	PUNCT
ap-6637	139	1	to	to	PART
ap-6637	139	2	ensure	ensure	VERB
ap-6637	139	3	4	4	NUM
ap-6637	139	4	turns	turn	NOUN
ap-6637	139	5	,	,	PUNCT
ap-6637	139	6	the	the	DET
ap-6637	139	7	profile	profile	NOUN
ap-6637	139	8	must	must	AUX
ap-6637	139	9	be	be	AUX
ap-6637	139	10	16	16	NUM
ap-6637	139	11	elements	element	NOUN
ap-6637	139	12	,	,	PUNCT
ap-6637	139	13	with	with	ADP
ap-6637	139	14	a	a	DET
ap-6637	139	15	radius	radius	NOUN
ap-6637	139	16	of	of	ADP
ap-6637	139	17	r	r	NOUN
ap-6637	139	18	=	=	SYM
ap-6637	139	19	25.13	25.13	NUM
ap-6637	139	20	(	(	PUNCT
ap-6637	139	21	fig	fig	NOUN
ap-6637	139	22	.	.	PUNCT
ap-6637	140	1	4,b	4,b	NUM
ap-6637	140	2	)	)	PUNCT
ap-6637	140	3	.	.	PUNCT
ap-6637	141	1	with	with	ADP
ap-6637	141	2	an	an	DET
ap-6637	141	3	unlimited	unlimited	ADJ
ap-6637	141	4	increase	increase	NOUN
ap-6637	141	5	in	in	ADP
ap-6637	141	6	the	the	DET
ap-6637	141	7	number	number	NOUN
ap-6637	141	8	n	n	NOUN
ap-6637	141	9	of	of	ADP
ap-6637	141	10	the	the	DET
ap-6637	141	11	sides	side	NOUN
ap-6637	141	12	of	of	ADP
ap-6637	141	13	a	a	DET
ap-6637	141	14	polygon	polygon	NOUN
ap-6637	141	15	,	,	PUNCT
ap-6637	141	16	it	it	PRON
ap-6637	141	17	transforms	transform	VERB
ap-6637	141	18	into	into	ADP
ap-6637	141	19	a	a	DET
ap-6637	141	20	circle	circle	NOUN
ap-6637	141	21	,	,	PUNCT
ap-6637	141	22	and	and	CCONJ
ap-6637	141	23	the	the	DET
ap-6637	141	24	radius	radius	NOUN
ap-6637	141	25	-	-	PUNCT
ap-6637	141	26	vector	vector	NOUN
ap-6637	141	27	ρ	ρ	NOUN
ap-6637	141	28	into	into	ADP
ap-6637	141	29	a	a	DET
ap-6637	141	30	constant	constant	ADJ
ap-6637	141	31	value	value	NOUN
ap-6637	141	32	r	r	NOUN
ap-6637	141	33	–	–	PUNCT
ap-6637	141	34	r	r	NOUN
ap-6637	141	35	,	,	PUNCT
ap-6637	141	36	that	that	ADV
ap-6637	141	37	is	is	ADV
ap-6637	141	38	,	,	PUNCT
ap-6637	141	39	rî	rî	PROPN
ap-6637	141	40	(	(	PUNCT
ap-6637	141	41	fig	fig	NOUN
ap-6637	141	42	.	.	PUNCT
ap-6637	142	1	1,a	1,a	NUM
ap-6637	142	2	)	)	PUNCT
ap-6637	142	3	.	.	PUNCT
ap-6637	143	1	the	the	DET
ap-6637	143	2	number	number	NOUN
ap-6637	143	3	of	of	ADP
ap-6637	143	4	turns	turn	NOUN
ap-6637	143	5	of	of	ADP
ap-6637	143	6	a	a	DET
ap-6637	143	7	circle	circle	NOUN
ap-6637	143	8	of	of	ADP
ap-6637	143	9	radius	radius	NOUN
ap-6637	143	10	r	r	PROPN
ap-6637	143	11	,	,	PUNCT
ap-6637	143	12	after	after	ADP
ap-6637	143	13	a	a	DET
ap-6637	143	14	completed	complete	VERB
ap-6637	143	15	rolling	rolling	NOUN
ap-6637	143	16	along	along	ADP
ap-6637	143	17	a	a	DET
ap-6637	143	18	circle	circle	NOUN
ap-6637	143	19	of	of	ADP
ap-6637	143	20	radius	radius	NOUN
ap-6637	143	21	rî	rî	PROPN
ap-6637	143	22	,	,	PUNCT
ap-6637	143	23	is	be	AUX
ap-6637	143	24	determined	determine	VERB
ap-6637	143	25	by	by	ADP
ap-6637	143	26	the	the	DET
ap-6637	143	27	ratio	ratio	NOUN
ap-6637	143	28	of	of	ADP
ap-6637	143	29	these	these	DET
ap-6637	143	30	radii	radius	NOUN
ap-6637	143	31	.	.	PUNCT
ap-6637	144	1	315	315	NUM
ap-6637	144	2	t.	t.	PROPN
ap-6637	144	3	kresan	kresan	PROPN
ap-6637	144	4	,	,	PUNCT
ap-6637	144	5	s.	s.	PROPN
ap-6637	144	6	pylypaka	pylypaka	PROPN
ap-6637	144	7	,	,	PUNCT
ap-6637	144	8	z.	z.	PROPN
ap-6637	144	9	ruzhylo	ruzhylo	PROPN
ap-6637	144	10	et	et	PROPN
ap-6637	144	11	al	al	PROPN
ap-6637	144	12	.	.	PROPN
ap-6637	144	13	acta	acta	PROPN
ap-6637	144	14	polytechnica	polytechnica	PROPN
ap-6637	144	15	(	(	PUNCT
ap-6637	144	16	a	a	NOUN
ap-6637	144	17	)	)	PUNCT
ap-6637	144	18	.	.	PUNCT
ap-6637	145	1	(	(	PUNCT
ap-6637	145	2	b	b	X
ap-6637	145	3	)	)	PUNCT
ap-6637	145	4	.	.	PUNCT
ap-6637	146	1	figure	figure	VERB
ap-6637	146	2	3	3	NUM
ap-6637	146	3	.	.	PUNCT
ap-6637	146	4	curvilinear	curvilinear	PROPN
ap-6637	146	5	profile	profile	NOUN
ap-6637	146	6	of	of	ADP
ap-6637	146	7	four	four	NUM
ap-6637	146	8	elements	element	NOUN
ap-6637	146	9	,	,	PUNCT
ap-6637	146	10	when	when	SCONJ
ap-6637	146	11	completely	completely	ADV
ap-6637	146	12	rolling	roll	VERB
ap-6637	146	13	along	along	ADP
ap-6637	146	14	it	it	PRON
ap-6637	146	15	,	,	PUNCT
ap-6637	146	16	the	the	DET
ap-6637	146	17	square	square	NOUN
ap-6637	146	18	makes	make	VERB
ap-6637	146	19	one	one	NUM
ap-6637	146	20	turn	turn	NOUN
ap-6637	146	21	:	:	PUNCT
ap-6637	147	1	a	a	X
ap-6637	147	2	)	)	PUNCT
ap-6637	147	3	the	the	DET
ap-6637	147	4	set	set	NOUN
ap-6637	147	5	of	of	ADP
ap-6637	147	6	positions	position	NOUN
ap-6637	147	7	of	of	ADP
ap-6637	147	8	the	the	DET
ap-6637	147	9	square	square	NOUN
ap-6637	147	10	when	when	SCONJ
ap-6637	147	11	it	it	PRON
ap-6637	147	12	is	be	AUX
ap-6637	147	13	rolling	roll	VERB
ap-6637	147	14	along	along	ADP
ap-6637	147	15	the	the	DET
ap-6637	147	16	arc	arc	NOUN
ap-6637	147	17	of	of	ADP
ap-6637	147	18	the	the	DET
ap-6637	147	19	profile	profile	NOUN
ap-6637	147	20	;	;	PUNCT
ap-6637	147	21	b	b	X
ap-6637	147	22	)	)	PUNCT
ap-6637	147	23	enlarged	enlarged	ADJ
ap-6637	147	24	fragment	fragment	NOUN
ap-6637	147	25	of	of	ADP
ap-6637	147	26	the	the	DET
ap-6637	147	27	profile	profile	NOUN
ap-6637	147	28	element	element	NOUN
ap-6637	147	29	(	(	PUNCT
ap-6637	147	30	a	a	NOUN
ap-6637	147	31	)	)	PUNCT
ap-6637	147	32	.	.	PUNCT
ap-6637	148	1	(	(	PUNCT
ap-6637	148	2	b	b	X
ap-6637	148	3	)	)	PUNCT
ap-6637	148	4	.	.	PUNCT
ap-6637	149	1	figure	figure	VERB
ap-6637	149	2	4	4	NUM
ap-6637	149	3	.	.	PUNCT
ap-6637	149	4	curvilinear	curvilinear	ADJ
ap-6637	149	5	profiles	profile	NOUN
ap-6637	149	6	with	with	ADP
ap-6637	149	7	different	different	ADJ
ap-6637	149	8	number	number	NOUN
ap-6637	149	9	of	of	ADP
ap-6637	149	10	turns	turn	NOUN
ap-6637	149	11	of	of	ADP
ap-6637	149	12	a	a	DET
ap-6637	149	13	square	square	NOUN
ap-6637	149	14	:	:	PUNCT
ap-6637	149	15	a	a	X
ap-6637	149	16	)	)	PUNCT
ap-6637	149	17	a	a	DET
ap-6637	149	18	square	square	NOUN
ap-6637	149	19	,	,	PUNCT
ap-6637	149	20	when	when	SCONJ
ap-6637	149	21	completely	completely	ADV
ap-6637	149	22	rolling	roll	VERB
ap-6637	149	23	along	along	ADP
ap-6637	149	24	the	the	DET
ap-6637	149	25	profile	profile	NOUN
ap-6637	149	26	,	,	PUNCT
ap-6637	149	27	makes	make	VERB
ap-6637	149	28	two	two	NUM
ap-6637	149	29	turns	turn	NOUN
ap-6637	149	30	;	;	PUNCT
ap-6637	149	31	b	b	X
ap-6637	149	32	)	)	PUNCT
ap-6637	149	33	a	a	DET
ap-6637	149	34	square	square	NOUN
ap-6637	149	35	,	,	PUNCT
ap-6637	149	36	when	when	SCONJ
ap-6637	149	37	completely	completely	ADV
ap-6637	149	38	rolling	roll	VERB
ap-6637	149	39	along	along	ADP
ap-6637	149	40	the	the	DET
ap-6637	149	41	profile	profile	NOUN
ap-6637	149	42	,	,	PUNCT
ap-6637	149	43	makes	make	VERB
ap-6637	149	44	four	four	NUM
ap-6637	149	45	turns	turn	NOUN
ap-6637	149	46	.	.	PUNCT
ap-6637	150	1	figure	figure	NOUN
ap-6637	150	2	5	5	NUM
ap-6637	150	3	.	.	PUNCT
ap-6637	151	1	polygons	polygon	NOUN
ap-6637	151	2	and	and	CCONJ
ap-6637	151	3	curvilinear	curvilinear	ADJ
ap-6637	151	4	profiles	profile	NOUN
ap-6637	151	5	with	with	ADP
ap-6637	151	6	different	different	ADJ
ap-6637	151	7	numbers	number	NOUN
ap-6637	151	8	of	of	ADP
ap-6637	151	9	sides	side	NOUN
ap-6637	151	10	and	and	CCONJ
ap-6637	151	11	curvilinear	curvilinear	ADJ
ap-6637	151	12	elements	element	NOUN
ap-6637	151	13	at	at	ADP
ap-6637	151	14	r	r	NOUN
ap-6637	151	15	=	=	SYM
ap-6637	151	16	100	100	NUM
ap-6637	151	17	:	:	PUNCT
ap-6637	151	18	a	a	X
ap-6637	151	19	)	)	PUNCT
ap-6637	151	20	a	a	DET
ap-6637	151	21	hexagon	hexagon	NOUN
ap-6637	151	22	with	with	ADP
ap-6637	151	23	a	a	DET
ap-6637	151	24	radius	radius	NOUN
ap-6637	151	25	of	of	ADP
ap-6637	151	26	the	the	DET
ap-6637	151	27	circumscribed	circumscribed	ADJ
ap-6637	151	28	circle	circle	NOUN
ap-6637	151	29	r	r	NOUN
ap-6637	151	30	=	=	PROPN
ap-6637	151	31	54.93	54.93	NUM
ap-6637	151	32	and	and	CCONJ
ap-6637	151	33	a	a	DET
ap-6637	151	34	corresponding	corresponding	ADJ
ap-6637	151	35	curvilinear	curvilinear	ADJ
ap-6637	151	36	profile	profile	NOUN
ap-6637	151	37	with	with	ADP
ap-6637	151	38	six	six	NUM
ap-6637	151	39	elements	element	NOUN
ap-6637	151	40	;	;	PUNCT
ap-6637	151	41	b	b	X
ap-6637	151	42	)	)	PUNCT
ap-6637	151	43	a	a	DET
ap-6637	151	44	pentagon	pentagon	PROPN
ap-6637	151	45	with	with	ADP
ap-6637	151	46	a	a	DET
ap-6637	151	47	radius	radius	NOUN
ap-6637	151	48	of	of	ADP
ap-6637	151	49	the	the	DET
ap-6637	151	50	circumscribed	circumscribed	ADJ
ap-6637	151	51	circle	circle	NOUN
ap-6637	151	52	r	r	NOUN
ap-6637	151	53	=	=	PUNCT
ap-6637	151	54	71.47	71.47	NUM
ap-6637	151	55	and	and	CCONJ
ap-6637	151	56	a	a	DET
ap-6637	151	57	corresponding	corresponding	ADJ
ap-6637	151	58	curvilinear	curvilinear	ADJ
ap-6637	151	59	profile	profile	NOUN
ap-6637	151	60	with	with	ADP
ap-6637	151	61	three	three	NUM
ap-6637	151	62	elements	element	NOUN
ap-6637	151	63	.	.	PUNCT
ap-6637	152	1	316	316	NUM
ap-6637	152	2	vol	vol	NOUN
ap-6637	152	3	.	.	PUNCT
ap-6637	153	1	60	60	NUM
ap-6637	153	2	no	no	INTJ
ap-6637	153	3	.	.	PUNCT
ap-6637	154	1	4/2020	4/2020	NUM
ap-6637	154	2	external	external	ADJ
ap-6637	154	3	rolling	rolling	NOUN
ap-6637	154	4	of	of	ADP
ap-6637	154	5	a	a	DET
ap-6637	154	6	polygon	polygon	NOUN
ap-6637	154	7	on	on	ADP
ap-6637	154	8	closed	close	VERB
ap-6637	154	9	curvilinear	curvilinear	PROPN
ap-6637	154	10	profile	profile	VERB
ap-6637	154	11	the	the	DET
ap-6637	154	12	correspondence	correspondence	NOUN
ap-6637	154	13	of	of	ADP
ap-6637	154	14	the	the	DET
ap-6637	154	15	number	number	NOUN
ap-6637	154	16	of	of	ADP
ap-6637	154	17	sides	side	NOUN
ap-6637	154	18	of	of	ADP
ap-6637	154	19	a	a	DET
ap-6637	154	20	polygon	polygon	NOUN
ap-6637	154	21	and	and	CCONJ
ap-6637	154	22	elements	element	NOUN
ap-6637	154	23	of	of	ADP
ap-6637	154	24	a	a	DET
ap-6637	154	25	curvilinear	curvilinear	NOUN
ap-6637	154	26	profile	profile	NOUN
ap-6637	154	27	can	can	AUX
ap-6637	154	28	be	be	AUX
ap-6637	154	29	different	different	ADJ
ap-6637	154	30	(	(	PUNCT
ap-6637	154	31	fig	fig	NOUN
ap-6637	154	32	.	.	PUNCT
ap-6637	155	1	5	5	NUM
ap-6637	155	2	)	)	PUNCT
ap-6637	155	3	.	.	PUNCT
ap-6637	156	1	such	such	ADJ
ap-6637	156	2	figures	figure	NOUN
ap-6637	156	3	can	can	AUX
ap-6637	156	4	roll	roll	VERB
ap-6637	156	5	one	one	NUM
ap-6637	156	6	by	by	ADP
ap-6637	156	7	one	one	NUM
ap-6637	156	8	with	with	ADP
ap-6637	156	9	simultaneous	simultaneous	ADJ
ap-6637	156	10	rotation	rotation	NOUN
ap-6637	156	11	around	around	ADP
ap-6637	156	12	fixed	fix	VERB
ap-6637	156	13	centres	centre	NOUN
ap-6637	156	14	o	o	NOUN
ap-6637	156	15	and	and	CCONJ
ap-6637	156	16	o1	o1	NOUN
ap-6637	156	17	with	with	ADP
ap-6637	156	18	angular	angular	ADJ
ap-6637	156	19	velocities	velocity	NOUN
ap-6637	156	20	ω	ω	PROPN
ap-6637	156	21	and	and	CCONJ
ap-6637	156	22	ω1	ω1	PROPN
ap-6637	156	23	,	,	PUNCT
ap-6637	156	24	that	that	ADV
ap-6637	156	25	is	is	ADV
ap-6637	156	26	,	,	PUNCT
ap-6637	156	27	they	they	PRON
ap-6637	156	28	can	can	AUX
ap-6637	156	29	serve	serve	VERB
ap-6637	156	30	as	as	ADP
ap-6637	156	31	centroids	centroid	NOUN
ap-6637	156	32	for	for	ADP
ap-6637	156	33	the	the	DET
ap-6637	156	34	design	design	NOUN
ap-6637	156	35	of	of	ADP
ap-6637	156	36	non	non	ADJ
ap-6637	156	37	-	-	ADJ
ap-6637	156	38	circular	circular	ADJ
ap-6637	156	39	gears	gear	NOUN
ap-6637	157	1	[	[	X
ap-6637	157	2	6–8	6–8	X
ap-6637	157	3	]	]	X
ap-6637	157	4	.	.	PUNCT
ap-6637	158	1	the	the	DET
ap-6637	158	2	predetermined	predetermine	VERB
ap-6637	158	3	value	value	NOUN
ap-6637	158	4	r	r	NOUN
ap-6637	158	5	is	be	AUX
ap-6637	158	6	the	the	DET
ap-6637	158	7	centre	centre	NOUN
ap-6637	158	8	to	to	PART
ap-6637	158	9	centre	centre	NOUN
ap-6637	158	10	distance	distance	NOUN
ap-6637	158	11	.	.	PUNCT
ap-6637	159	1	when	when	SCONJ
ap-6637	159	2	rotating	rotate	VERB
ap-6637	159	3	one	one	NUM
ap-6637	159	4	non	non	ADJ
ap-6637	159	5	-	-	ADJ
ap-6637	159	6	circular	circular	ADJ
ap-6637	159	7	wheel	wheel	NOUN
ap-6637	159	8	at	at	ADP
ap-6637	159	9	a	a	DET
ap-6637	159	10	constant	constant	ADJ
ap-6637	159	11	angular	angular	ADJ
ap-6637	159	12	velocity	velocity	NOUN
ap-6637	159	13	,	,	PUNCT
ap-6637	159	14	the	the	DET
ap-6637	159	15	second	second	NOUN
ap-6637	159	16	will	will	AUX
ap-6637	159	17	rotate	rotate	VERB
ap-6637	159	18	at	at	ADP
ap-6637	159	19	a	a	DET
ap-6637	159	20	variable	variable	ADJ
ap-6637	159	21	angular	angular	ADJ
ap-6637	159	22	velocity	velocity	NOUN
ap-6637	159	23	.	.	PUNCT
ap-6637	160	1	this	this	PRON
ap-6637	160	2	is	be	AUX
ap-6637	160	3	due	due	ADJ
ap-6637	160	4	to	to	ADP
ap-6637	160	5	the	the	DET
ap-6637	160	6	variable	variable	ADJ
ap-6637	160	7	radius	radius	NOUN
ap-6637	160	8	from	from	ADP
ap-6637	160	9	the	the	DET
ap-6637	160	10	centres	centre	NOUN
ap-6637	160	11	of	of	ADP
ap-6637	160	12	the	the	DET
ap-6637	160	13	wheels	wheel	NOUN
ap-6637	160	14	to	to	ADP
ap-6637	160	15	the	the	DET
ap-6637	160	16	point	point	NOUN
ap-6637	160	17	of	of	ADP
ap-6637	160	18	the	the	DET
ap-6637	160	19	contact	contact	NOUN
ap-6637	160	20	during	during	ADP
ap-6637	160	21	the	the	DET
ap-6637	160	22	rotation	rotation	NOUN
ap-6637	160	23	.	.	PUNCT
ap-6637	161	1	the	the	DET
ap-6637	161	2	radius	radius	NOUN
ap-6637	161	3	-	-	PUNCT
ap-6637	161	4	vector	vector	NOUN
ap-6637	161	5	ρ	ρ	NOUN
ap-6637	161	6	changes	change	NOUN
ap-6637	161	7	from	from	ADP
ap-6637	161	8	the	the	DET
ap-6637	161	9	maximum	maximum	ADJ
ap-6637	161	10	value	value	NOUN
ap-6637	161	11	at	at	ADP
ap-6637	161	12	α	α	NOUN
ap-6637	161	13	=	=	NOUN
ap-6637	161	14	0	0	NUM
ap-6637	161	15	to	to	ADP
ap-6637	161	16	the	the	DET
ap-6637	161	17	minimum	minimum	ADJ
ap-6637	161	18	ρ	ρ	NOUN
ap-6637	161	19	=	=	SYM
ap-6637	161	20	ri	ri	PROPN
ap-6637	161	21	=	=	SYM
ap-6637	161	22	r	r	NOUN
ap-6637	161	23	−	−	NOUN
ap-6637	161	24	r	r	NOUN
ap-6637	161	25	(	(	PUNCT
ap-6637	161	26	fig	fig	NOUN
ap-6637	161	27	.	.	PUNCT
ap-6637	162	1	1,a	1,a	NUM
ap-6637	162	2	,	,	PUNCT
ap-6637	162	3	points	point	VERB
ap-6637	162	4	a	a	PRON
ap-6637	162	5	and	and	CCONJ
ap-6637	162	6	a	a	PRON
ap-6637	162	7	’	'	PUNCT
ap-6637	162	8	)	)	PUNCT
ap-6637	162	9	.	.	PUNCT
ap-6637	163	1	this	this	DET
ap-6637	163	2	distance	distance	NOUN
ap-6637	163	3	difference	difference	NOUN
ap-6637	163	4	is	be	AUX
ap-6637	163	5	the	the	DET
ap-6637	163	6	difference	difference	NOUN
ap-6637	163	7	between	between	ADP
ap-6637	163	8	the	the	DET
ap-6637	163	9	maximum	maximum	ADJ
ap-6637	163	10	and	and	CCONJ
ap-6637	163	11	minimum	minimum	ADJ
ap-6637	163	12	values	value	NOUN
ap-6637	163	13	of	of	ADP
ap-6637	163	14	the	the	DET
ap-6637	163	15	distance	distance	NOUN
ap-6637	163	16	from	from	ADP
ap-6637	163	17	the	the	DET
ap-6637	163	18	axis	axis	NOUN
ap-6637	163	19	of	of	ADP
ap-6637	163	20	rotation	rotation	NOUN
ap-6637	163	21	of	of	ADP
ap-6637	163	22	the	the	DET
ap-6637	163	23	polygon	polygon	NOUN
ap-6637	163	24	to	to	ADP
ap-6637	163	25	the	the	DET
ap-6637	163	26	point	point	NOUN
ap-6637	163	27	of	of	ADP
ap-6637	163	28	contact	contact	NOUN
ap-6637	163	29	with	with	ADP
ap-6637	163	30	the	the	DET
ap-6637	163	31	curvilinear	curvilinear	ADJ
ap-6637	163	32	profile	profile	NOUN
ap-6637	163	33	.	.	PUNCT
ap-6637	164	1	it	it	PRON
ap-6637	164	2	decreases	decrease	VERB
ap-6637	164	3	as	as	SCONJ
ap-6637	164	4	the	the	DET
ap-6637	164	5	number	number	NOUN
ap-6637	164	6	of	of	ADP
ap-6637	164	7	sides	side	NOUN
ap-6637	164	8	of	of	ADP
ap-6637	164	9	a	a	DET
ap-6637	164	10	polygon	polygon	NOUN
ap-6637	164	11	increases	increase	NOUN
ap-6637	164	12	as	as	ADV
ap-6637	164	13	well	well	ADV
ap-6637	164	14	as	as	ADP
ap-6637	164	15	increase	increase	VERB
ap-6637	164	16	the	the	DET
ap-6637	164	17	number	number	NOUN
ap-6637	164	18	of	of	ADP
ap-6637	164	19	curvilinear	curvilinear	ADJ
ap-6637	164	20	elements	element	NOUN
ap-6637	164	21	of	of	ADP
ap-6637	164	22	the	the	DET
ap-6637	164	23	profile	profile	NOUN
ap-6637	164	24	that	that	PRON
ap-6637	164	25	can	can	AUX
ap-6637	164	26	be	be	AUX
ap-6637	164	27	traced	trace	VERB
ap-6637	164	28	by	by	ADP
ap-6637	164	29	the	the	DET
ap-6637	164	30	example	example	NOUN
ap-6637	164	31	of	of	ADP
ap-6637	164	32	the	the	DET
ap-6637	164	33	square	square	NOUN
ap-6637	164	34	in	in	ADP
ap-6637	164	35	fig	fig	NOUN
ap-6637	164	36	.	.	PUNCT
ap-6637	165	1	2	2	NUM
ap-6637	165	2	4	4	NUM
ap-6637	165	3	.	.	NOUN
ap-6637	166	1	4	4	NUM
ap-6637	166	2	.	.	X
ap-6637	166	3	conclusions	conclusion	NOUN
ap-6637	166	4	and	and	CCONJ
ap-6637	166	5	prospects	prospect	NOUN
ap-6637	166	6	for	for	ADP
ap-6637	166	7	further	further	ADJ
ap-6637	166	8	research	research	NOUN
ap-6637	166	9	an	an	DET
ap-6637	166	10	analytical	analytical	ADJ
ap-6637	166	11	description	description	NOUN
ap-6637	166	12	of	of	ADP
ap-6637	166	13	the	the	DET
ap-6637	166	14	rolling	rolling	NOUN
ap-6637	166	15	of	of	ADP
ap-6637	166	16	a	a	DET
ap-6637	166	17	polygon	polygon	NOUN
ap-6637	166	18	along	along	ADP
ap-6637	166	19	a	a	DET
ap-6637	166	20	curvilinear	curvilinear	NOUN
ap-6637	166	21	closed	close	VERB
ap-6637	166	22	profile	profile	NOUN
ap-6637	166	23	can	can	AUX
ap-6637	166	24	be	be	AUX
ap-6637	166	25	used	use	VERB
ap-6637	166	26	to	to	PART
ap-6637	166	27	design	design	VERB
ap-6637	166	28	non	non	ADJ
ap-6637	166	29	-	-	ADJ
ap-6637	166	30	circular	circular	ADJ
ap-6637	166	31	gear	gear	NOUN
ap-6637	166	32	wheels	wheel	NOUN
ap-6637	166	33	.	.	PUNCT
ap-6637	167	1	the	the	DET
ap-6637	167	2	number	number	NOUN
ap-6637	167	3	of	of	ADP
ap-6637	167	4	sides	side	NOUN
ap-6637	167	5	of	of	ADP
ap-6637	167	6	a	a	DET
ap-6637	167	7	polygon	polygon	NOUN
ap-6637	167	8	must	must	AUX
ap-6637	167	9	be	be	AUX
ap-6637	167	10	at	at	ADV
ap-6637	167	11	least	least	ADJ
ap-6637	167	12	four	four	NUM
ap-6637	167	13	in	in	ADP
ap-6637	167	14	order	order	NOUN
ap-6637	167	15	to	to	PART
ap-6637	167	16	be	be	AUX
ap-6637	167	17	physically	physically	ADV
ap-6637	167	18	rolling	rolling	ADJ
ap-6637	167	19	.	.	PUNCT
ap-6637	168	1	to	to	PART
ap-6637	168	2	design	design	VERB
ap-6637	168	3	a	a	DET
ap-6637	168	4	curvilinear	curvilinear	ADJ
ap-6637	168	5	centroid	centroid	NOUN
ap-6637	168	6	,	,	PUNCT
ap-6637	168	7	it	it	PRON
ap-6637	168	8	is	be	AUX
ap-6637	168	9	necessary	necessary	ADJ
ap-6637	168	10	to	to	PART
ap-6637	168	11	specify	specify	VERB
ap-6637	168	12	the	the	DET
ap-6637	168	13	distance	distance	NOUN
ap-6637	168	14	from	from	ADP
ap-6637	168	15	centre	centre	NOUN
ap-6637	168	16	to	to	ADP
ap-6637	168	17	centre	centre	NOUN
ap-6637	168	18	,	,	PUNCT
ap-6637	168	19	the	the	DET
ap-6637	168	20	number	number	NOUN
ap-6637	168	21	of	of	ADP
ap-6637	168	22	sides	side	NOUN
ap-6637	168	23	of	of	ADP
ap-6637	168	24	a	a	DET
ap-6637	168	25	polygon	polygon	NOUN
ap-6637	168	26	,	,	PUNCT
ap-6637	168	27	that	that	PRON
ap-6637	168	28	is	be	AUX
ap-6637	168	29	another	another	DET
ap-6637	168	30	centroid	centroid	NOUN
ap-6637	168	31	,	,	PUNCT
ap-6637	168	32	and	and	CCONJ
ap-6637	168	33	the	the	DET
ap-6637	168	34	correspondence	correspondence	NOUN
ap-6637	168	35	of	of	ADP
ap-6637	168	36	the	the	DET
ap-6637	168	37	number	number	NOUN
ap-6637	168	38	of	of	ADP
ap-6637	168	39	turns	turn	NOUN
ap-6637	168	40	of	of	ADP
ap-6637	168	41	these	these	DET
ap-6637	168	42	centroids	centroid	NOUN
ap-6637	168	43	.	.	PUNCT
ap-6637	169	1	the	the	DET
ap-6637	169	2	length	length	NOUN
ap-6637	169	3	of	of	ADP
ap-6637	169	4	the	the	DET
ap-6637	169	5	centroid	centroid	NOUN
ap-6637	169	6	element	element	NOUN
ap-6637	169	7	is	be	AUX
ap-6637	169	8	equal	equal	ADJ
ap-6637	169	9	to	to	ADP
ap-6637	169	10	the	the	DET
ap-6637	169	11	length	length	NOUN
ap-6637	169	12	of	of	ADP
ap-6637	169	13	the	the	DET
ap-6637	169	14	side	side	NOUN
ap-6637	169	15	of	of	ADP
ap-6637	169	16	the	the	DET
ap-6637	169	17	polygon	polygon	NOUN
ap-6637	169	18	.	.	PUNCT
ap-6637	170	1	the	the	DET
ap-6637	170	2	number	number	NOUN
ap-6637	170	3	of	of	ADP
ap-6637	170	4	elements	element	NOUN
ap-6637	170	5	of	of	ADP
ap-6637	170	6	a	a	DET
ap-6637	170	7	centroid	centroid	NOUN
ap-6637	170	8	can	can	AUX
ap-6637	170	9	be	be	AUX
ap-6637	170	10	any	any	DET
ap-6637	170	11	integer	integer	NOUN
ap-6637	170	12	,	,	PUNCT
ap-6637	170	13	starting	start	VERB
ap-6637	170	14	with	with	ADP
ap-6637	170	15	one	one	NUM
ap-6637	170	16	.	.	PUNCT
ap-6637	171	1	increasing	increase	VERB
ap-6637	171	2	the	the	DET
ap-6637	171	3	number	number	NOUN
ap-6637	171	4	of	of	ADP
ap-6637	171	5	curvilinear	curvilinear	ADJ
ap-6637	171	6	centroid	centroid	NOUN
ap-6637	171	7	elements	element	NOUN
ap-6637	171	8	and	and	CCONJ
ap-6637	171	9	the	the	DET
ap-6637	171	10	number	number	NOUN
ap-6637	171	11	of	of	ADP
ap-6637	171	12	sides	side	NOUN
ap-6637	171	13	of	of	ADP
ap-6637	171	14	a	a	DET
ap-6637	171	15	polygon	polygon	NOUN
ap-6637	171	16	increases	increase	VERB
ap-6637	171	17	the	the	DET
ap-6637	171	18	rotation	rotation	NOUN
ap-6637	171	19	uniformity	uniformity	NOUN
ap-6637	171	20	of	of	ADP
ap-6637	171	21	one	one	NUM
ap-6637	171	22	centroid	centroid	NOUN
ap-6637	171	23	with	with	ADP
ap-6637	171	24	respect	respect	NOUN
ap-6637	171	25	to	to	ADP
ap-6637	171	26	another	another	PRON
ap-6637	171	27	.	.	PUNCT
ap-6637	172	1	references	reference	NOUN
ap-6637	172	2	[	[	X
ap-6637	172	3	1	1	NUM
ap-6637	172	4	]	]	PUNCT
ap-6637	172	5	p.	p.	NOUN
ap-6637	172	6	m.	m.	NOUN
ap-6637	172	7	zaika	zaika	PROPN
ap-6637	172	8	.	.	PUNCT
ap-6637	173	1	selected	select	VERB
ap-6637	173	2	problems	problem	NOUN
ap-6637	173	3	of	of	ADP
ap-6637	173	4	agricultural	agricultural	ADJ
ap-6637	173	5	mechanics	mechanic	NOUN
ap-6637	173	6	.	.	PUNCT
ap-6637	174	1	ukrainian	ukrainian	ADJ
ap-6637	174	2	agricultural	agricultural	PROPN
ap-6637	174	3	academy	academy	PROPN
ap-6637	174	4	publishing	publishing	PROPN
ap-6637	174	5	house	house	PROPN
ap-6637	174	6	,	,	PUNCT
ap-6637	174	7	kyiv	kyiv	PROPN
ap-6637	174	8	,	,	PUNCT
ap-6637	174	9	1992	1992	NUM
ap-6637	174	10	.	.	PUNCT
ap-6637	175	1	[	[	X
ap-6637	175	2	2	2	NUM
ap-6637	175	3	]	]	PUNCT
ap-6637	175	4	a.	a.	NOUN
ap-6637	175	5	a.	a.	NOUN
ap-6637	175	6	savelov	savelov	PROPN
ap-6637	175	7	.	.	PUNCT
ap-6637	176	1	flat	flat	ADJ
ap-6637	176	2	curves	curve	NOUN
ap-6637	176	3	.	.	PUNCT
ap-6637	177	1	systematics	systematic	NOUN
ap-6637	177	2	,	,	PUNCT
ap-6637	177	3	properties	property	NOUN
ap-6637	177	4	,	,	PUNCT
ap-6637	177	5	applications	application	NOUN
ap-6637	177	6	.	.	PUNCT
ap-6637	178	1	state	state	NOUN
ap-6637	178	2	publishing	publishing	PROPN
ap-6637	178	3	house	house	PROPN
ap-6637	178	4	of	of	ADP
ap-6637	178	5	physical	physical	ADJ
ap-6637	178	6	and	and	CCONJ
ap-6637	178	7	mathematical	mathematical	ADJ
ap-6637	178	8	literature	literature	NOUN
ap-6637	178	9	,	,	PUNCT
ap-6637	178	10	moskov	moskov	PROPN
ap-6637	178	11	,	,	PUNCT
ap-6637	178	12	1960	1960	NUM
ap-6637	178	13	.	.	PUNCT
ap-6637	179	1	[	[	X
ap-6637	179	2	3	3	X
ap-6637	179	3	]	]	X
ap-6637	179	4	d.	d.	PROPN
ap-6637	179	5	hilbert	hilbert	PROPN
ap-6637	179	6	,	,	PUNCT
ap-6637	179	7	s.	s.	PROPN
ap-6637	179	8	kon	kon	PROPN
ap-6637	179	9	-	-	PUNCT
ap-6637	179	10	vossen	vossen	NOUN
ap-6637	179	11	.	.	PUNCT
ap-6637	180	1	visual	visual	ADJ
ap-6637	180	2	geometry	geometry	NOUN
ap-6637	180	3	.	.	PUNCT
ap-6637	181	1	science	science	NOUN
ap-6637	181	2	,	,	PUNCT
ap-6637	181	3	moskov	moskov	PROPN
ap-6637	181	4	,	,	PUNCT
ap-6637	181	5	1981	1981	NUM
ap-6637	181	6	.	.	PUNCT
ap-6637	182	1	[	[	X
ap-6637	182	2	4	4	X
ap-6637	182	3	]	]	X
ap-6637	182	4	v.	v.	ADP
ap-6637	182	5	bulgakov	bulgakov	PROPN
ap-6637	182	6	,	,	PUNCT
ap-6637	182	7	s.	s.	PROPN
ap-6637	182	8	pilipaka	pilipaka	PROPN
ap-6637	182	9	,	,	PUNCT
ap-6637	182	10	v.	v.	ADP
ap-6637	182	11	adamchuk	adamchuk	PROPN
ap-6637	182	12	,	,	PUNCT
ap-6637	182	13	j.	j.	PROPN
ap-6637	182	14	olt	olt	PROPN
ap-6637	182	15	.	.	PUNCT
ap-6637	183	1	theory	theory	NOUN
ap-6637	183	2	of	of	ADP
ap-6637	183	3	motion	motion	NOUN
ap-6637	183	4	of	of	ADP
ap-6637	183	5	a	a	DET
ap-6637	183	6	material	material	NOUN
ap-6637	183	7	point	point	NOUN
ap-6637	183	8	along	along	ADP
ap-6637	183	9	a	a	DET
ap-6637	183	10	plane	plane	NOUN
ap-6637	183	11	curve	curve	NOUN
ap-6637	183	12	with	with	ADP
ap-6637	183	13	a	a	DET
ap-6637	183	14	constant	constant	ADJ
ap-6637	183	15	pressure	pressure	NOUN
ap-6637	183	16	and	and	CCONJ
ap-6637	183	17	velocity	velocity	NOUN
ap-6637	183	18	.	.	PUNCT
ap-6637	184	1	agronomy	agronomy	NOUN
ap-6637	184	2	research	research	NOUN
ap-6637	184	3	12(3):937	12(3):937	NUM
ap-6637	184	4	–	–	PUNCT
ap-6637	184	5	948	948	NUM
ap-6637	184	6	,	,	PUNCT
ap-6637	184	7	2014	2014	NUM
ap-6637	184	8	.	.	PUNCT
ap-6637	185	1	[	[	X
ap-6637	185	2	5	5	X
ap-6637	185	3	]	]	PUNCT
ap-6637	185	4	f.	f.	PROPN
ap-6637	185	5	l.	l.	PROPN
ap-6637	185	6	litvin	litvin	PROPN
ap-6637	185	7	.	.	PUNCT
ap-6637	186	1	theory	theory	NOUN
ap-6637	186	2	of	of	ADP
ap-6637	186	3	gears	gear	NOUN
ap-6637	186	4	.	.	PUNCT
ap-6637	187	1	science	science	NOUN
ap-6637	187	2	,	,	PUNCT
ap-6637	187	3	moskov	moskov	PROPN
ap-6637	187	4	,	,	PUNCT
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ap-6637	187	6	.	.	PUNCT
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ap-6637	188	11	.	.	PUNCT
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ap-6637	189	10	.	.	PUNCT
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ap-6637	190	13	–	–	PUNCT
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ap-6637	190	17	.	.	PUNCT
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ap-6637	192	13	.	.	PUNCT
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ap-6637	193	8	:	:	PUNCT
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ap-6637	193	17	2):59	2):59	NUM
ap-6637	193	18	–	–	SYM
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ap-6637	193	20	,	,	PUNCT
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ap-6637	193	22	.	.	PUNCT
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ap-6637	194	2	8	8	NUM
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ap-6637	194	7	.	.	PUNCT
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ap-6637	195	12	.	.	PUNCT
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ap-6637	196	6	:	:	PUNCT
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ap-6637	196	14	–	–	PUNCT
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ap-6637	196	16	,	,	PUNCT
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ap-6637	196	18	.	.	PUNCT
ap-6637	197	1	[	[	X
ap-6637	197	2	9	9	NUM
ap-6637	197	3	]	]	PUNCT
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ap-6637	197	5	p.	p.	PROPN
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ap-6637	199	9	,	,	PUNCT
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ap-6637	199	11	.	.	PUNCT
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ap-6637	201	10	.	.	PUNCT
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ap-6637	202	8	"	"	PUNCT
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ap-6637	202	12	,	,	PUNCT
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ap-6637	202	14	.	.	PUNCT
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ap-6637	204	5	-	-	PUNCT
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ap-6637	204	13	.	.	PUNCT
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ap-6637	205	8	,	,	PUNCT
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ap-6637	205	10	.	.	PUNCT
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ap-6637	206	4	.	.	PUNCT
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ap-6637	207	3	]	]	PUNCT
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ap-6637	208	16	.	.	PUNCT
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ap-6637	212	6	–	–	PUNCT
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ap-6637	212	8	,	,	PUNCT
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ap-6637	212	10	.	.	PUNCT
ap-6637	213	1	doi:10.1016	doi:10.1016	PROPN
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ap-6637	216	8	,	,	PUNCT
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ap-6637	216	10	.	.	PUNCT
ap-6637	217	1	doi:10.1016	doi:10.1016	PROPN
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ap-6637	218	9	.	.	PUNCT
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ap-6637	220	18	.	.	PUNCT
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ap-6637	221	6	,	,	PUNCT
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ap-6637	221	8	.	.	PUNCT
ap-6637	222	1	doi:10.1016	doi:10.1016	PROPN
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ap-6637	222	6	-	-	SYM
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ap-6637	225	8	.	.	PUNCT
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ap-6637	226	7	.	.	PUNCT
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ap-6637	227	8	.	.	PUNCT
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ap-6637	228	4	,	,	PUNCT
ap-6637	228	5	2011	2011	NUM
ap-6637	228	6	.	.	PUNCT
ap-6637	229	1	317	317	NUM
ap-6637	229	2	http://dx.doi.org/10.1088/1742-6596/1050/1/012049	http://dx.doi.org/10.1088/1742-6596/1050/1/012049	PROPN
ap-6637	229	3	http://dx.doi.org/10.1016/j.mechmachtheory.2005.06.003	http://dx.doi.org/10.1016/j.mechmachtheory.2005.06.003	NOUN
ap-6637	229	4	http://dx.doi.org/10.1016/j.mechmachtheory.2007.07.004	http://dx.doi.org/10.1016/j.mechmachtheory.2007.07.004	PROPN
ap-6637	229	5	http://dx.doi.org/10.1016/s0007-8506(07)60811-7	http://dx.doi.org/10.1016/s0007-8506(07)60811-7	AUX
ap-6637	229	6	acta	acta	PROPN
ap-6637	229	7	polytechnica	polytechnica	PROPN
ap-6637	229	8	60(4):1–5	60(4):1–5	PROPN
ap-6637	229	9	,	,	PUNCT
ap-6637	229	10	2020	2020	NUM
ap-6637	229	11	1	1	NUM
ap-6637	229	12	introduction	introduction	NOUN
ap-6637	229	13	2	2	NUM
ap-6637	229	14	material	material	NOUN
ap-6637	229	15	and	and	CCONJ
ap-6637	229	16	method	method	NOUN
ap-6637	229	17	3	3	NUM
ap-6637	229	18	result	result	NOUN
ap-6637	229	19	4	4	NUM
ap-6637	229	20	conclusions	conclusion	NOUN
ap-6637	229	21	and	and	CCONJ
ap-6637	229	22	prospects	prospect	NOUN
ap-6637	229	23	for	for	ADP
ap-6637	229	24	further	further	ADJ
ap-6637	229	25	research	research	NOUN
ap-6637	229	26	references	reference	NOUN