id	sid	tid	token	lemma	pos
ap-6074	1	1	acta	acta	PROPN
ap-6074	1	2	polytechnica	polytechnica	PROPN
ap-6074	1	3	https://doi.org/10.14311/ap.2021.61.0099	https://doi.org/10.14311/ap.2021.61.0099	PROPN
ap-6074	1	4	acta	acta	PROPN
ap-6074	1	5	polytechnica	polytechnica	PROPN
ap-6074	1	6	61(si):99–109	61(si):99–109	NUM
ap-6074	1	7	,	,	PUNCT
ap-6074	1	8	2021	2021	NUM
ap-6074	1	9	©	©	ADP
ap-6074	1	10	2021	2021	NUM
ap-6074	1	11	the	the	DET
ap-6074	1	12	author(s	author(s	NOUN
ap-6074	1	13	)	)	PUNCT
ap-6074	1	14	.	.	PUNCT
ap-6074	2	1	licensed	license	VERB
ap-6074	2	2	under	under	ADP
ap-6074	2	3	a	a	DET
ap-6074	2	4	cc	cc	NOUN
ap-6074	2	5	-	-	PUNCT
ap-6074	2	6	by	by	ADP
ap-6074	2	7	4.0	4.0	NUM
ap-6074	2	8	licence	licence	NOUN
ap-6074	2	9	published	publish	VERB
ap-6074	2	10	by	by	ADP
ap-6074	2	11	the	the	DET
ap-6074	2	12	czech	czech	PROPN
ap-6074	2	13	technical	technical	PROPN
ap-6074	2	14	university	university	PROPN
ap-6074	2	15	in	in	ADP
ap-6074	2	16	prague	prague	PROPN
ap-6074	2	17	application	application	NOUN
ap-6074	2	18	of	of	ADP
ap-6074	2	19	ruled	rule	VERB
ap-6074	2	20	surfaces	surface	NOUN
ap-6074	2	21	in	in	ADP
ap-6074	2	22	freeform	freeform	NOUN
ap-6074	2	23	and	and	CCONJ
ap-6074	2	24	gear	gear	NOUN
ap-6074	2	25	metrology	metrology	NOUN
ap-6074	2	26	ivana	ivana	PROPN
ap-6074	2	27	linkeováa,∗	linkeováa,∗	PROPN
ap-6074	2	28	,	,	PUNCT
ap-6074	2	29	vít	vít	PROPN
ap-6074	2	30	zelenýb	zelenýb	PROPN
ap-6074	2	31	a	a	DET
ap-6074	2	32	czech	czech	PROPN
ap-6074	2	33	technical	technical	PROPN
ap-6074	2	34	university	university	PROPN
ap-6074	2	35	in	in	ADP
ap-6074	2	36	prague	prague	PROPN
ap-6074	2	37	,	,	PUNCT
ap-6074	2	38	faculty	faculty	NOUN
ap-6074	2	39	of	of	ADP
ap-6074	2	40	mechanical	mechanical	ADJ
ap-6074	2	41	engineering	engineering	NOUN
ap-6074	2	42	,	,	PUNCT
ap-6074	2	43	department	department	NOUN
ap-6074	2	44	of	of	ADP
ap-6074	2	45	technical	technical	ADJ
ap-6074	2	46	mathematics	mathematic	NOUN
ap-6074	2	47	,	,	PUNCT
ap-6074	2	48	karlovo	karlovo	PROPN
ap-6074	2	49	nám	nám	PROPN
ap-6074	2	50	.	.	PROPN
ap-6074	3	1	13	13	NUM
ap-6074	3	2	,	,	PUNCT
ap-6074	3	3	121	121	NUM
ap-6074	3	4	35	35	NUM
ap-6074	3	5	prague	prague	NOUN
ap-6074	3	6	,	,	PUNCT
ap-6074	3	7	czech	czech	PROPN
ap-6074	3	8	republic	republic	PROPN
ap-6074	3	9	b	b	PROPN
ap-6074	3	10	czech	czech	PROPN
ap-6074	3	11	metrology	metrology	NOUN
ap-6074	3	12	institute	institute	NOUN
ap-6074	3	13	,	,	PUNCT
ap-6074	3	14	laboratories	laboratory	NOUN
ap-6074	3	15	of	of	ADP
ap-6074	3	16	fundamental	fundamental	ADJ
ap-6074	3	17	metrology	metrology	NOUN
ap-6074	3	18	,	,	PUNCT
ap-6074	3	19	v	v	ADP
ap-6074	3	20	botanice	botanice	NOUN
ap-6074	3	21	1504/4	1504/4	NUM
ap-6074	3	22	,	,	PUNCT
ap-6074	3	23	150	150	NUM
ap-6074	3	24	72	72	NUM
ap-6074	3	25	prague	prague	NOUN
ap-6074	3	26	,	,	PUNCT
ap-6074	3	27	czech	czech	PROPN
ap-6074	3	28	republic	republic	NOUN
ap-6074	3	29	∗	∗	NOUN
ap-6074	3	30	corresponding	correspond	VERB
ap-6074	3	31	author	author	NOUN
ap-6074	3	32	:	:	PUNCT
ap-6074	3	33	ivana.linkeova@fs.cvut.cz	ivana.linkeova@fs.cvut.cz	ADJ
ap-6074	3	34	abstract	abstract	NOUN
ap-6074	3	35	.	.	PUNCT
ap-6074	4	1	an	an	DET
ap-6074	4	2	application	application	NOUN
ap-6074	4	3	of	of	ADP
ap-6074	4	4	two	two	NUM
ap-6074	4	5	ruled	rule	VERB
ap-6074	4	6	surfaces	surface	NOUN
ap-6074	4	7	(	(	PUNCT
ap-6074	4	8	i.e.	i.e.	X
ap-6074	4	9	,	,	PUNCT
ap-6074	4	10	surfaces	surface	NOUN
ap-6074	4	11	generated	generate	VERB
ap-6074	4	12	by	by	ADP
ap-6074	4	13	a	a	DET
ap-6074	4	14	motion	motion	NOUN
ap-6074	4	15	of	of	ADP
ap-6074	4	16	a	a	DET
ap-6074	4	17	straight	straight	ADJ
ap-6074	4	18	line	line	NOUN
ap-6074	4	19	)	)	PUNCT
ap-6074	4	20	,	,	PUNCT
ap-6074	4	21	a	a	DET
ap-6074	4	22	surface	surface	NOUN
ap-6074	4	23	of	of	ADP
ap-6074	4	24	hyperbolic	hyperbolic	ADJ
ap-6074	4	25	paraboloid	paraboloid	NOUN
ap-6074	4	26	and	and	CCONJ
ap-6074	4	27	a	a	DET
ap-6074	4	28	tangent	tangent	ADJ
ap-6074	4	29	surface	surface	NOUN
ap-6074	4	30	of	of	ADP
ap-6074	4	31	a	a	DET
ap-6074	4	32	cylindrical	cylindrical	ADJ
ap-6074	4	33	helix	helix	NOUN
ap-6074	4	34	in	in	ADP
ap-6074	4	35	freeform	freeform	NOUN
ap-6074	4	36	and	and	CCONJ
ap-6074	4	37	gear	gear	NOUN
ap-6074	4	38	metrology	metrology	NOUN
ap-6074	4	39	is	be	AUX
ap-6074	4	40	introduced	introduce	VERB
ap-6074	4	41	in	in	ADP
ap-6074	4	42	this	this	DET
ap-6074	4	43	paper	paper	NOUN
ap-6074	4	44	.	.	PUNCT
ap-6074	5	1	both	both	DET
ap-6074	5	2	surfaces	surface	NOUN
ap-6074	5	3	have	have	AUX
ap-6074	5	4	been	be	AUX
ap-6074	5	5	implemented	implement	VERB
ap-6074	5	6	as	as	ADP
ap-6074	5	7	the	the	DET
ap-6074	5	8	main	main	ADJ
ap-6074	5	9	functional	functional	ADJ
ap-6074	5	10	figures	figure	NOUN
ap-6074	5	11	in	in	ADP
ap-6074	5	12	several	several	ADJ
ap-6074	5	13	artefacts	artefact	NOUN
ap-6074	5	14	–	–	PUNCT
ap-6074	5	15	metrological	metrological	ADJ
ap-6074	5	16	calibration	calibration	NOUN
ap-6074	5	17	standards	standard	NOUN
ap-6074	5	18	intended	intend	VERB
ap-6074	5	19	for	for	ADP
ap-6074	5	20	testing	test	VERB
ap-6074	5	21	the	the	DET
ap-6074	5	22	freeform	freeform	ADJ
ap-6074	5	23	capabilities	capability	NOUN
ap-6074	5	24	of	of	ADP
ap-6074	5	25	various	various	ADJ
ap-6074	5	26	measuring	measuring	NOUN
ap-6074	5	27	technologies	technology	NOUN
ap-6074	5	28	(	(	PUNCT
ap-6074	5	29	e.g.	e.g.	ADV
ap-6074	5	30	,	,	PUNCT
ap-6074	5	31	tactile	tactile	ADJ
ap-6074	5	32	point	point	NOUN
ap-6074	5	33	-	-	PUNCT
ap-6074	5	34	to	to	ADP
ap-6074	5	35	-	-	PUNCT
ap-6074	5	36	point	point	NOUN
ap-6074	5	37	measurement	measurement	NOUN
ap-6074	5	38	and	and	CCONJ
ap-6074	5	39	tactile	tactile	ADJ
ap-6074	5	40	scanning	scanning	NOUN
ap-6074	5	41	on	on	ADP
ap-6074	5	42	coordinate	coordinate	NOUN
ap-6074	5	43	measuring	measure	VERB
ap-6074	5	44	machine	machine	NOUN
ap-6074	5	45	,	,	PUNCT
ap-6074	5	46	optical	optical	ADJ
ap-6074	5	47	scanning	scanning	NOUN
ap-6074	5	48	,	,	PUNCT
ap-6074	5	49	computer	computer	NOUN
ap-6074	5	50	tomography	tomography	NOUN
ap-6074	5	51	)	)	PUNCT
ap-6074	5	52	.	.	PUNCT
ap-6074	6	1	geometrical	geometrical	ADJ
ap-6074	6	2	and	and	CCONJ
ap-6074	6	3	mathematical	mathematical	ADJ
ap-6074	6	4	properties	property	NOUN
ap-6074	6	5	of	of	ADP
ap-6074	6	6	the	the	DET
ap-6074	6	7	surface	surface	NOUN
ap-6074	6	8	used	use	VERB
ap-6074	6	9	are	be	AUX
ap-6074	6	10	summarised	summarise	VERB
ap-6074	6	11	,	,	PUNCT
ap-6074	6	12	cad	cad	NOUN
ap-6074	6	13	models	model	NOUN
ap-6074	6	14	of	of	ADP
ap-6074	6	15	all	all	DET
ap-6074	6	16	the	the	DET
ap-6074	6	17	developed	develop	VERB
ap-6074	6	18	standards	standard	NOUN
ap-6074	6	19	are	be	AUX
ap-6074	6	20	presented	present	VERB
ap-6074	6	21	and	and	CCONJ
ap-6074	6	22	photos	photo	NOUN
ap-6074	6	23	of	of	ADP
ap-6074	6	24	the	the	DET
ap-6074	6	25	manufactured	manufacture	VERB
ap-6074	6	26	standards	standard	NOUN
ap-6074	6	27	are	be	AUX
ap-6074	6	28	shown	show	VERB
ap-6074	6	29	.	.	PUNCT
ap-6074	7	1	keywords	keyword	NOUN
ap-6074	7	2	:	:	PUNCT
ap-6074	7	3	hyperbolic	hyperbolic	ADJ
ap-6074	7	4	paraboloid	paraboloid	ADJ
ap-6074	7	5	,	,	PUNCT
ap-6074	7	6	tangent	tangent	ADJ
ap-6074	7	7	surface	surface	NOUN
ap-6074	7	8	of	of	ADP
ap-6074	7	9	a	a	DET
ap-6074	7	10	helix	helix	NOUN
ap-6074	7	11	,	,	PUNCT
ap-6074	7	12	cad	cad	PROPN
ap-6074	7	13	model	model	NOUN
ap-6074	7	14	,	,	PUNCT
ap-6074	7	15	freeform	freeform	ADJ
ap-6074	7	16	metrology	metrology	NOUN
ap-6074	7	17	,	,	PUNCT
ap-6074	7	18	calibration	calibration	NOUN
ap-6074	7	19	standard	standard	NOUN
ap-6074	7	20	.	.	PUNCT
ap-6074	8	1	1	1	X
ap-6074	8	2	.	.	X
ap-6074	8	3	introduction	introduction	NOUN
ap-6074	8	4	in	in	ADP
ap-6074	8	5	precision	precision	NOUN
ap-6074	8	6	engineering	engineering	NOUN
ap-6074	8	7	,	,	PUNCT
ap-6074	8	8	an	an	DET
ap-6074	8	9	inspection	inspection	NOUN
ap-6074	8	10	of	of	ADP
ap-6074	8	11	components	component	NOUN
ap-6074	8	12	with	with	ADP
ap-6074	8	13	functional	functional	ADJ
ap-6074	8	14	freeform	freeform	NOUN
ap-6074	8	15	surfaces	surface	NOUN
ap-6074	8	16	lay	lie	VERB
ap-6074	8	17	great	great	ADJ
ap-6074	8	18	demands	demand	NOUN
ap-6074	8	19	on	on	ADP
ap-6074	8	20	metrological	metrological	ADJ
ap-6074	8	21	procedures	procedure	NOUN
ap-6074	8	22	.	.	PUNCT
ap-6074	9	1	a	a	DET
ap-6074	9	2	freeform	freeform	ADJ
ap-6074	9	3	shape	shape	NOUN
ap-6074	9	4	means	mean	VERB
ap-6074	9	5	a	a	DET
ap-6074	9	6	shape	shape	NOUN
ap-6074	9	7	that	that	PRON
ap-6074	9	8	does	do	AUX
ap-6074	9	9	not	not	PART
ap-6074	9	10	belong	belong	VERB
ap-6074	9	11	to	to	ADP
ap-6074	9	12	the	the	DET
ap-6074	9	13	basic	basic	ADJ
ap-6074	9	14	geometrical	geometrical	ADJ
ap-6074	9	15	elements	element	NOUN
ap-6074	9	16	(	(	PUNCT
ap-6074	9	17	such	such	ADJ
ap-6074	9	18	as	as	ADP
ap-6074	9	19	,	,	PUNCT
ap-6074	9	20	plane	plane	NOUN
ap-6074	9	21	,	,	PUNCT
ap-6074	9	22	sphere	sphere	NOUN
ap-6074	9	23	,	,	PUNCT
ap-6074	9	24	cylinder	cylinder	NOUN
ap-6074	9	25	,	,	PUNCT
ap-6074	9	26	cone	cone	NOUN
ap-6074	9	27	,	,	PUNCT
ap-6074	9	28	torus	torus	NOUN
ap-6074	9	29	,	,	PUNCT
ap-6074	9	30	...	...	PUNCT
ap-6074	9	31	)	)	PUNCT
ap-6074	9	32	and	and	CCONJ
ap-6074	9	33	is	be	AUX
ap-6074	9	34	difficult	difficult	ADJ
ap-6074	9	35	to	to	PART
ap-6074	9	36	describe	describe	VERB
ap-6074	9	37	it	it	PRON
ap-6074	9	38	mathematically	mathematically	ADV
ap-6074	9	39	.	.	PUNCT
ap-6074	10	1	usually	usually	ADV
ap-6074	10	2	,	,	PUNCT
ap-6074	10	3	the	the	DET
ap-6074	10	4	nominal	nominal	ADJ
ap-6074	10	5	shape	shape	NOUN
ap-6074	10	6	and	and	CCONJ
ap-6074	10	7	dimensions	dimension	NOUN
ap-6074	10	8	of	of	ADP
ap-6074	10	9	the	the	DET
ap-6074	10	10	component	component	NOUN
ap-6074	10	11	with	with	ADP
ap-6074	10	12	freeform	freeform	ADJ
ap-6074	10	13	surface	surface	NOUN
ap-6074	10	14	is	be	AUX
ap-6074	10	15	represented	represent	VERB
ap-6074	10	16	by	by	ADP
ap-6074	10	17	cad	cad	PROPN
ap-6074	10	18	(	(	PUNCT
ap-6074	10	19	computer	computer	NOUN
ap-6074	10	20	aided	aid	VERB
ap-6074	10	21	design	design	NOUN
ap-6074	10	22	)	)	PUNCT
ap-6074	10	23	model	model	NOUN
ap-6074	10	24	and	and	CCONJ
ap-6074	10	25	metrology	metrology	NOUN
ap-6074	10	26	procedure	procedure	NOUN
ap-6074	10	27	applied	apply	VERB
ap-6074	10	28	in	in	ADP
ap-6074	10	29	inspection	inspection	NOUN
ap-6074	10	30	is	be	AUX
ap-6074	10	31	a	a	DET
ap-6074	10	32	so	so	ADV
ap-6074	10	33	called	call	VERB
ap-6074	10	34	cadbased	cadbase	VERB
ap-6074	10	35	measurement	measurement	NOUN
ap-6074	10	36	.	.	PUNCT
ap-6074	11	1	a	a	DET
ap-6074	11	2	reliable	reliable	ADJ
ap-6074	11	3	evaluation	evaluation	NOUN
ap-6074	11	4	of	of	ADP
ap-6074	11	5	freeform	freeform	ADJ
ap-6074	11	6	cad	cad	NOUN
ap-6074	11	7	-	-	PUNCT
ap-6074	11	8	based	base	VERB
ap-6074	11	9	measurement	measurement	NOUN
ap-6074	11	10	leads	lead	VERB
ap-6074	11	11	to	to	ADP
ap-6074	11	12	the	the	DET
ap-6074	11	13	development	development	NOUN
ap-6074	11	14	of	of	ADP
ap-6074	11	15	reference	reference	NOUN
ap-6074	11	16	standards	standard	NOUN
ap-6074	11	17	with	with	ADP
ap-6074	11	18	a	a	DET
ap-6074	11	19	sufficient	sufficient	ADJ
ap-6074	11	20	precision	precision	NOUN
ap-6074	11	21	and	and	CCONJ
ap-6074	11	22	specific	specific	ADJ
ap-6074	11	23	properties	property	NOUN
ap-6074	11	24	.	.	PUNCT
ap-6074	12	1	calibration	calibration	NOUN
ap-6074	12	2	standards	standard	NOUN
ap-6074	12	3	of	of	ADP
ap-6074	12	4	regular	regular	ADJ
ap-6074	12	5	shapes	shape	NOUN
ap-6074	12	6	(	(	PUNCT
ap-6074	12	7	basic	basic	ADJ
ap-6074	12	8	geometrical	geometrical	ADJ
ap-6074	12	9	elements	element	NOUN
ap-6074	12	10	)	)	PUNCT
ap-6074	12	11	are	be	AUX
ap-6074	12	12	well	well	ADV
ap-6074	12	13	developed	develop	VERB
ap-6074	12	14	[	[	X
ap-6074	12	15	1	1	NUM
ap-6074	12	16	]	]	PUNCT
ap-6074	12	17	,	,	PUNCT
ap-6074	12	18	while	while	SCONJ
ap-6074	12	19	the	the	DET
ap-6074	12	20	traceability	traceability	NOUN
ap-6074	12	21	and	and	CCONJ
ap-6074	12	22	quality	quality	NOUN
ap-6074	12	23	inspection	inspection	NOUN
ap-6074	12	24	in	in	ADP
ap-6074	12	25	freeform	freeform	ADJ
ap-6074	12	26	manufacturing	manufacturing	NOUN
ap-6074	12	27	are	be	AUX
ap-6074	12	28	issues	issue	NOUN
ap-6074	12	29	,	,	PUNCT
ap-6074	12	30	due	due	ADP
ap-6074	12	31	to	to	ADP
ap-6074	12	32	the	the	DET
ap-6074	12	33	lack	lack	NOUN
ap-6074	12	34	of	of	ADP
ap-6074	12	35	traceable	traceable	ADJ
ap-6074	12	36	verification	verification	NOUN
ap-6074	12	37	standards	standard	NOUN
ap-6074	12	38	[	[	X
ap-6074	12	39	2	2	NUM
ap-6074	12	40	]	]	PUNCT
ap-6074	12	41	.	.	PUNCT
ap-6074	13	1	based	base	VERB
ap-6074	13	2	on	on	ADP
ap-6074	13	3	a	a	DET
ap-6074	13	4	geometrical	geometrical	ADJ
ap-6074	13	5	-	-	PUNCT
ap-6074	13	6	mathematical	mathematical	ADJ
ap-6074	13	7	approach	approach	NOUN
ap-6074	13	8	,	,	PUNCT
ap-6074	13	9	several	several	ADJ
ap-6074	13	10	freeform	freeform	ADJ
ap-6074	13	11	reference	reference	NOUN
ap-6074	13	12	standards	standard	NOUN
ap-6074	13	13	and	and	CCONJ
ap-6074	13	14	gear	gear	NOUN
ap-6074	13	15	measurement	measurement	NOUN
ap-6074	13	16	standard	standard	NOUN
ap-6074	13	17	for	for	ADP
ap-6074	13	18	testing	test	VERB
ap-6074	13	19	the	the	DET
ap-6074	13	20	freeform	freeform	ADJ
ap-6074	13	21	and	and	CCONJ
ap-6074	13	22	gear	gear	NOUN
ap-6074	13	23	measurement	measurement	NOUN
ap-6074	13	24	capability	capability	NOUN
ap-6074	13	25	of	of	ADP
ap-6074	13	26	coordinate	coordinate	NOUN
ap-6074	13	27	measuring	measure	VERB
ap-6074	13	28	machines	machine	NOUN
ap-6074	13	29	and	and	CCONJ
ap-6074	13	30	machine	machine	NOUN
ap-6074	13	31	tools	tool	NOUN
ap-6074	13	32	has	have	AUX
ap-6074	13	33	been	be	AUX
ap-6074	13	34	developed	develop	VERB
ap-6074	13	35	in	in	ADP
ap-6074	13	36	the	the	DET
ap-6074	13	37	czech	czech	PROPN
ap-6074	13	38	metrology	metrology	PROPN
ap-6074	13	39	institute	institute	PROPN
ap-6074	13	40	(	(	PUNCT
ap-6074	13	41	cmi	cmi	PROPN
ap-6074	13	42	)	)	PUNCT
ap-6074	13	43	in	in	ADP
ap-6074	13	44	cooperation	cooperation	NOUN
ap-6074	13	45	with	with	ADP
ap-6074	13	46	the	the	DET
ap-6074	13	47	czech	czech	PROPN
ap-6074	13	48	technical	technical	PROPN
ap-6074	13	49	university	university	PROPN
ap-6074	13	50	in	in	ADP
ap-6074	13	51	prague	prague	PROPN
ap-6074	13	52	(	(	PUNCT
ap-6074	13	53	ctu	ctu	PROPN
ap-6074	13	54	)	)	PUNCT
ap-6074	14	1	[	[	X
ap-6074	14	2	3	3	NUM
ap-6074	14	3	]	]	PUNCT
ap-6074	14	4	.	.	PUNCT
ap-6074	15	1	the	the	DET
ap-6074	15	2	development	development	NOUN
ap-6074	15	3	of	of	ADP
ap-6074	15	4	all	all	DET
ap-6074	15	5	the	the	DET
ap-6074	15	6	standards	standard	NOUN
ap-6074	15	7	consists	consist	VERB
ap-6074	15	8	in	in	ADP
ap-6074	15	9	a	a	DET
ap-6074	15	10	purposeful	purposeful	ADJ
ap-6074	15	11	application	application	NOUN
ap-6074	15	12	of	of	ADP
ap-6074	15	13	a	a	DET
ap-6074	15	14	surface	surface	NOUN
ap-6074	15	15	of	of	ADP
ap-6074	15	16	hyperbolic	hyperbolic	ADJ
ap-6074	15	17	paraboloid	paraboloid	NOUN
ap-6074	15	18	and	and	CCONJ
ap-6074	15	19	tangent	tangent	ADJ
ap-6074	15	20	surface	surface	NOUN
ap-6074	15	21	of	of	ADP
ap-6074	15	22	the	the	DET
ap-6074	15	23	cylindrical	cylindrical	ADJ
ap-6074	15	24	helix	helix	NOUN
ap-6074	15	25	and	and	CCONJ
ap-6074	15	26	effective	effective	ADJ
ap-6074	15	27	usage	usage	NOUN
ap-6074	15	28	of	of	ADP
ap-6074	15	29	their	their	PRON
ap-6074	15	30	excellent	excellent	ADJ
ap-6074	15	31	geometrical	geometrical	ADJ
ap-6074	15	32	-	-	PUNCT
ap-6074	15	33	mathematical	mathematical	ADJ
ap-6074	15	34	properties	property	NOUN
ap-6074	15	35	[	[	X
ap-6074	15	36	4	4	NUM
ap-6074	15	37	]	]	PUNCT
ap-6074	15	38	.	.	PUNCT
ap-6074	16	1	three	three	NUM
ap-6074	16	2	of	of	ADP
ap-6074	16	3	the	the	DET
ap-6074	16	4	standards	standard	NOUN
ap-6074	16	5	developed	develop	VERB
ap-6074	16	6	,	,	PUNCT
ap-6074	16	7	i.e.	i.e.	X
ap-6074	16	8	freeform	freeform	ADJ
ap-6074	16	9	standard	standard	ADJ
ap-6074	16	10	hyperbolic	hyperbolic	ADJ
ap-6074	16	11	paraboloid	paraboloid	NOUN
ap-6074	16	12	,	,	PUNCT
ap-6074	16	13	spatial	spatial	ADJ
ap-6074	16	14	hyperbolic	hyperbolic	ADJ
ap-6074	16	15	paraboloid	paraboloid	ADJ
ap-6074	16	16	standard	standard	NOUN
ap-6074	16	17	and	and	CCONJ
ap-6074	16	18	smart	smart	ADJ
ap-6074	16	19	gear	gear	NOUN
ap-6074	16	20	measurement	measurement	NOUN
ap-6074	16	21	standard	standard	NOUN
ap-6074	16	22	,	,	PUNCT
ap-6074	16	23	are	be	AUX
ap-6074	16	24	mentioned	mention	VERB
ap-6074	16	25	in	in	ADP
ap-6074	16	26	this	this	DET
ap-6074	16	27	paper	paper	NOUN
ap-6074	16	28	.	.	PUNCT
ap-6074	17	1	the	the	DET
ap-6074	17	2	paper	paper	NOUN
ap-6074	17	3	is	be	AUX
ap-6074	17	4	organised	organise	VERB
ap-6074	17	5	as	as	SCONJ
ap-6074	17	6	follows	follow	VERB
ap-6074	17	7	.	.	PUNCT
ap-6074	18	1	a	a	DET
ap-6074	18	2	mathematical	mathematical	ADJ
ap-6074	18	3	model	model	NOUN
ap-6074	18	4	and	and	CCONJ
ap-6074	18	5	geometrical	geometrical	ADJ
ap-6074	18	6	properties	property	NOUN
ap-6074	18	7	of	of	ADP
ap-6074	18	8	a	a	DET
ap-6074	18	9	surface	surface	NOUN
ap-6074	18	10	of	of	ADP
ap-6074	18	11	hyperbolic	hyperbolic	ADJ
ap-6074	18	12	paraboloid	paraboloid	NOUN
ap-6074	18	13	and	and	CCONJ
ap-6074	18	14	its	its	PRON
ap-6074	18	15	application	application	NOUN
ap-6074	18	16	in	in	ADP
ap-6074	18	17	the	the	DET
ap-6074	18	18	development	development	NOUN
ap-6074	18	19	of	of	ADP
ap-6074	18	20	the	the	DET
ap-6074	18	21	freeform	freeform	ADJ
ap-6074	18	22	standard	standard	ADJ
ap-6074	18	23	hyperbolic	hyperbolic	ADJ
ap-6074	18	24	paraboloid	paraboloid	NOUN
ap-6074	18	25	is	be	AUX
ap-6074	18	26	described	describe	VERB
ap-6074	18	27	in	in	ADP
ap-6074	18	28	chapter	chapter	NOUN
ap-6074	18	29	2	2	NUM
ap-6074	18	30	.	.	PUNCT
ap-6074	19	1	the	the	DET
ap-6074	19	2	solid	solid	NOUN
ap-6074	19	3	of	of	ADP
ap-6074	19	4	hyperbolic	hyperbolic	ADJ
ap-6074	19	5	paraboloid	paraboloid	NOUN
ap-6074	19	6	applied	apply	VERB
ap-6074	19	7	in	in	ADP
ap-6074	19	8	the	the	DET
ap-6074	19	9	spatial	spatial	ADJ
ap-6074	19	10	hyperbolic	hyperbolic	ADJ
ap-6074	19	11	paraboloid	paraboloid	ADJ
ap-6074	19	12	standard	standard	NOUN
ap-6074	19	13	is	be	AUX
ap-6074	19	14	presented	present	VERB
ap-6074	19	15	in	in	ADP
ap-6074	19	16	chapter	chapter	NOUN
ap-6074	19	17	3	3	NUM
ap-6074	19	18	.	.	PUNCT
ap-6074	20	1	the	the	DET
ap-6074	20	2	relationship	relationship	NOUN
ap-6074	20	3	among	among	ADP
ap-6074	20	4	the	the	DET
ap-6074	20	5	surfaces	surface	NOUN
ap-6074	20	6	generated	generate	VERB
ap-6074	20	7	by	by	ADP
ap-6074	20	8	screw	screw	VERB
ap-6074	20	9	motion	motion	NOUN
ap-6074	20	10	of	of	ADP
ap-6074	20	11	a	a	DET
ap-6074	20	12	circle	circle	NOUN
ap-6074	20	13	involute	involute	NOUN
ap-6074	20	14	,	,	PUNCT
ap-6074	20	15	tangent	tangent	ADJ
ap-6074	20	16	surface	surface	NOUN
ap-6074	20	17	of	of	ADP
ap-6074	20	18	the	the	DET
ap-6074	20	19	cylindrical	cylindrical	ADJ
ap-6074	20	20	helix	helix	NOUN
ap-6074	20	21	and	and	CCONJ
ap-6074	20	22	flank	flank	NOUN
ap-6074	20	23	surface	surface	NOUN
ap-6074	20	24	of	of	ADP
ap-6074	20	25	the	the	DET
ap-6074	20	26	involute	involute	ADJ
ap-6074	20	27	gear	gear	NOUN
ap-6074	20	28	is	be	AUX
ap-6074	20	29	introduced	introduce	VERB
ap-6074	20	30	in	in	ADP
ap-6074	20	31	chapter	chapter	NOUN
ap-6074	20	32	4	4	NUM
ap-6074	20	33	.	.	PUNCT
ap-6074	20	34	smart	smart	ADJ
ap-6074	20	35	gear	gear	NOUN
ap-6074	20	36	measurement	measurement	NOUN
ap-6074	20	37	standard	standard	NOUN
ap-6074	20	38	that	that	PRON
ap-6074	20	39	has	have	AUX
ap-6074	20	40	been	be	AUX
ap-6074	20	41	developed	develop	VERB
ap-6074	20	42	based	base	VERB
ap-6074	20	43	on	on	ADP
ap-6074	20	44	this	this	DET
ap-6074	20	45	relationship	relationship	NOUN
ap-6074	20	46	is	be	AUX
ap-6074	20	47	mentioned	mention	VERB
ap-6074	20	48	in	in	ADP
ap-6074	20	49	this	this	DET
ap-6074	20	50	chapter	chapter	NOUN
ap-6074	20	51	,	,	PUNCT
ap-6074	20	52	too	too	ADV
ap-6074	20	53	.	.	PUNCT
ap-6074	21	1	for	for	ADP
ap-6074	21	2	each	each	DET
ap-6074	21	3	standard	standard	NOUN
ap-6074	21	4	,	,	PUNCT
ap-6074	21	5	the	the	DET
ap-6074	21	6	mathematical	mathematical	ADJ
ap-6074	21	7	model	model	NOUN
ap-6074	21	8	and	and	CCONJ
ap-6074	21	9	geometrical	geometrical	ADJ
ap-6074	21	10	properties	property	NOUN
ap-6074	21	11	of	of	ADP
ap-6074	21	12	the	the	DET
ap-6074	21	13	main	main	ADJ
ap-6074	21	14	functional	functional	ADJ
ap-6074	21	15	figure	figure	NOUN
ap-6074	21	16	is	be	AUX
ap-6074	21	17	described	describe	VERB
ap-6074	21	18	first	first	ADV
ap-6074	21	19	.	.	PUNCT
ap-6074	22	1	after	after	ADP
ap-6074	22	2	that	that	PRON
ap-6074	22	3	,	,	PUNCT
ap-6074	22	4	the	the	DET
ap-6074	22	5	cad	cad	PROPN
ap-6074	22	6	model	model	NOUN
ap-6074	22	7	of	of	ADP
ap-6074	22	8	the	the	DET
ap-6074	22	9	standard	standard	NOUN
ap-6074	22	10	is	be	AUX
ap-6074	22	11	introduced	introduce	VERB
ap-6074	22	12	and	and	CCONJ
ap-6074	22	13	finally	finally	ADV
ap-6074	22	14	,	,	PUNCT
ap-6074	22	15	the	the	DET
ap-6074	22	16	photo	photo	NOUN
ap-6074	22	17	of	of	ADP
ap-6074	22	18	the	the	DET
ap-6074	22	19	manufactured	manufacture	VERB
ap-6074	22	20	standard	standard	NOUN
ap-6074	22	21	is	be	AUX
ap-6074	22	22	presented	present	VERB
ap-6074	22	23	.	.	PUNCT
ap-6074	23	1	2	2	X
ap-6074	23	2	.	.	X
ap-6074	23	3	surface	surface	NOUN
ap-6074	23	4	of	of	ADP
ap-6074	23	5	hyperbolic	hyperbolic	ADJ
ap-6074	23	6	paraboloid	paraboloid	NOUN
ap-6074	23	7	consider	consider	VERB
ap-6074	23	8	a	a	DET
ap-6074	23	9	one	one	NUM
ap-6074	23	10	-	-	PUNCT
ap-6074	23	11	dimensional	dimensional	ADJ
ap-6074	23	12	situation	situation	NOUN
ap-6074	23	13	first	first	ADV
ap-6074	23	14	.	.	PUNCT
ap-6074	24	1	given	give	VERB
ap-6074	24	2	two	two	NUM
ap-6074	24	3	points	point	NOUN
ap-6074	24	4	in	in	ADP
ap-6074	24	5	three	three	NUM
ap-6074	24	6	-	-	PUNCT
ap-6074	24	7	dimensional	dimensional	ADJ
ap-6074	24	8	space	space	NOUN
ap-6074	24	9	with	with	ADP
ap-6074	24	10	cartesian	cartesian	ADJ
ap-6074	24	11	coordinate	coordinate	NOUN
ap-6074	24	12	system	system	NOUN
ap-6074	24	13	(	(	PUNCT
ap-6074	24	14	o	o	NOUN
ap-6074	24	15	,	,	PUNCT
ap-6074	24	16	x	x	PROPN
ap-6074	24	17	,	,	PUNCT
ap-6074	24	18	y	y	PROPN
ap-6074	24	19	,	,	PUNCT
ap-6074	24	20	z	z	NOUN
ap-6074	24	21	)	)	PUNCT
ap-6074	24	22	p0	p0	NOUN
ap-6074	24	23	=	=	SYM
ap-6074	24	24	(	(	PUNCT
ap-6074	24	25	x0	x0	PROPN
ap-6074	24	26	,	,	PUNCT
ap-6074	24	27	y0	y0	PROPN
ap-6074	24	28	,	,	PUNCT
ap-6074	24	29	z0	z0	PROPN
ap-6074	24	30	)	)	PUNCT
ap-6074	24	31	,	,	PUNCT
ap-6074	24	32	p1	p1	NOUN
ap-6074	24	33	=	=	SYM
ap-6074	24	34	(	(	PUNCT
ap-6074	24	35	x1	x1	PROPN
ap-6074	24	36	,	,	PUNCT
ap-6074	24	37	y1	y1	PROPN
ap-6074	24	38	,	,	PUNCT
ap-6074	24	39	z1	z1	PROPN
ap-6074	24	40	)	)	PUNCT
ap-6074	24	41	,	,	PUNCT
ap-6074	24	42	the	the	DET
ap-6074	24	43	straight	straight	ADJ
ap-6074	24	44	line	line	NOUN
ap-6074	24	45	segment	segment	NOUN
ap-6074	24	46	obtained	obtain	VERB
ap-6074	24	47	by	by	ADP
ap-6074	24	48	linear	linear	ADJ
ap-6074	24	49	interpolation	interpolation	NOUN
ap-6074	24	50	between	between	ADP
ap-6074	24	51	these	these	DET
ap-6074	24	52	points	point	NOUN
ap-6074	24	53	is	be	AUX
ap-6074	24	54	given	give	VERB
ap-6074	24	55	by	by	ADP
ap-6074	24	56	c(u	c(u	PROPN
ap-6074	24	57	)	)	PUNCT
ap-6074	24	58	=	=	SYM
ap-6074	24	59	n0,1(u)p0	n0,1(u)p0	PROPN
ap-6074	25	1	+	+	ADV
ap-6074	25	2	n1,1(u)p1	n1,1(u)p1	ADJ
ap-6074	25	3	,	,	PUNCT
ap-6074	25	4	u	u	NOUN
ap-6074	25	5	∈	∈	PROPN
ap-6074	26	1	[	[	X
ap-6074	26	2	0	0	NUM
ap-6074	26	3	,	,	PUNCT
ap-6074	26	4	1	1	NUM
ap-6074	26	5	]	]	PUNCT
ap-6074	26	6	,	,	PUNCT
ap-6074	26	7	(	(	PUNCT
ap-6074	26	8	1	1	X
ap-6074	26	9	)	)	PUNCT
ap-6074	26	10	99	99	NUM
ap-6074	26	11	https://doi.org/10.14311/ap.2021.61.0099	https://doi.org/10.14311/ap.2021.61.0099	NOUN
ap-6074	26	12	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6074	26	13	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6074	26	14	ivana	ivana	PROPN
ap-6074	26	15	linkeová	linkeová	PROPN
ap-6074	26	16	,	,	PUNCT
ap-6074	26	17	vít	vít	PROPN
ap-6074	26	18	zelený	zelený	PROPN
ap-6074	26	19	acta	acta	PROPN
ap-6074	26	20	polytechnica	polytechnica	PROPN
ap-6074	26	21	where	where	SCONJ
ap-6074	26	22	u	u	NOUN
ap-6074	26	23	is	be	AUX
ap-6074	26	24	a	a	DET
ap-6074	26	25	parameter	parameter	NOUN
ap-6074	26	26	,	,	PUNCT
ap-6074	26	27	c(u	c(u	PROPN
ap-6074	26	28	)	)	PUNCT
ap-6074	26	29	is	be	AUX
ap-6074	26	30	one	one	NUM
ap-6074	26	31	-	-	PUNCT
ap-6074	26	32	variate	variate	NOUN
ap-6074	26	33	vector	vector	NOUN
ap-6074	26	34	function	function	NOUN
ap-6074	26	35	and	and	CCONJ
ap-6074	26	36	n0,1(u	n0,1(u	PROPN
ap-6074	26	37	)	)	PUNCT
ap-6074	26	38	=	=	SYM
ap-6074	26	39	1−	1−	NUM
ap-6074	26	40	u	u	NOUN
ap-6074	26	41	,	,	PUNCT
ap-6074	26	42	n1,1(u	n1,1(u	PROPN
ap-6074	26	43	)	)	PUNCT
ap-6074	26	44	=	=	SYM
ap-6074	26	45	u	u	NOUN
ap-6074	26	46	(	(	PUNCT
ap-6074	26	47	2	2	NUM
ap-6074	26	48	)	)	PUNCT
ap-6074	26	49	are	be	AUX
ap-6074	26	50	uniform	uniform	ADJ
ap-6074	26	51	b	b	X
ap-6074	26	52	-	-	PUNCT
ap-6074	26	53	spline	spline	NOUN
ap-6074	26	54	basis	basis	NOUN
ap-6074	26	55	functions	function	NOUN
ap-6074	26	56	of	of	ADP
ap-6074	26	57	the	the	DET
ap-6074	26	58	first	first	ADJ
ap-6074	26	59	degree	degree	NOUN
ap-6074	27	1	[	[	X
ap-6074	27	2	5	5	NUM
ap-6074	27	3	]	]	PUNCT
ap-6074	27	4	.	.	PUNCT
ap-6074	28	1	equation	equation	NOUN
ap-6074	28	2	(	(	PUNCT
ap-6074	28	3	1	1	X
ap-6074	28	4	)	)	PUNCT
ap-6074	28	5	represents	represent	VERB
ap-6074	28	6	the	the	DET
ap-6074	28	7	straight	straight	ADJ
ap-6074	28	8	line	line	NOUN
ap-6074	28	9	segment	segment	NOUN
ap-6074	28	10	as	as	ADP
ap-6074	28	11	a	a	DET
ap-6074	28	12	uniform	uniform	NOUN
ap-6074	28	13	clamped	clamp	VERB
ap-6074	28	14	b	b	NUM
ap-6074	28	15	-	-	PUNCT
ap-6074	28	16	spline	spline	NOUN
ap-6074	28	17	curve	curve	NOUN
ap-6074	28	18	defined	define	VERB
ap-6074	28	19	on	on	ADP
ap-6074	28	20	a	a	DET
ap-6074	28	21	normalised	normalise	VERB
ap-6074	28	22	domain	domain	NOUN
ap-6074	28	23	of	of	ADP
ap-6074	28	24	parameterization	parameterization	NOUN
ap-6074	28	25	u	u	NOUN
ap-6074	28	26	∈	∈	PROPN
ap-6074	29	1	[	[	X
ap-6074	29	2	0	0	NUM
ap-6074	29	3	,	,	PUNCT
ap-6074	29	4	1	1	NUM
ap-6074	29	5	]	]	PUNCT
ap-6074	29	6	.	.	PUNCT
ap-6074	30	1	a	a	DET
ap-6074	30	2	surface	surface	NOUN
ap-6074	30	3	of	of	ADP
ap-6074	30	4	hyperbolic	hyperbolic	ADJ
ap-6074	30	5	paraboloid	paraboloid	NOUN
ap-6074	30	6	is	be	AUX
ap-6074	30	7	a	a	DET
ap-6074	30	8	linear	linear	ADJ
ap-6074	30	9	interpolation	interpolation	NOUN
ap-6074	30	10	among	among	ADP
ap-6074	30	11	four	four	NUM
ap-6074	30	12	points	point	NOUN
ap-6074	30	13	in	in	ADP
ap-6074	30	14	the	the	DET
ap-6074	30	15	three	three	NUM
ap-6074	30	16	-	-	PUNCT
ap-6074	30	17	dimensional	dimensional	ADJ
ap-6074	30	18	space	space	NOUN
ap-6074	30	19	.	.	PUNCT
ap-6074	31	1	denoting	denote	VERB
ap-6074	31	2	p00	p00	PROPN
ap-6074	31	3	=	=	SYM
ap-6074	31	4	(	(	PUNCT
ap-6074	31	5	x00	x00	PROPN
ap-6074	31	6	,	,	PUNCT
ap-6074	31	7	y00	y00	NOUN
ap-6074	31	8	,	,	PUNCT
ap-6074	31	9	z00	z00	NOUN
ap-6074	31	10	)	)	PUNCT
ap-6074	31	11	,	,	PUNCT
ap-6074	31	12	p01	p01	NOUN
ap-6074	31	13	=	=	SYM
ap-6074	31	14	(	(	PUNCT
ap-6074	31	15	x01	x01	PROPN
ap-6074	31	16	,	,	PUNCT
ap-6074	31	17	y01	y01	NOUN
ap-6074	31	18	,	,	PUNCT
ap-6074	31	19	z01	z01	NUM
ap-6074	31	20	)	)	PUNCT
ap-6074	31	21	,	,	PUNCT
ap-6074	31	22	p10	p10	NOUN
ap-6074	31	23	=	=	SYM
ap-6074	31	24	(	(	PUNCT
ap-6074	31	25	x10	x10	NOUN
ap-6074	31	26	,	,	PUNCT
ap-6074	31	27	y10	y10	NOUN
ap-6074	31	28	,	,	PUNCT
ap-6074	31	29	z10	z10	NOUN
ap-6074	31	30	)	)	PUNCT
ap-6074	31	31	,	,	PUNCT
ap-6074	31	32	p11	p11	NOUN
ap-6074	31	33	=	=	SYM
ap-6074	31	34	(	(	PUNCT
ap-6074	31	35	x11	x11	PROPN
ap-6074	31	36	,	,	PUNCT
ap-6074	31	37	y11	y11	NOUN
ap-6074	31	38	,	,	PUNCT
ap-6074	31	39	z11	z11	NOUN
ap-6074	31	40	)	)	PUNCT
ap-6074	31	41	,	,	PUNCT
ap-6074	31	42	the	the	DET
ap-6074	31	43	surface	surface	NOUN
ap-6074	31	44	of	of	ADP
ap-6074	31	45	hyperbolic	hyperbolic	ADJ
ap-6074	31	46	paraboloid	paraboloid	NOUN
ap-6074	31	47	(	(	PUNCT
ap-6074	31	48	bilinear	bilinear	PROPN
ap-6074	31	49	b	b	X
ap-6074	31	50	-	-	PUNCT
ap-6074	31	51	spline	spline	NOUN
ap-6074	31	52	clamped	clamp	VERB
ap-6074	31	53	surface	surface	NOUN
ap-6074	31	54	defined	define	VERB
ap-6074	31	55	on	on	ADP
ap-6074	31	56	a	a	DET
ap-6074	31	57	normalised	normalise	VERB
ap-6074	31	58	domain	domain	NOUN
ap-6074	31	59	of	of	ADP
ap-6074	31	60	parameterization	parameterization	NOUN
ap-6074	31	61	(	(	PUNCT
ap-6074	31	62	u	u	NOUN
ap-6074	31	63	,	,	PUNCT
ap-6074	31	64	v	v	NOUN
ap-6074	31	65	)	)	PUNCT
ap-6074	31	66	∈	∈	PROPN
ap-6074	32	1	[	[	X
ap-6074	32	2	0	0	NUM
ap-6074	32	3	,	,	PUNCT
ap-6074	32	4	1]2	1]2	NUM
ap-6074	32	5	)	)	PUNCT
ap-6074	32	6	is	be	AUX
ap-6074	32	7	given	give	VERB
ap-6074	32	8	by	by	ADP
ap-6074	32	9	s(u	s(u	PROPN
ap-6074	32	10	,	,	PUNCT
ap-6074	32	11	v	v	NOUN
ap-6074	32	12	)	)	PUNCT
ap-6074	32	13	=	=	SYM
ap-6074	32	14	(	(	PUNCT
ap-6074	32	15	x(u	x(u	PROPN
ap-6074	32	16	,	,	PUNCT
ap-6074	32	17	v	v	NOUN
ap-6074	32	18	)	)	PUNCT
ap-6074	32	19	,	,	PUNCT
ap-6074	32	20	y(u	y(u	PROPN
ap-6074	32	21	,	,	PUNCT
ap-6074	32	22	v	v	NOUN
ap-6074	32	23	)	)	PUNCT
ap-6074	32	24	,	,	PUNCT
ap-6074	32	25	z(u	z(u	PROPN
ap-6074	32	26	,	,	PUNCT
ap-6074	32	27	v	v	NOUN
ap-6074	32	28	)	)	PUNCT
ap-6074	32	29	)	)	PUNCT
ap-6074	33	1	=	=	PUNCT
ap-6074	33	2	(	(	PUNCT
ap-6074	33	3	3	3	X
ap-6074	33	4	)	)	PUNCT
ap-6074	33	5	=	=	SYM
ap-6074	33	6	(	(	PUNCT
ap-6074	33	7	1−	1−	NUM
ap-6074	33	8	u	u	NOUN
ap-6074	33	9	u	u	NOUN
ap-6074	33	10	)	)	PUNCT
ap-6074	33	11	·	·	PUNCT
ap-6074	33	12	(	(	PUNCT
ap-6074	33	13	p00	p00	NUM
ap-6074	33	14	p01	p01	PROPN
ap-6074	33	15	p10	p10	NOUN
ap-6074	33	16	p11	p11	NOUN
ap-6074	33	17	)	)	PUNCT
ap-6074	33	18	·	·	PUNCT
ap-6074	34	1	(	(	PUNCT
ap-6074	34	2	1−	1−	NUM
ap-6074	34	3	v	v	NUM
ap-6074	34	4	v	v	NOUN
ap-6074	34	5	)	)	PUNCT
ap-6074	34	6	with	with	ADP
ap-6074	34	7	coordinate	coordinate	NOUN
ap-6074	34	8	functions	function	NOUN
ap-6074	34	9	x(u	x(u	PROPN
ap-6074	34	10	,	,	PUNCT
ap-6074	34	11	v	v	NOUN
ap-6074	34	12	)	)	PUNCT
ap-6074	34	13	=	=	PUNCT
ap-6074	34	14	(	(	PUNCT
ap-6074	34	15	1−	1−	NUM
ap-6074	34	16	u)(1−	u)(1−	NUM
ap-6074	34	17	v)x00	v)x00	X
ap-6074	34	18	+	+	CCONJ
ap-6074	34	19	(	(	PUNCT
ap-6074	34	20	1−	1−	NUM
ap-6074	34	21	u)vx01	u)vx01	NOUN
ap-6074	34	22	+	+	CCONJ
ap-6074	34	23	(	(	PUNCT
ap-6074	34	24	4	4	NUM
ap-6074	34	25	)	)	PUNCT
ap-6074	34	26	+	+	CCONJ
ap-6074	34	27	u(1−	u(1−	PROPN
ap-6074	34	28	v)x10	v)x10	PROPN
ap-6074	34	29	+	+	NUM
ap-6074	34	30	uvx11	uvx11	PROPN
ap-6074	34	31	,	,	PUNCT
ap-6074	34	32	y(u	y(u	PROPN
ap-6074	34	33	,	,	PUNCT
ap-6074	34	34	v	v	NOUN
ap-6074	34	35	)	)	PUNCT
ap-6074	34	36	=	=	PUNCT
ap-6074	34	37	(	(	PUNCT
ap-6074	34	38	1−	1−	NUM
ap-6074	34	39	u)(1−	u)(1−	PROPN
ap-6074	34	40	v)y00	v)y00	PROPN
ap-6074	34	41	+	+	CCONJ
ap-6074	34	42	(	(	PUNCT
ap-6074	34	43	1−	1−	NUM
ap-6074	34	44	u)vy01	u)vy01	NOUN
ap-6074	34	45	+	+	CCONJ
ap-6074	34	46	(	(	PUNCT
ap-6074	34	47	5	5	NUM
ap-6074	34	48	)	)	PUNCT
ap-6074	34	49	+	+	CCONJ
ap-6074	34	50	u(1−	u(1−	ADJ
ap-6074	34	51	v)y10	v)y10	NOUN
ap-6074	34	52	+	+	CCONJ
ap-6074	34	53	uvy11	uvy11	PROPN
ap-6074	34	54	,	,	PUNCT
ap-6074	34	55	z(u	z(u	PROPN
ap-6074	34	56	,	,	PUNCT
ap-6074	34	57	v	v	NOUN
ap-6074	34	58	)	)	PUNCT
ap-6074	34	59	=	=	PUNCT
ap-6074	34	60	(	(	PUNCT
ap-6074	34	61	1−	1−	NUM
ap-6074	34	62	u)(1−	u)(1−	PROPN
ap-6074	34	63	v)z00	v)z00	PROPN
ap-6074	34	64	+	+	CCONJ
ap-6074	34	65	(	(	PUNCT
ap-6074	34	66	1−	1−	NUM
ap-6074	34	67	u)vz01	u)vz01	X
ap-6074	34	68	+	+	CCONJ
ap-6074	34	69	(	(	PUNCT
ap-6074	34	70	6	6	NUM
ap-6074	34	71	)	)	PUNCT
ap-6074	34	72	+	+	CCONJ
ap-6074	34	73	u(1−	u(1−	ADJ
ap-6074	34	74	v)z10	v)z10	NOUN
ap-6074	34	75	+	+	CCONJ
ap-6074	34	76	uvz11	uvz11	NOUN
ap-6074	34	77	.	.	PUNCT
ap-6074	35	1	in	in	ADP
ap-6074	35	2	computations	computation	NOUN
ap-6074	35	3	,	,	PUNCT
ap-6074	35	4	it	it	PRON
ap-6074	35	5	is	be	AUX
ap-6074	35	6	suitable	suitable	ADJ
ap-6074	35	7	to	to	PART
ap-6074	35	8	use	use	VERB
ap-6074	35	9	an	an	DET
ap-6074	35	10	explicit	explicit	ADJ
ap-6074	35	11	expression	expression	NOUN
ap-6074	35	12	of	of	ADP
ap-6074	35	13	the	the	DET
ap-6074	35	14	surface	surface	NOUN
ap-6074	35	15	of	of	ADP
ap-6074	35	16	hyperbolic	hyperbolic	ADJ
ap-6074	35	17	paraboloid	paraboloid	NOUN
ap-6074	35	18	.	.	PUNCT
ap-6074	36	1	to	to	PART
ap-6074	36	2	be	be	AUX
ap-6074	36	3	able	able	ADJ
ap-6074	36	4	to	to	PART
ap-6074	36	5	express	express	VERB
ap-6074	36	6	the	the	DET
ap-6074	36	7	surface	surface	NOUN
ap-6074	36	8	(	(	PUNCT
ap-6074	36	9	3	3	X
ap-6074	36	10	)	)	PUNCT
ap-6074	36	11	explicitly	explicitly	ADV
ap-6074	36	12	,	,	PUNCT
ap-6074	36	13	the	the	DET
ap-6074	36	14	orthogonal	orthogonal	ADJ
ap-6074	36	15	projection	projection	NOUN
ap-6074	36	16	of	of	ADP
ap-6074	36	17	quadrilateral	quadrilateral	ADJ
ap-6074	36	18	p00p01p10p11	p00p01p10p11	NOUN
ap-6074	36	19	to	to	ADP
ap-6074	36	20	the	the	DET
ap-6074	36	21	(	(	PUNCT
ap-6074	36	22	x	x	NOUN
ap-6074	36	23	,	,	PUNCT
ap-6074	36	24	y	y	NOUN
ap-6074	36	25	)	)	PUNCT
ap-6074	36	26	plane	plane	NOUN
ap-6074	36	27	has	have	VERB
ap-6074	36	28	to	to	PART
ap-6074	36	29	be	be	AUX
ap-6074	36	30	an	an	DET
ap-6074	36	31	axis	axis	NOUN
ap-6074	36	32	-	-	PUNCT
ap-6074	36	33	aligned	aligned	ADJ
ap-6074	36	34	rectangle	rectangle	NOUN
ap-6074	36	35	.	.	PUNCT
ap-6074	37	1	then	then	ADV
ap-6074	37	2	,	,	PUNCT
ap-6074	37	3	the	the	DET
ap-6074	37	4	explicit	explicit	ADJ
ap-6074	37	5	equation	equation	NOUN
ap-6074	37	6	of	of	ADP
ap-6074	37	7	the	the	DET
ap-6074	37	8	surface	surface	NOUN
ap-6074	37	9	of	of	ADP
ap-6074	37	10	hyperbolic	hyperbolic	ADJ
ap-6074	37	11	paraboloid	paraboloid	NOUN
ap-6074	37	12	is	be	AUX
ap-6074	37	13	given	give	VERB
ap-6074	37	14	by	by	ADP
ap-6074	37	15	z(x	z(x	PROPN
ap-6074	37	16	,	,	PUNCT
ap-6074	37	17	y	y	NOUN
ap-6074	37	18	)	)	PUNCT
ap-6074	38	1	=	=	PRON
ap-6074	38	2	p+	p+	PROPN
ap-6074	38	3	k(x−m)(y	k(x−m)(y	PROPN
ap-6074	38	4	−	−	PROPN
ap-6074	38	5	n	n	CCONJ
ap-6074	38	6	)	)	PUNCT
ap-6074	38	7	,	,	PUNCT
ap-6074	38	8	(	(	PUNCT
ap-6074	38	9	7	7	X
ap-6074	38	10	)	)	PUNCT
ap-6074	38	11	where	where	SCONJ
ap-6074	38	12	v	v	NOUN
ap-6074	38	13	=	=	SYM
ap-6074	38	14	(	(	PUNCT
ap-6074	38	15	m	m	PROPN
ap-6074	38	16	,	,	PUNCT
ap-6074	38	17	n	n	CCONJ
ap-6074	38	18	,	,	PUNCT
ap-6074	38	19	p	p	NOUN
ap-6074	38	20	)	)	PUNCT
ap-6074	38	21	is	be	AUX
ap-6074	38	22	the	the	DET
ap-6074	38	23	vertex	vertex	NOUN
ap-6074	38	24	of	of	ADP
ap-6074	38	25	the	the	DET
ap-6074	38	26	hyperbolic	hyperbolic	ADJ
ap-6074	38	27	paraboloid	paraboloid	NOUN
ap-6074	38	28	and	and	CCONJ
ap-6074	38	29	k	k	PROPN
ap-6074	38	30	is	be	AUX
ap-6074	38	31	a	a	DET
ap-6074	38	32	shape	shape	NOUN
ap-6074	38	33	coefficient	coefficient	NOUN
ap-6074	38	34	.	.	PUNCT
ap-6074	39	1	regarding	regard	VERB
ap-6074	39	2	the	the	DET
ap-6074	39	3	future	future	ADJ
ap-6074	39	4	application	application	NOUN
ap-6074	39	5	of	of	ADP
ap-6074	39	6	this	this	DET
ap-6074	39	7	surface	surface	NOUN
ap-6074	39	8	in	in	ADP
ap-6074	39	9	the	the	DET
ap-6074	39	10	design	design	NOUN
ap-6074	39	11	of	of	ADP
ap-6074	39	12	a	a	DET
ap-6074	39	13	freeform	freeform	ADJ
ap-6074	39	14	standard	standard	NOUN
ap-6074	39	15	,	,	PUNCT
ap-6074	39	16	consider	consider	VERB
ap-6074	39	17	the	the	DET
ap-6074	39	18	control	control	NOUN
ap-6074	39	19	vertices	vertice	VERB
ap-6074	39	20	lying	lie	VERB
ap-6074	39	21	above	above	ADP
ap-6074	39	22	the	the	DET
ap-6074	39	23	vertices	vertex	NOUN
ap-6074	39	24	of	of	ADP
ap-6074	39	25	the	the	DET
ap-6074	39	26	axis	axis	NOUN
ap-6074	39	27	-	-	PUNCT
ap-6074	39	28	aligned	align	VERB
ap-6074	39	29	square	square	NOUN
ap-6074	39	30	with	with	ADP
ap-6074	39	31	centre	centre	NOUN
ap-6074	39	32	at	at	ADP
ap-6074	39	33	the	the	DET
ap-6074	39	34	origin	origin	NOUN
ap-6074	39	35	of	of	ADP
ap-6074	39	36	the	the	DET
ap-6074	39	37	coordinate	coordinate	NOUN
ap-6074	39	38	system	system	NOUN
ap-6074	39	39	and	and	CCONJ
ap-6074	39	40	length	length	NOUN
ap-6074	39	41	of	of	ADP
ap-6074	39	42	the	the	DET
ap-6074	39	43	edge	edge	NOUN
ap-6074	39	44	equal	equal	ADJ
ap-6074	39	45	to	to	ADP
ap-6074	39	46	2a	2a	NUM
ap-6074	39	47	,	,	PUNCT
ap-6074	39	48	fig	fig	NOUN
ap-6074	39	49	.	.	PUNCT
ap-6074	40	1	1	1	X
ap-6074	40	2	.	.	X
ap-6074	40	3	then	then	ADV
ap-6074	40	4	p00	p00	PROPN
ap-6074	40	5	=	=	SYM
ap-6074	40	6	(	(	PUNCT
ap-6074	40	7	−a,−a	−a,−a	PROPN
ap-6074	40	8	,	,	PUNCT
ap-6074	40	9	z00	z00	NOUN
ap-6074	40	10	)	)	PUNCT
ap-6074	40	11	,	,	PUNCT
ap-6074	40	12	p01	p01	NOUN
ap-6074	40	13	=	=	SYM
ap-6074	40	14	(	(	PUNCT
ap-6074	40	15	−a	−a	ADJ
ap-6074	40	16	,	,	PUNCT
ap-6074	40	17	a	a	DET
ap-6074	40	18	,	,	PUNCT
ap-6074	40	19	z01	z01	NUM
ap-6074	40	20	)	)	PUNCT
ap-6074	40	21	,	,	PUNCT
ap-6074	40	22	(	(	PUNCT
ap-6074	40	23	8)	8)	NUM
ap-6074	40	24	p10	p10	NOUN
ap-6074	40	25	=	=	SYM
ap-6074	40	26	(	(	PUNCT
ap-6074	40	27	a,−a	a,−a	ADJ
ap-6074	40	28	,	,	PUNCT
ap-6074	40	29	z10	z10	NOUN
ap-6074	40	30	)	)	PUNCT
ap-6074	40	31	,	,	PUNCT
ap-6074	40	32	p11	p11	NOUN
ap-6074	40	33	=	=	SYM
ap-6074	40	34	(	(	PUNCT
ap-6074	40	35	a	a	PRON
ap-6074	40	36	,	,	PUNCT
ap-6074	40	37	a	a	PRON
ap-6074	40	38	,	,	PUNCT
ap-6074	40	39	z11	z11	NOUN
ap-6074	40	40	)	)	PUNCT
ap-6074	40	41	.	.	PUNCT
ap-6074	41	1	after	after	ADP
ap-6074	41	2	substitution	substitution	NOUN
ap-6074	41	3	of	of	ADP
ap-6074	41	4	control	control	NOUN
ap-6074	41	5	points	point	NOUN
ap-6074	41	6	coordinates	coordinate	NOUN
ap-6074	41	7	(	(	PUNCT
ap-6074	41	8	8)	8)	NUM
ap-6074	41	9	in	in	ADP
ap-6074	41	10	(	(	PUNCT
ap-6074	41	11	4	4	NUM
ap-6074	41	12	)	)	PUNCT
ap-6074	41	13	and	and	CCONJ
ap-6074	41	14	(	(	PUNCT
ap-6074	41	15	5	5	NUM
ap-6074	41	16	)	)	PUNCT
ap-6074	41	17	,	,	PUNCT
ap-6074	41	18	x(u	x(u	PROPN
ap-6074	41	19	,	,	PUNCT
ap-6074	41	20	v	v	NOUN
ap-6074	41	21	)	)	PUNCT
ap-6074	41	22	and	and	CCONJ
ap-6074	41	23	y(u	y(u	PROPN
ap-6074	41	24	,	,	PUNCT
ap-6074	41	25	v	v	NOUN
ap-6074	41	26	)	)	PUNCT
ap-6074	41	27	coordinate	coordinate	NOUN
ap-6074	41	28	functions	function	NOUN
ap-6074	41	29	are	be	AUX
ap-6074	41	30	as	as	SCONJ
ap-6074	41	31	follows	follow	VERB
ap-6074	41	32	x(u	x(u	PROPN
ap-6074	41	33	,	,	PUNCT
ap-6074	41	34	v	v	NOUN
ap-6074	41	35	)	)	PUNCT
ap-6074	41	36	=	=	SYM
ap-6074	41	37	a(2u−	a(2u−	NUM
ap-6074	41	38	1	1	NUM
ap-6074	41	39	)	)	PUNCT
ap-6074	41	40	,	,	PUNCT
ap-6074	41	41	y(u	y(u	PROPN
ap-6074	41	42	,	,	PUNCT
ap-6074	41	43	v	v	NOUN
ap-6074	41	44	)	)	PUNCT
ap-6074	41	45	=	=	PUNCT
ap-6074	41	46	a(2v	a(2v	PROPN
ap-6074	41	47	−	−	NOUN
ap-6074	41	48	1	1	NUM
ap-6074	41	49	)	)	PUNCT
ap-6074	41	50	.	.	PUNCT
ap-6074	42	1	(	(	PUNCT
ap-6074	42	2	9	9	X
ap-6074	42	3	)	)	PUNCT
ap-6074	42	4	a	a	PRON
ap-6074	42	5	x	x	SYM
ap-6074	42	6	p	p	X
ap-6074	42	7	y	y	PROPN
ap-6074	42	8	11	11	NUM
ap-6074	42	9	-a	-a	PUNCT
ap-6074	42	10	a	a	DET
ap-6074	42	11	-a	-a	PROPN
ap-6074	42	12	v	v	NOUN
ap-6074	42	13	p	p	PROPN
ap-6074	42	14	10	10	NUM
ap-6074	42	15	01	01	NUM
ap-6074	42	16	00	00	NUM
ap-6074	43	1	p	p	X
ap-6074	43	2	p	p	X
ap-6074	43	3	z	z	NOUN
ap-6074	43	4	figure	figure	NOUN
ap-6074	43	5	1	1	NUM
ap-6074	43	6	.	.	PUNCT
ap-6074	43	7	surface	surface	NOUN
ap-6074	43	8	of	of	ADP
ap-6074	43	9	hyperbolic	hyperbolic	ADJ
ap-6074	43	10	paraboloid	paraboloid	NOUN
ap-6074	43	11	.	.	PUNCT
ap-6074	44	1	now	now	ADV
ap-6074	44	2	,	,	PUNCT
ap-6074	44	3	it	it	PRON
ap-6074	44	4	is	be	AUX
ap-6074	44	5	possible	possible	ADJ
ap-6074	44	6	to	to	PART
ap-6074	44	7	solve	solve	VERB
ap-6074	44	8	(	(	PUNCT
ap-6074	44	9	9	9	NUM
ap-6074	44	10	)	)	PUNCT
ap-6074	44	11	with	with	ADP
ap-6074	44	12	respect	respect	NOUN
ap-6074	44	13	to	to	ADP
ap-6074	44	14	parameters	parameter	NOUN
ap-6074	44	15	u	u	NOUN
ap-6074	44	16	and	and	CCONJ
ap-6074	44	17	v	v	ADP
ap-6074	44	18	u	u	NOUN
ap-6074	44	19	=	=	NOUN
ap-6074	44	20	x+	x+	PROPN
ap-6074	44	21	a	a	DET
ap-6074	44	22	2a	2a	NUM
ap-6074	44	23	,	,	PUNCT
ap-6074	44	24	v	v	NOUN
ap-6074	44	25	=	=	SYM
ap-6074	44	26	y	y	PROPN
ap-6074	44	27	+	+	CCONJ
ap-6074	44	28	a	a	DET
ap-6074	44	29	2a	2a	NUM
ap-6074	44	30	(	(	PUNCT
ap-6074	44	31	10	10	NUM
ap-6074	44	32	)	)	PUNCT
ap-6074	44	33	and	and	CCONJ
ap-6074	44	34	substitute	substitute	NOUN
ap-6074	44	35	(	(	PUNCT
ap-6074	44	36	10	10	NUM
ap-6074	44	37	)	)	PUNCT
ap-6074	44	38	in	in	ADP
ap-6074	44	39	(	(	PUNCT
ap-6074	44	40	6	6	NUM
ap-6074	44	41	)	)	PUNCT
ap-6074	44	42	z(x	z(x	NUM
ap-6074	44	43	,	,	PUNCT
ap-6074	44	44	y	y	NOUN
ap-6074	44	45	)	)	PUNCT
ap-6074	44	46	=	=	PUNCT
ap-6074	45	1	xy	xy	PROPN
ap-6074	45	2	4a2	4a2	NUM
ap-6074	46	1	(	(	PUNCT
ap-6074	46	2	z00	z00	NOUN
ap-6074	46	3	−	−	PROPN
ap-6074	46	4	z01	z01	NUM
ap-6074	46	5	−	−	NOUN
ap-6074	46	6	z10	z10	NOUN
ap-6074	46	7	+	+	CCONJ
ap-6074	47	1	z11)+	z11)+	PROPN
ap-6074	48	1	(	(	PUNCT
ap-6074	48	2	11	11	NUM
ap-6074	48	3	)	)	PUNCT
ap-6074	49	1	+	+	CCONJ
ap-6074	49	2	x	x	SYM
ap-6074	49	3	4a	4a	X
ap-6074	49	4	(	(	PUNCT
ap-6074	49	5	−z00	−z00	PUNCT
ap-6074	49	6	−	−	PROPN
ap-6074	49	7	z01	z01	X
ap-6074	49	8	+	+	CCONJ
ap-6074	49	9	z10	z10	NOUN
ap-6074	49	10	+	+	CCONJ
ap-6074	49	11	z11)+	z11)+	PROPN
ap-6074	49	12	+	+	PROPN
ap-6074	49	13	y	y	PROPN
ap-6074	49	14	4a	4a	NUM
ap-6074	49	15	(	(	PUNCT
ap-6074	49	16	−z00	−z00	PUNCT
ap-6074	49	17	+	+	CCONJ
ap-6074	49	18	z01	z01	ADJ
ap-6074	49	19	−	−	NOUN
ap-6074	49	20	z10	z10	NOUN
ap-6074	49	21	+	+	CCONJ
ap-6074	49	22	z11)+	z11)+	PROPN
ap-6074	49	23	+	+	NUM
ap-6074	49	24	1	1	NUM
ap-6074	49	25	4(z00	4(z00	NUM
ap-6074	49	26	+	+	CCONJ
ap-6074	49	27	z01	z01	ADJ
ap-6074	49	28	+	+	CCONJ
ap-6074	49	29	z10	z10	NOUN
ap-6074	49	30	+	+	CCONJ
ap-6074	49	31	z11	z11	NOUN
ap-6074	49	32	)	)	PUNCT
ap-6074	49	33	.	.	PUNCT
ap-6074	50	1	denote	denote	VERB
ap-6074	50	2	a	a	DET
ap-6074	50	3	=	=	NOUN
ap-6074	50	4	z00	z00	NOUN
ap-6074	50	5	−	−	PROPN
ap-6074	50	6	z01	z01	ADJ
ap-6074	50	7	−	−	NOUN
ap-6074	50	8	z10	z10	NOUN
ap-6074	50	9	+	+	CCONJ
ap-6074	50	10	z11	z11	NOUN
ap-6074	50	11	,	,	PUNCT
ap-6074	50	12	(	(	PUNCT
ap-6074	50	13	12	12	NUM
ap-6074	50	14	)	)	PUNCT
ap-6074	50	15	b	b	NOUN
ap-6074	50	16	=	=	PUNCT
ap-6074	50	17	−z00	−z00	PUNCT
ap-6074	50	18	−	−	PROPN
ap-6074	50	19	z01	z01	X
ap-6074	50	20	+	+	CCONJ
ap-6074	50	21	z10	z10	NOUN
ap-6074	50	22	+	+	CCONJ
ap-6074	50	23	z11	z11	NOUN
ap-6074	50	24	,	,	PUNCT
ap-6074	50	25	c	c	NOUN
ap-6074	50	26	=	=	PUNCT
ap-6074	50	27	−z00	−z00	PUNCT
ap-6074	50	28	+	+	CCONJ
ap-6074	50	29	z01	z01	NUM
ap-6074	50	30	−	−	NOUN
ap-6074	50	31	z10	z10	NOUN
ap-6074	50	32	+	+	CCONJ
ap-6074	50	33	z11	z11	NOUN
ap-6074	50	34	,	,	PUNCT
ap-6074	50	35	d	d	NOUN
ap-6074	50	36	=	=	PUNCT
ap-6074	50	37	z00	z00	NOUN
ap-6074	50	38	+	+	CCONJ
ap-6074	50	39	z01	z01	ADJ
ap-6074	51	1	+	+	CCONJ
ap-6074	51	2	z10	z10	NOUN
ap-6074	51	3	+	+	CCONJ
ap-6074	51	4	z11	z11	NOUN
ap-6074	51	5	.	.	PUNCT
ap-6074	52	1	then	then	ADV
ap-6074	52	2	z(x	z(x	NUM
ap-6074	52	3	,	,	PUNCT
ap-6074	52	4	y	y	NOUN
ap-6074	52	5	)	)	PUNCT
ap-6074	52	6	=	=	SYM
ap-6074	52	7	1	1	NUM
ap-6074	52	8	4	4	NUM
ap-6074	52	9	(	(	PUNCT
ap-6074	52	10	d	d	NOUN
ap-6074	52	11	−	−	PROPN
ap-6074	52	12	cb	cb	PROPN
ap-6074	52	13	a	a	X
ap-6074	52	14	)	)	PUNCT
ap-6074	53	1	+	+	CCONJ
ap-6074	53	2	a	a	DET
ap-6074	53	3	4a2	4a2	NUM
ap-6074	53	4	(	(	PUNCT
ap-6074	53	5	x+	x+	X
ap-6074	53	6	ca	ca	NOUN
ap-6074	53	7	a	a	PRON
ap-6074	53	8	)	)	PUNCT
ap-6074	53	9	(	(	PUNCT
ap-6074	53	10	y	y	PROPN
ap-6074	54	1	+	+	CCONJ
ap-6074	54	2	ba	ba	PROPN
ap-6074	54	3	a	a	PRON
ap-6074	54	4	)	)	PUNCT
ap-6074	54	5	.	.	PUNCT
ap-6074	55	1	cartesian	cartesian	ADJ
ap-6074	55	2	coordinates	coordinate	NOUN
ap-6074	55	3	of	of	ADP
ap-6074	55	4	the	the	DET
ap-6074	55	5	vertex	vertex	NOUN
ap-6074	55	6	of	of	ADP
ap-6074	55	7	the	the	DET
ap-6074	55	8	hyperbolic	hyperbolic	ADJ
ap-6074	55	9	paraboloid	paraboloid	NOUN
ap-6074	55	10	are	be	AUX
ap-6074	55	11	m	m	ADJ
ap-6074	55	12	=	=	PRON
ap-6074	55	13	−ca	−ca	NOUN
ap-6074	55	14	a	a	PRON
ap-6074	55	15	,	,	PUNCT
ap-6074	55	16	n	n	NOUN
ap-6074	55	17	=	=	SYM
ap-6074	55	18	−ba	−ba	PROPN
ap-6074	55	19	a	a	PRON
ap-6074	55	20	,	,	PUNCT
ap-6074	55	21	p	p	X
ap-6074	55	22	=	=	NOUN
ap-6074	55	23	1	1	NUM
ap-6074	55	24	4	4	NUM
ap-6074	55	25	(	(	PUNCT
ap-6074	55	26	d	d	NOUN
ap-6074	55	27	−	−	PROPN
ap-6074	55	28	cb	cb	PROPN
ap-6074	55	29	a	a	NOUN
ap-6074	55	30	)	)	PUNCT
ap-6074	55	31	(	(	PUNCT
ap-6074	55	32	13	13	NUM
ap-6074	55	33	)	)	PUNCT
ap-6074	55	34	and	and	CCONJ
ap-6074	55	35	shape	shape	VERB
ap-6074	55	36	coefficient	coefficient	NOUN
ap-6074	55	37	k	k	X
ap-6074	55	38	=	=	PUNCT
ap-6074	55	39	a	a	DET
ap-6074	55	40	4a2	4a2	NUM
ap-6074	55	41	.	.	PUNCT
ap-6074	56	1	(	(	PUNCT
ap-6074	56	2	14	14	NUM
ap-6074	56	3	)	)	PUNCT
ap-6074	56	4	if	if	SCONJ
ap-6074	56	5	the	the	DET
ap-6074	56	6	centre	centre	NOUN
ap-6074	56	7	of	of	ADP
ap-6074	56	8	the	the	DET
ap-6074	56	9	square	square	NOUN
ap-6074	56	10	,	,	PUNCT
ap-6074	56	11	above	above	ADP
ap-6074	56	12	whose	whose	DET
ap-6074	56	13	vertices	vertex	NOUN
ap-6074	56	14	the	the	DET
ap-6074	56	15	control	control	NOUN
ap-6074	56	16	points	point	NOUN
ap-6074	56	17	lie	lie	VERB
ap-6074	56	18	,	,	PUNCT
ap-6074	56	19	is	be	AUX
ap-6074	56	20	shifted	shift	VERB
ap-6074	56	21	to	to	PART
ap-6074	56	22	point	point	VERB
ap-6074	56	23	(	(	PUNCT
ap-6074	56	24	q	q	X
ap-6074	56	25	,	,	PUNCT
ap-6074	56	26	r	r	NOUN
ap-6074	56	27	,	,	PUNCT
ap-6074	56	28	0	0	NUM
ap-6074	56	29	)	)	PUNCT
ap-6074	56	30	,	,	PUNCT
ap-6074	56	31	the	the	DET
ap-6074	56	32	coordinates	coordinate	NOUN
ap-6074	56	33	of	of	ADP
ap-6074	56	34	the	the	DET
ap-6074	56	35	hyperbolic	hyperbolic	ADJ
ap-6074	56	36	paraboloid	paraboloid	ADJ
ap-6074	56	37	vertex	vertex	NOUN
ap-6074	56	38	are	be	AUX
ap-6074	56	39	m	m	VERB
ap-6074	56	40	=	=	ADJ
ap-6074	56	41	q−	q−	PROPN
ap-6074	56	42	ca	can	AUX
ap-6074	56	43	a	a	PRON
ap-6074	56	44	,	,	PUNCT
ap-6074	56	45	n	n	NOUN
ap-6074	56	46	=	=	PUNCT
ap-6074	56	47	r−ba	r−ba	PROPN
ap-6074	56	48	a	a	PRON
ap-6074	56	49	,	,	PUNCT
ap-6074	56	50	p	p	X
ap-6074	56	51	=	=	NOUN
ap-6074	56	52	1	1	NUM
ap-6074	56	53	4	4	NUM
ap-6074	56	54	(	(	PUNCT
ap-6074	56	55	d	d	NOUN
ap-6074	56	56	−	−	PROPN
ap-6074	56	57	cb	cb	PROPN
ap-6074	56	58	a	a	NOUN
ap-6074	56	59	)	)	PUNCT
ap-6074	56	60	.	.	PUNCT
ap-6074	57	1	(	(	PUNCT
ap-6074	57	2	15	15	NUM
ap-6074	57	3	)	)	SYM
ap-6074	57	4	100	100	NUM
ap-6074	57	5	vol	vol	NOUN
ap-6074	57	6	.	.	PUNCT
ap-6074	58	1	61	61	NUM
ap-6074	58	2	special	special	ADJ
ap-6074	58	3	issue/2021	issue/2021	NOUN
ap-6074	58	4	application	application	NOUN
ap-6074	58	5	of	of	ADP
ap-6074	58	6	ruled	rule	VERB
ap-6074	58	7	surfaces	surface	NOUN
ap-6074	58	8	in	in	ADP
ap-6074	58	9	freeform	freeform	NOUN
ap-6074	58	10	and	and	CCONJ
ap-6074	58	11	gear	gear	NOUN
ap-6074	58	12	metrology	metrology	NOUN
ap-6074	58	13	considering	consider	VERB
ap-6074	58	14	(	(	PUNCT
ap-6074	58	15	7	7	NUM
ap-6074	58	16	)	)	PUNCT
ap-6074	58	17	,	,	PUNCT
ap-6074	58	18	a	a	DET
ap-6074	58	19	point	point	NOUN
ap-6074	58	20	on	on	ADP
ap-6074	58	21	the	the	DET
ap-6074	58	22	surface	surface	NOUN
ap-6074	58	23	is	be	AUX
ap-6074	58	24	obtained	obtain	VERB
ap-6074	58	25	by	by	ADP
ap-6074	58	26	a	a	DET
ap-6074	58	27	substitution	substitution	NOUN
ap-6074	58	28	of	of	ADP
ap-6074	58	29	a	a	DET
ap-6074	58	30	pair	pair	NOUN
ap-6074	58	31	of	of	ADP
ap-6074	58	32	variables	variable	NOUN
ap-6074	58	33	x	x	PUNCT
ap-6074	58	34	=	=	SYM
ap-6074	58	35	α	α	PROPN
ap-6074	58	36	and	and	CCONJ
ap-6074	58	37	y	y	PROPN
ap-6074	58	38	=	=	SYM
ap-6074	58	39	β	β	X
ap-6074	58	40	,	,	PUNCT
ap-6074	58	41	(	(	PUNCT
ap-6074	58	42	α	α	X
ap-6074	58	43	,	,	PUNCT
ap-6074	58	44	β	β	NOUN
ap-6074	58	45	)	)	PUNCT
ap-6074	58	46	∈	∈	NOUN
ap-6074	58	47	r2	r2	NOUN
ap-6074	58	48	.	.	PUNCT
ap-6074	59	1	specially	specially	ADV
ap-6074	59	2	,	,	PUNCT
ap-6074	59	3	the	the	DET
ap-6074	59	4	control	control	NOUN
ap-6074	59	5	points	point	NOUN
ap-6074	59	6	(	(	PUNCT
ap-6074	59	7	8)	8)	NUM
ap-6074	59	8	are	be	AUX
ap-6074	59	9	the	the	DET
ap-6074	59	10	following	follow	VERB
ap-6074	59	11	function	function	NOUN
ap-6074	59	12	values	value	NOUN
ap-6074	59	13	of	of	ADP
ap-6074	59	14	surface	surface	NOUN
ap-6074	59	15	(	(	PUNCT
ap-6074	59	16	7	7	NUM
ap-6074	59	17	)	)	PUNCT
ap-6074	59	18	p00	p00	NOUN
ap-6074	59	19	=	=	PUNCT
ap-6074	59	20	z(−a,−a	z(−a,−a	NUM
ap-6074	59	21	)	)	PUNCT
ap-6074	59	22	,	,	PUNCT
ap-6074	59	23	p01	p01	NOUN
ap-6074	59	24	=	=	SYM
ap-6074	59	25	z(−a	z(−a	NOUN
ap-6074	59	26	,	,	PUNCT
ap-6074	59	27	a	a	PRON
ap-6074	59	28	)	)	PUNCT
ap-6074	59	29	,	,	PUNCT
ap-6074	59	30	p10	p10	NOUN
ap-6074	59	31	=	=	SYM
ap-6074	59	32	z(a,−a	z(a,−a	NUM
ap-6074	59	33	)	)	PUNCT
ap-6074	59	34	,	,	PUNCT
ap-6074	59	35	p11	p11	NOUN
ap-6074	59	36	=	=	SYM
ap-6074	59	37	z(a	z(a	NOUN
ap-6074	59	38	,	,	PUNCT
ap-6074	59	39	a	a	PRON
ap-6074	59	40	)	)	PUNCT
ap-6074	59	41	and	and	CCONJ
ap-6074	59	42	vertex	vertex	NOUN
ap-6074	59	43	v	v	X
ap-6074	59	44	=	=	SYM
ap-6074	59	45	z(m	z(m	NOUN
ap-6074	59	46	,	,	PUNCT
ap-6074	59	47	n	n	CCONJ
ap-6074	59	48	)	)	PUNCT
ap-6074	59	49	.	.	PUNCT
ap-6074	60	1	there	there	PRON
ap-6074	60	2	are	be	VERB
ap-6074	60	3	three	three	NUM
ap-6074	60	4	types	type	NOUN
ap-6074	60	5	of	of	ADP
ap-6074	60	6	curves	curve	NOUN
ap-6074	60	7	on	on	ADP
ap-6074	60	8	the	the	DET
ap-6074	60	9	surface	surface	NOUN
ap-6074	60	10	of	of	ADP
ap-6074	60	11	hyperbolic	hyperbolic	ADJ
ap-6074	60	12	paraboloid	paraboloid	NOUN
ap-6074	60	13	:	:	PUNCT
ap-6074	60	14	two	two	NUM
ap-6074	60	15	systems	system	NOUN
ap-6074	60	16	of	of	ADP
ap-6074	60	17	parametric	parametric	ADJ
ap-6074	60	18	straight	straight	ADJ
ap-6074	60	19	lines	line	NOUN
ap-6074	60	20	,	,	PUNCT
ap-6074	60	21	two	two	NUM
ap-6074	60	22	systems	system	NOUN
ap-6074	60	23	of	of	ADP
ap-6074	60	24	parabolas	parabola	NOUN
ap-6074	60	25	and	and	CCONJ
ap-6074	60	26	one	one	NUM
ap-6074	60	27	system	system	NOUN
ap-6074	60	28	of	of	ADP
ap-6074	60	29	hyperbolas	hyperbolas	PROPN
ap-6074	60	30	.	.	PUNCT
ap-6074	61	1	the	the	DET
ap-6074	61	2	parametric	parametric	ADJ
ap-6074	61	3	straight	straight	ADJ
ap-6074	61	4	lines	line	NOUN
ap-6074	61	5	(	(	PUNCT
ap-6074	61	6	by	by	ADP
ap-6074	61	7	means	mean	NOUN
ap-6074	61	8	of	of	ADP
ap-6074	61	9	which	which	PRON
ap-6074	61	10	the	the	DET
ap-6074	61	11	surface	surface	NOUN
ap-6074	61	12	in	in	ADP
ap-6074	61	13	fig	fig	NOUN
ap-6074	61	14	.	.	PUNCT
ap-6074	61	15	1	1	NUM
ap-6074	61	16	is	be	AUX
ap-6074	61	17	depicted	depict	VERB
ap-6074	61	18	)	)	PUNCT
ap-6074	61	19	are	be	AUX
ap-6074	61	20	obtained	obtain	VERB
ap-6074	61	21	by	by	ADP
ap-6074	61	22	a	a	DET
ap-6074	61	23	substitution	substitution	NOUN
ap-6074	61	24	of	of	ADP
ap-6074	61	25	the	the	DET
ap-6074	61	26	constant	constant	ADJ
ap-6074	61	27	value	value	NOUN
ap-6074	61	28	x	x	X
ap-6074	61	29	=	=	SYM
ap-6074	61	30	α	α	PROPN
ap-6074	61	31	or	or	CCONJ
ap-6074	61	32	y	y	PROPN
ap-6074	61	33	=	=	SYM
ap-6074	62	1	β	β	X
ap-6074	62	2	in	in	ADP
ap-6074	62	3	(	(	PUNCT
ap-6074	62	4	7	7	NUM
ap-6074	62	5	)	)	PUNCT
ap-6074	62	6	z(x	z(x	NUM
ap-6074	62	7	,	,	PUNCT
ap-6074	62	8	β	β	X
ap-6074	62	9	)	)	PUNCT
ap-6074	63	1	=	=	SYM
ap-6074	63	2	k(β	k(β	PROPN
ap-6074	63	3	−	−	NOUN
ap-6074	63	4	n)x+	n)x+	NUM
ap-6074	63	5	p−	p−	NOUN
ap-6074	63	6	km(β	km(β	NOUN
ap-6074	63	7	−	−	NOUN
ap-6074	63	8	n	n	CCONJ
ap-6074	63	9	)	)	PUNCT
ap-6074	63	10	,	,	PUNCT
ap-6074	63	11	(	(	PUNCT
ap-6074	63	12	16	16	X
ap-6074	63	13	)	)	PUNCT
ap-6074	63	14	z(α	z(α	PROPN
ap-6074	63	15	,	,	PUNCT
ap-6074	63	16	y	y	NOUN
ap-6074	63	17	)	)	PUNCT
ap-6074	63	18	=	=	VERB
ap-6074	64	1	k(α−m)y	k(α−m)y	NOUN
ap-6074	64	2	+	+	CCONJ
ap-6074	64	3	p−	p−	NOUN
ap-6074	64	4	kn(a−m	kn(a−m	PROPN
ap-6074	64	5	)	)	PUNCT
ap-6074	64	6	.	.	PUNCT
ap-6074	65	1	(	(	PUNCT
ap-6074	65	2	17	17	NUM
ap-6074	65	3	)	)	PUNCT
ap-6074	65	4	equations	equation	NOUN
ap-6074	65	5	(	(	PUNCT
ap-6074	65	6	16	16	NUM
ap-6074	65	7	)	)	PUNCT
ap-6074	65	8	and	and	CCONJ
ap-6074	65	9	(	(	PUNCT
ap-6074	65	10	17	17	NUM
ap-6074	65	11	)	)	PUNCT
ap-6074	65	12	geometrically	geometrically	ADV
ap-6074	65	13	express	express	VERB
ap-6074	65	14	the	the	DET
ap-6074	65	15	intersection	intersection	NOUN
ap-6074	65	16	of	of	ADP
ap-6074	65	17	the	the	DET
ap-6074	65	18	surface	surface	NOUN
ap-6074	65	19	of	of	ADP
ap-6074	65	20	the	the	DET
ap-6074	65	21	hyperbolic	hyperbolic	ADJ
ap-6074	65	22	paraboloid	paraboloid	NOUN
ap-6074	65	23	and	and	CCONJ
ap-6074	65	24	planes	plane	NOUN
ap-6074	65	25	parallel	parallel	NOUN
ap-6074	65	26	with	with	ADP
ap-6074	65	27	(	(	PUNCT
ap-6074	65	28	x	x	NOUN
ap-6074	65	29	,	,	PUNCT
ap-6074	65	30	z	z	NOUN
ap-6074	65	31	)	)	PUNCT
ap-6074	65	32	and	and	CCONJ
ap-6074	65	33	(	(	PUNCT
ap-6074	65	34	y	y	PROPN
ap-6074	65	35	,	,	PUNCT
ap-6074	65	36	z	z	NOUN
ap-6074	65	37	)	)	PUNCT
ap-6074	65	38	planes	plane	NOUN
ap-6074	65	39	in	in	ADP
ap-6074	65	40	the	the	DET
ap-6074	65	41	given	give	VERB
ap-6074	65	42	order	order	NOUN
ap-6074	65	43	.	.	PUNCT
ap-6074	66	1	specially	specially	ADV
ap-6074	66	2	,	,	PUNCT
ap-6074	66	3	the	the	DET
ap-6074	66	4	boundaries	boundary	NOUN
ap-6074	66	5	of	of	ADP
ap-6074	66	6	the	the	DET
ap-6074	66	7	hyperbolic	hyperbolic	ADJ
ap-6074	66	8	paraboloid	paraboloid	NOUN
ap-6074	66	9	are	be	AUX
ap-6074	66	10	obtained	obtain	VERB
ap-6074	66	11	by	by	ADP
ap-6074	66	12	z(x,−a	z(x,−a	NOUN
ap-6074	66	13	)	)	PUNCT
ap-6074	66	14	,	,	PUNCT
ap-6074	66	15	z(x	z(x	PROPN
ap-6074	66	16	,	,	PUNCT
ap-6074	66	17	a	a	PRON
ap-6074	66	18	)	)	PUNCT
ap-6074	66	19	,	,	PUNCT
ap-6074	66	20	z(−a	z(−a	NUM
ap-6074	66	21	,	,	PUNCT
ap-6074	66	22	y	y	PROPN
ap-6074	66	23	)	)	PUNCT
ap-6074	66	24	,	,	PUNCT
ap-6074	66	25	z(a	z(a	PROPN
ap-6074	66	26	,	,	PUNCT
ap-6074	66	27	y	y	PROPN
ap-6074	66	28	)	)	PUNCT
ap-6074	66	29	and	and	CCONJ
ap-6074	66	30	the	the	DET
ap-6074	66	31	straight	straight	ADJ
ap-6074	66	32	lines	line	NOUN
ap-6074	66	33	passing	pass	VERB
ap-6074	66	34	through	through	ADP
ap-6074	66	35	the	the	DET
ap-6074	66	36	vertex	vertex	NOUN
ap-6074	66	37	(	(	PUNCT
ap-6074	66	38	red	red	ADJ
ap-6074	66	39	lines	line	NOUN
ap-6074	66	40	on	on	ADP
ap-6074	66	41	fig	fig	NOUN
ap-6074	66	42	.	.	PUNCT
ap-6074	67	1	2	2	NUM
ap-6074	67	2	)	)	PUNCT
ap-6074	67	3	are	be	AUX
ap-6074	67	4	given	give	VERB
ap-6074	67	5	by	by	ADP
ap-6074	67	6	z(x	z(x	NUM
ap-6074	67	7	,	,	PUNCT
ap-6074	67	8	n	n	CCONJ
ap-6074	67	9	)	)	PUNCT
ap-6074	67	10	=	=	SYM
ap-6074	67	11	p	p	NOUN
ap-6074	67	12	,	,	PUNCT
ap-6074	67	13	z(m	z(m	PROPN
ap-6074	67	14	,	,	PUNCT
ap-6074	67	15	y	y	NOUN
ap-6074	67	16	)	)	PUNCT
ap-6074	68	1	=	=	VERB
ap-6074	69	1	p.	p.	NOUN
ap-6074	69	2	(	(	PUNCT
ap-6074	69	3	18	18	NUM
ap-6074	69	4	)	)	PUNCT
ap-6074	69	5	obviously	obviously	ADV
ap-6074	69	6	,	,	PUNCT
ap-6074	69	7	equations	equation	NOUN
ap-6074	69	8	(	(	PUNCT
ap-6074	69	9	16	16	NUM
ap-6074	69	10	)	)	PUNCT
ap-6074	69	11	and	and	CCONJ
ap-6074	69	12	(	(	PUNCT
ap-6074	69	13	17	17	NUM
ap-6074	69	14	)	)	PUNCT
ap-6074	69	15	represent	represent	VERB
ap-6074	69	16	two	two	NUM
ap-6074	69	17	systems	system	NOUN
ap-6074	69	18	of	of	ADP
ap-6074	69	19	straight	straight	ADJ
ap-6074	69	20	lines	line	NOUN
ap-6074	69	21	on	on	ADP
ap-6074	69	22	the	the	DET
ap-6074	69	23	surface	surface	NOUN
ap-6074	69	24	of	of	ADP
ap-6074	69	25	hyperbolic	hyperbolic	ADJ
ap-6074	69	26	paraboloid	paraboloid	NOUN
ap-6074	69	27	.	.	PUNCT
ap-6074	70	1	each	each	DET
ap-6074	70	2	straight	straight	ADJ
ap-6074	70	3	line	line	NOUN
ap-6074	70	4	from	from	ADP
ap-6074	70	5	the	the	DET
ap-6074	70	6	first	first	ADJ
ap-6074	70	7	system	system	NOUN
ap-6074	70	8	intersects	intersect	VERB
ap-6074	70	9	all	all	DET
ap-6074	70	10	straight	straight	ADJ
ap-6074	70	11	lines	line	NOUN
ap-6074	70	12	from	from	ADP
ap-6074	70	13	the	the	DET
ap-6074	70	14	second	second	ADJ
ap-6074	70	15	system	system	NOUN
ap-6074	70	16	and	and	CCONJ
ap-6074	70	17	is	be	AUX
ap-6074	70	18	perpendicular	perpendicular	ADJ
ap-6074	70	19	to	to	ADP
ap-6074	70	20	them	they	PRON
ap-6074	70	21	.	.	PUNCT
ap-6074	71	1	straight	straight	ADJ
ap-6074	71	2	lines	line	NOUN
ap-6074	71	3	(	(	PUNCT
ap-6074	71	4	18	18	NUM
ap-6074	71	5	)	)	PUNCT
ap-6074	71	6	passing	pass	VERB
ap-6074	71	7	through	through	ADP
ap-6074	71	8	the	the	DET
ap-6074	71	9	vertex	vertex	NOUN
ap-6074	71	10	are	be	AUX
ap-6074	71	11	parallel	parallel	ADJ
ap-6074	71	12	with	with	ADP
ap-6074	71	13	(	(	PUNCT
ap-6074	71	14	x	x	NOUN
ap-6074	71	15	,	,	PUNCT
ap-6074	71	16	y	y	NOUN
ap-6074	71	17	)	)	PUNCT
ap-6074	71	18	plane	plane	NOUN
ap-6074	71	19	.	.	PUNCT
ap-6074	72	1	two	two	NUM
ap-6074	72	2	system	system	NOUN
ap-6074	72	3	of	of	ADP
ap-6074	72	4	parabolas	parabola	NOUN
ap-6074	72	5	on	on	ADP
ap-6074	72	6	the	the	DET
ap-6074	72	7	surface	surface	NOUN
ap-6074	72	8	of	of	ADP
ap-6074	72	9	hyperbolic	hyperbolic	ADJ
ap-6074	72	10	paraboloid	paraboloid	NOUN
ap-6074	72	11	are	be	AUX
ap-6074	72	12	obtained	obtain	VERB
ap-6074	72	13	as	as	ADP
ap-6074	72	14	intersections	intersection	NOUN
ap-6074	72	15	of	of	ADP
ap-6074	72	16	the	the	DET
ap-6074	72	17	surface	surface	NOUN
ap-6074	72	18	and	and	CCONJ
ap-6074	72	19	planes	plane	NOUN
ap-6074	72	20	parallel	parallel	NOUN
ap-6074	72	21	with	with	ADP
ap-6074	72	22	the	the	DET
ap-6074	72	23	plane	plane	NOUN
ap-6074	72	24	y	y	NOUN
ap-6074	73	1	=	=	PUNCT
ap-6074	74	1	x	x	PROPN
ap-6074	74	2	or	or	CCONJ
ap-6074	74	3	y	y	PROPN
ap-6074	74	4	=	=	PUNCT
ap-6074	74	5	−x	−x	NOUN
ap-6074	74	6	,	,	PUNCT
ap-6074	74	7	i.e.	i.e.	X
ap-6074	74	8	z(x	z(x	NUM
ap-6074	74	9	,	,	PUNCT
ap-6074	74	10	x+	x+	ADJ
ap-6074	74	11	d	d	NOUN
ap-6074	74	12	)	)	PUNCT
ap-6074	74	13	=	=	SYM
ap-6074	75	1	=	=	SYM
ap-6074	75	2	kx2	kx2	PROPN
ap-6074	75	3	−	−	PROPN
ap-6074	76	1	(	(	PUNCT
ap-6074	76	2	m+	m+	PRON
ap-6074	76	3	d−	d−	PROPN
ap-6074	76	4	n)kx+	n)kx+	NOUN
ap-6074	76	5	km(n−	km(n−	PROPN
ap-6074	76	6	d	d	PROPN
ap-6074	76	7	)	)	PUNCT
ap-6074	77	1	+	+	CCONJ
ap-6074	77	2	p	p	ADJ
ap-6074	77	3	,	,	PUNCT
ap-6074	77	4	z(x,−x+	z(x,−x+	NUM
ap-6074	77	5	d	d	NOUN
ap-6074	77	6	)	)	PUNCT
ap-6074	77	7	=	=	SYM
ap-6074	77	8	−kx2	−kx2	NOUN
ap-6074	77	9	+	+	CCONJ
ap-6074	77	10	(	(	PUNCT
ap-6074	77	11	m+	m+	PRON
ap-6074	77	12	d−	d−	PROPN
ap-6074	77	13	n)kx+	n)kx+	NOUN
ap-6074	77	14	km(n−	km(n−	PROPN
ap-6074	77	15	d	d	PROPN
ap-6074	77	16	)	)	PUNCT
ap-6074	78	1	+	+	CCONJ
ap-6074	79	1	p	p	X
ap-6074	79	2	,	,	PUNCT
ap-6074	79	3	where	where	SCONJ
ap-6074	79	4	d	d	NOUN
ap-6074	79	5	is	be	AUX
ap-6074	79	6	y	y	NOUN
ap-6074	79	7	-	-	PUNCT
ap-6074	79	8	intercept	intercept	NOUN
ap-6074	79	9	of	of	ADP
ap-6074	79	10	the	the	DET
ap-6074	79	11	plane	plane	NOUN
ap-6074	79	12	y	y	NOUN
ap-6074	79	13	=	=	PUNCT
ap-6074	79	14	x	x	PROPN
ap-6074	80	1	+	+	CCONJ
ap-6074	80	2	d	d	NOUN
ap-6074	80	3	or	or	CCONJ
ap-6074	80	4	y	y	PROPN
ap-6074	80	5	=	=	PUNCT
ap-6074	80	6	−x+	−x+	PROPN
ap-6074	80	7	d.	d.	PROPN
ap-6074	80	8	specially	specially	ADV
ap-6074	80	9	,	,	PUNCT
ap-6074	80	10	the	the	DET
ap-6074	80	11	parabolas	parabola	NOUN
ap-6074	80	12	passing	pass	VERB
ap-6074	80	13	through	through	ADP
ap-6074	80	14	the	the	DET
ap-6074	80	15	vertex	vertex	NOUN
ap-6074	80	16	are	be	AUX
ap-6074	80	17	given	give	VERB
ap-6074	80	18	by	by	ADP
ap-6074	80	19	z(x	z(x	NUM
ap-6074	80	20	,	,	PUNCT
ap-6074	80	21	x	x	X
ap-6074	80	22	)	)	PUNCT
ap-6074	81	1	=	=	SYM
ap-6074	81	2	p+	p+	PROPN
ap-6074	81	3	k(x−m)(x−	k(x−m)(x−	PROPN
ap-6074	81	4	n	n	CCONJ
ap-6074	81	5	)	)	PUNCT
ap-6074	81	6	(	(	PUNCT
ap-6074	81	7	19	19	NUM
ap-6074	81	8	)	)	PUNCT
ap-6074	81	9	z(x,−x	z(x,−x	NUM
ap-6074	81	10	)	)	PUNCT
ap-6074	81	11	=	=	PRON
ap-6074	81	12	p+	p+	PROPN
ap-6074	81	13	k(x−m)(−x−	k(x−m)(−x−	X
ap-6074	81	14	n	n	CCONJ
ap-6074	81	15	)	)	PUNCT
ap-6074	81	16	.	.	PUNCT
ap-6074	82	1	(	(	PUNCT
ap-6074	82	2	20	20	NUM
ap-6074	82	3	)	)	PUNCT
ap-6074	82	4	equation	equation	NOUN
ap-6074	82	5	(	(	PUNCT
ap-6074	82	6	19	19	NUM
ap-6074	82	7	)	)	PUNCT
ap-6074	82	8	represents	represent	VERB
ap-6074	82	9	the	the	DET
ap-6074	82	10	blue	blue	ADJ
ap-6074	82	11	parabola	parabola	NOUN
ap-6074	82	12	and	and	CCONJ
ap-6074	82	13	(	(	PUNCT
ap-6074	82	14	20	20	NUM
ap-6074	82	15	)	)	PUNCT
ap-6074	82	16	the	the	DET
ap-6074	82	17	green	green	PROPN
ap-6074	82	18	parabola	parabola	PROPN
ap-6074	82	19	in	in	ADP
ap-6074	82	20	fig	fig	NOUN
ap-6074	82	21	.	.	PUNCT
ap-6074	83	1	2	2	NUM
ap-6074	83	2	.	.	NUM
ap-6074	83	3	00	00	NUM
ap-6074	84	1	10	10	NUM
ap-6074	84	2	p	p	PRON
ap-6074	84	3	a	a	DET
ap-6074	84	4	11	11	NUM
ap-6074	84	5	p	p	NOUN
ap-6074	84	6	a	a	DET
ap-6074	84	7	01	01	NUM
ap-6074	84	8	p	p	NOUN
ap-6074	84	9	-a	-a	PROPN
ap-6074	84	10	v	v	PROPN
ap-6074	84	11	p	p	X
ap-6074	84	12	y	y	PROPN
ap-6074	84	13	a	a	PROPN
ap-6074	84	14	)	)	PUNCT
ap-6074	84	15	x	x	SYM
ap-6074	84	16	-a	-a	PROPN
ap-6074	84	17	z	z	X
ap-6074	84	18	p	p	X
ap-6074	84	19	-a	-a	PROPN
ap-6074	84	20	a	a	PROPN
ap-6074	84	21	y	y	PROPN
ap-6074	84	22	a	a	DET
ap-6074	84	23	p	p	NOUN
ap-6074	84	24	10	10	NUM
ap-6074	84	25	01	01	NUM
ap-6074	84	26	ap	ap	PROPN
ap-6074	84	27	11	11	NUM
ap-6074	84	28	v	v	PROPN
ap-6074	84	29	b	b	NOUN
ap-6074	84	30	)	)	PUNCT
ap-6074	84	31	x	x	X
ap-6074	85	1	p	p	NOUN
ap-6074	85	2	00	00	NUM
ap-6074	85	3	figure	figure	NOUN
ap-6074	85	4	2	2	NUM
ap-6074	85	5	.	.	PUNCT
ap-6074	85	6	curves	curve	NOUN
ap-6074	85	7	on	on	ADP
ap-6074	85	8	surface	surface	NOUN
ap-6074	85	9	of	of	ADP
ap-6074	85	10	hyperbolic	hyperbolic	ADJ
ap-6074	85	11	paraboloid	paraboloid	NOUN
ap-6074	85	12	a	a	PRON
ap-6074	85	13	)	)	PUNCT
ap-6074	85	14	axonometric	axonometric	NOUN
ap-6074	85	15	view	view	NOUN
ap-6074	85	16	,	,	PUNCT
ap-6074	85	17	b	b	NOUN
ap-6074	85	18	)	)	PUNCT
ap-6074	85	19	top	top	ADJ
ap-6074	85	20	view	view	NOUN
ap-6074	85	21	.	.	PUNCT
ap-6074	86	1	hyperbolas	hyperbola	NOUN
ap-6074	86	2	on	on	ADP
ap-6074	86	3	the	the	DET
ap-6074	86	4	surface	surface	NOUN
ap-6074	86	5	of	of	ADP
ap-6074	86	6	hyperbolic	hyperbolic	ADJ
ap-6074	86	7	paraboloid	paraboloid	NOUN
ap-6074	86	8	are	be	AUX
ap-6074	86	9	obtained	obtain	VERB
ap-6074	86	10	as	as	ADP
ap-6074	86	11	intersections	intersection	NOUN
ap-6074	86	12	of	of	ADP
ap-6074	86	13	the	the	DET
ap-6074	86	14	surface	surface	NOUN
ap-6074	86	15	and	and	CCONJ
ap-6074	86	16	planes	plane	NOUN
ap-6074	86	17	parallel	parallel	NOUN
ap-6074	86	18	with	with	ADP
ap-6074	86	19	(	(	PUNCT
ap-6074	86	20	x	x	NOUN
ap-6074	86	21	,	,	PUNCT
ap-6074	86	22	y	y	NOUN
ap-6074	86	23	)	)	PUNCT
ap-6074	86	24	plane	plane	NOUN
ap-6074	86	25	,	,	PUNCT
ap-6074	86	26	i.e.	i.e.	X
ap-6074	86	27	z	z	NOUN
ap-6074	86	28	=	=	SYM
ap-6074	86	29	γ	γ	X
ap-6074	86	30	,	,	PUNCT
ap-6074	86	31	where	where	SCONJ
ap-6074	86	32	γ	γ	PROPN
ap-6074	86	33	is	be	AUX
ap-6074	86	34	a	a	DET
ap-6074	86	35	real	real	ADV
ap-6074	86	36	constant	constant	ADJ
ap-6074	86	37	p+	p+	NOUN
ap-6074	86	38	k(x−m)(y	k(x−m)(y	PROPN
ap-6074	86	39	−	−	PROPN
ap-6074	86	40	n	n	CCONJ
ap-6074	86	41	)	)	PUNCT
ap-6074	86	42	=	=	SYM
ap-6074	87	1	γ	γ	X
ap-6074	87	2	.	.	PROPN
ap-6074	87	3	(	(	PUNCT
ap-6074	87	4	21	21	NUM
ap-6074	87	5	)	)	PUNCT
ap-6074	87	6	specially	specially	ADV
ap-6074	87	7	,	,	PUNCT
ap-6074	87	8	for	for	ADP
ap-6074	87	9	γ	γ	X
ap-6074	87	10	=	=	SYM
ap-6074	87	11	p	p	X
ap-6074	87	12	we	we	PRON
ap-6074	87	13	get	get	VERB
ap-6074	87	14	(	(	PUNCT
ap-6074	87	15	18	18	NUM
ap-6074	87	16	)	)	PUNCT
ap-6074	87	17	,	,	PUNCT
ap-6074	87	18	i.e.	i.e.	X
ap-6074	87	19	asymptotes	asymptote	NOUN
ap-6074	87	20	of	of	ADP
ap-6074	87	21	all	all	DET
ap-6074	87	22	the	the	DET
ap-6074	87	23	hyperbolas	hyperbola	NOUN
ap-6074	87	24	in	in	ADP
ap-6074	87	25	the	the	DET
ap-6074	87	26	top	top	ADJ
ap-6074	87	27	view	view	NOUN
ap-6074	87	28	,	,	PUNCT
ap-6074	87	29	see	see	VERB
ap-6074	87	30	red	red	ADJ
ap-6074	87	31	straight	straight	ADJ
ap-6074	87	32	lines	line	NOUN
ap-6074	87	33	in	in	ADP
ap-6074	87	34	fig	fig	NOUN
ap-6074	87	35	.	.	PUNCT
ap-6074	88	1	2	2	NUM
ap-6074	88	2	b	b	NOUN
ap-6074	88	3	)	)	PUNCT
ap-6074	88	4	.	.	PUNCT
ap-6074	89	1	the	the	DET
ap-6074	89	2	magenta	magenta	NOUN
ap-6074	89	3	hyperbola	hyperbola	PROPN
ap-6074	89	4	in	in	ADP
ap-6074	89	5	fig	fig	NOUN
ap-6074	89	6	.	.	PUNCT
ap-6074	90	1	2	2	NUM
ap-6074	90	2	corresponds	correspond	NOUN
ap-6074	90	3	to	to	ADP
ap-6074	90	4	γ	γ	PROPN
ap-6074	90	5	>	>	X
ap-6074	90	6	p	p	X
ap-6074	90	7	,	,	PUNCT
ap-6074	90	8	the	the	DET
ap-6074	90	9	cyan	cyan	NOUN
ap-6074	90	10	hyperbola	hyperbola	PROPN
ap-6074	90	11	corresponds	correspond	VERB
ap-6074	90	12	to	to	ADP
ap-6074	90	13	γ	γ	X
ap-6074	90	14	<	<	X
ap-6074	90	15	p.	p.	NOUN
ap-6074	90	16	2.1	2.1	NUM
ap-6074	90	17	.	.	PUNCT
ap-6074	91	1	freeform	freeform	ADJ
ap-6074	91	2	standard	standard	ADJ
ap-6074	91	3	hyperbolic	hyperbolic	ADJ
ap-6074	91	4	paraboloid	paraboloid	NOUN
ap-6074	91	5	the	the	DET
ap-6074	91	6	cad	cad	PROPN
ap-6074	91	7	model	model	NOUN
ap-6074	91	8	of	of	ADP
ap-6074	91	9	the	the	DET
ap-6074	91	10	standard	standard	NOUN
ap-6074	91	11	is	be	AUX
ap-6074	91	12	depicted	depict	VERB
ap-6074	91	13	in	in	ADP
ap-6074	91	14	fig	fig	NOUN
ap-6074	91	15	.	.	PUNCT
ap-6074	92	1	3	3	NUM
ap-6074	92	2	a	a	NOUN
ap-6074	92	3	)	)	PUNCT
ap-6074	92	4	.	.	PUNCT
ap-6074	93	1	the	the	DET
ap-6074	93	2	surface	surface	NOUN
ap-6074	93	3	of	of	ADP
ap-6074	93	4	hyperbolic	hyperbolic	ADJ
ap-6074	93	5	paraboloid	paraboloid	NOUN
ap-6074	93	6	(	(	PUNCT
ap-6074	93	7	green	green	ADJ
ap-6074	93	8	)	)	PUNCT
ap-6074	93	9	is	be	AUX
ap-6074	93	10	created	create	VERB
ap-6074	93	11	in	in	ADP
ap-6074	93	12	the	the	DET
ap-6074	93	13	cad	cad	NOUN
ap-6074	93	14	system	system	NOUN
ap-6074	93	15	as	as	ADP
ap-6074	93	16	bilinear	bilinear	PROPN
ap-6074	93	17	b	b	PROPN
ap-6074	93	18	-	-	PUNCT
ap-6074	93	19	spline	spline	NOUN
ap-6074	93	20	surface	surface	NOUN
ap-6074	93	21	given	give	VERB
ap-6074	93	22	by	by	ADP
ap-6074	93	23	control	control	NOUN
ap-6074	93	24	points	point	NOUN
ap-6074	93	25	p00	p00	PROPN
ap-6074	93	26	=	=	SYM
ap-6074	93	27	(	(	PUNCT
ap-6074	93	28	−9,−9	−9,−9	NOUN
ap-6074	93	29	,	,	PUNCT
ap-6074	93	30	73	73	NUM
ap-6074	93	31	)	)	PUNCT
ap-6074	93	32	,	,	PUNCT
ap-6074	93	33	p01	p01	NOUN
ap-6074	93	34	=	=	SYM
ap-6074	93	35	(	(	PUNCT
ap-6074	93	36	−9	−9	NOUN
ap-6074	93	37	,	,	PUNCT
ap-6074	93	38	87,−11	87,−11	NUM
ap-6074	93	39	)	)	PUNCT
ap-6074	93	40	,	,	PUNCT
ap-6074	93	41	(	(	PUNCT
ap-6074	93	42	22	22	X
ap-6074	93	43	)	)	PUNCT
ap-6074	93	44	p10	p10	NOUN
ap-6074	93	45	=	=	SYM
ap-6074	93	46	(	(	PUNCT
ap-6074	93	47	87,−9,−11	87,−9,−11	NUM
ap-6074	93	48	)	)	PUNCT
ap-6074	93	49	,	,	PUNCT
ap-6074	93	50	p11	p11	NOUN
ap-6074	93	51	=	=	SYM
ap-6074	93	52	(	(	PUNCT
ap-6074	93	53	87	87	NUM
ap-6074	93	54	,	,	PUNCT
ap-6074	93	55	87	87	NUM
ap-6074	93	56	,	,	PUNCT
ap-6074	93	57	49	49	NUM
ap-6074	93	58	)	)	PUNCT
ap-6074	93	59	.	.	PUNCT
ap-6074	94	1	101	101	NUM
ap-6074	94	2	ivana	ivana	PROPN
ap-6074	94	3	linkeová	linkeová	PROPN
ap-6074	94	4	,	,	PUNCT
ap-6074	94	5	vít	vít	PROPN
ap-6074	94	6	zelený	zelený	PROPN
ap-6074	94	7	acta	acta	PROPN
ap-6074	94	8	polytechnica	polytechnica	PROPN
ap-6074	94	9	figure	figure	NOUN
ap-6074	94	10	3	3	NUM
ap-6074	94	11	.	.	PUNCT
ap-6074	94	12	freeform	freeform	PROPN
ap-6074	94	13	standard	standard	ADJ
ap-6074	94	14	hyperbolic	hyperbolic	ADJ
ap-6074	94	15	paraboloid	paraboloid	NOUN
ap-6074	94	16	a	a	PRON
ap-6074	94	17	)	)	PUNCT
ap-6074	94	18	cad	cad	PROPN
ap-6074	94	19	model	model	NOUN
ap-6074	94	20	,	,	PUNCT
ap-6074	94	21	b	b	NOUN
ap-6074	94	22	)	)	PUNCT
ap-6074	94	23	hyperbolic	hyperbolic	ADJ
ap-6074	94	24	sections	section	NOUN
ap-6074	94	25	by	by	ADP
ap-6074	94	26	planes	plane	NOUN
ap-6074	94	27	parallel	parallel	NOUN
ap-6074	94	28	with	with	ADP
ap-6074	94	29	(	(	PUNCT
ap-6074	94	30	x	x	NOUN
ap-6074	94	31	,	,	PUNCT
ap-6074	94	32	y	y	NOUN
ap-6074	94	33	)	)	PUNCT
ap-6074	94	34	plane	plane	NOUN
ap-6074	94	35	,	,	PUNCT
ap-6074	94	36	c	c	NOUN
ap-6074	94	37	)	)	PUNCT
ap-6074	94	38	linear	linear	ADJ
ap-6074	94	39	sections	section	NOUN
ap-6074	94	40	by	by	ADP
ap-6074	94	41	planes	plane	NOUN
ap-6074	94	42	parallel	parallel	NOUN
ap-6074	94	43	with	with	ADP
ap-6074	94	44	(	(	PUNCT
ap-6074	94	45	x	x	NOUN
ap-6074	94	46	,	,	PUNCT
ap-6074	94	47	z	z	NOUN
ap-6074	94	48	)	)	PUNCT
ap-6074	94	49	plane	plane	NOUN
ap-6074	94	50	,	,	PUNCT
ap-6074	94	51	d	d	NOUN
ap-6074	94	52	)	)	PUNCT
ap-6074	94	53	linear	linear	ADJ
ap-6074	94	54	sections	section	NOUN
ap-6074	94	55	by	by	ADP
ap-6074	94	56	planes	plane	NOUN
ap-6074	94	57	parallel	parallel	NOUN
ap-6074	94	58	with	with	ADP
ap-6074	94	59	(	(	PUNCT
ap-6074	94	60	y	y	PROPN
ap-6074	94	61	,	,	PUNCT
ap-6074	94	62	z	z	NOUN
ap-6074	94	63	)	)	PUNCT
ap-6074	94	64	plane	plane	NOUN
ap-6074	94	65	,	,	PUNCT
ap-6074	94	66	e	e	NOUN
ap-6074	94	67	)	)	PUNCT
ap-6074	94	68	parabolic	parabolic	ADJ
ap-6074	94	69	sections	section	NOUN
ap-6074	94	70	by	by	ADP
ap-6074	94	71	planes	plane	NOUN
ap-6074	94	72	parallel	parallel	NOUN
ap-6074	94	73	with	with	ADP
ap-6074	94	74	plane	plane	NOUN
ap-6074	94	75	y	y	NOUN
ap-6074	94	76	=	=	SYM
ap-6074	94	77	x	x	PROPN
ap-6074	94	78	,	,	PUNCT
ap-6074	94	79	f	f	X
ap-6074	94	80	)	)	PUNCT
ap-6074	94	81	parabolic	parabolic	ADJ
ap-6074	94	82	sections	section	NOUN
ap-6074	94	83	by	by	ADP
ap-6074	94	84	planes	plane	NOUN
ap-6074	94	85	parallel	parallel	NOUN
ap-6074	94	86	with	with	ADP
ap-6074	94	87	plane	plane	NOUN
ap-6074	94	88	y	y	NOUN
ap-6074	94	89	=	=	PUNCT
ap-6074	94	90	−x	−x	NOUN
ap-6074	94	91	.	.	PUNCT
ap-6074	94	92	102	102	NUM
ap-6074	94	93	vol	vol	NOUN
ap-6074	94	94	.	.	PUNCT
ap-6074	94	95	61	61	NUM
ap-6074	94	96	special	special	ADJ
ap-6074	94	97	issue/2021	issue/2021	NOUN
ap-6074	94	98	application	application	NOUN
ap-6074	94	99	of	of	ADP
ap-6074	94	100	ruled	rule	VERB
ap-6074	94	101	surfaces	surface	NOUN
ap-6074	94	102	in	in	ADP
ap-6074	94	103	freeform	freeform	NOUN
ap-6074	94	104	and	and	CCONJ
ap-6074	94	105	gear	gear	NOUN
ap-6074	94	106	metrology	metrology	NOUN
ap-6074	94	107	control	control	NOUN
ap-6074	94	108	points	point	NOUN
ap-6074	94	109	(	(	PUNCT
ap-6074	94	110	22	22	NUM
ap-6074	94	111	)	)	PUNCT
ap-6074	94	112	are	be	AUX
ap-6074	94	113	located	locate	VERB
ap-6074	94	114	above	above	ADP
ap-6074	94	115	the	the	DET
ap-6074	94	116	vertices	vertex	NOUN
ap-6074	94	117	of	of	ADP
ap-6074	94	118	axis	axis	NOUN
ap-6074	94	119	aligned	aligned	ADJ
ap-6074	94	120	square	square	NOUN
ap-6074	94	121	with	with	ADP
ap-6074	94	122	the	the	DET
ap-6074	94	123	centre	centre	NOUN
ap-6074	94	124	at	at	ADP
ap-6074	94	125	point	point	NOUN
ap-6074	94	126	(	(	PUNCT
ap-6074	94	127	q	q	NOUN
ap-6074	94	128	,	,	PUNCT
ap-6074	94	129	r	r	NOUN
ap-6074	94	130	,	,	PUNCT
ap-6074	94	131	0	0	NUM
ap-6074	94	132	)	)	PUNCT
ap-6074	94	133	=	=	NOUN
ap-6074	94	134	(	(	PUNCT
ap-6074	94	135	39	39	NUM
ap-6074	94	136	,	,	PUNCT
ap-6074	94	137	39	39	NUM
ap-6074	94	138	,	,	PUNCT
ap-6074	94	139	0	0	NUM
ap-6074	94	140	)	)	PUNCT
ap-6074	94	141	and	and	CCONJ
ap-6074	94	142	length	length	NOUN
ap-6074	94	143	of	of	ADP
ap-6074	94	144	the	the	DET
ap-6074	94	145	edge	edge	NOUN
ap-6074	95	1	2a	2a	NUM
ap-6074	95	2	=	=	SYM
ap-6074	95	3	96	96	NUM
ap-6074	95	4	(	(	PUNCT
ap-6074	95	5	all	all	DET
ap-6074	95	6	dimensions	dimension	NOUN
ap-6074	95	7	are	be	AUX
ap-6074	95	8	in	in	ADP
ap-6074	95	9	mm	mm	PROPN
ap-6074	95	10	)	)	PUNCT
ap-6074	95	11	.	.	PUNCT
ap-6074	96	1	using	use	VERB
ap-6074	96	2	(	(	PUNCT
ap-6074	96	3	12	12	NUM
ap-6074	96	4	)	)	PUNCT
ap-6074	96	5	,	,	PUNCT
ap-6074	96	6	(	(	PUNCT
ap-6074	96	7	14	14	NUM
ap-6074	96	8	)	)	PUNCT
ap-6074	96	9	and	and	CCONJ
ap-6074	96	10	15	15	NUM
ap-6074	96	11	,	,	PUNCT
ap-6074	96	12	the	the	DET
ap-6074	96	13	explicit	explicit	ADJ
ap-6074	96	14	equation	equation	NOUN
ap-6074	96	15	of	of	ADP
ap-6074	96	16	the	the	DET
ap-6074	96	17	functional	functional	ADJ
ap-6074	96	18	surface	surface	NOUN
ap-6074	96	19	of	of	ADP
ap-6074	96	20	the	the	DET
ap-6074	96	21	standard	standard	NOUN
ap-6074	96	22	is	be	AUX
ap-6074	96	23	given	give	VERB
ap-6074	96	24	by	by	ADP
ap-6074	96	25	z(x	z(x	PROPN
ap-6074	96	26	,	,	PUNCT
ap-6074	96	27	y	y	NOUN
ap-6074	96	28	)	)	PUNCT
ap-6074	96	29	=	=	SYM
ap-6074	97	1	24	24	NUM
ap-6074	97	2	+	+	CCONJ
ap-6074	97	3	1	1	NUM
ap-6074	97	4	64(x−	64(x−	NUM
ap-6074	97	5	47)(y	47)(y	NOUN
ap-6074	97	6	−	−	NOUN
ap-6074	97	7	47	47	NUM
ap-6074	97	8	)	)	PUNCT
ap-6074	97	9	.	.	PUNCT
ap-6074	98	1	this	this	DET
ap-6074	98	2	equation	equation	NOUN
ap-6074	98	3	is	be	AUX
ap-6074	98	4	useful	useful	ADJ
ap-6074	98	5	when	when	SCONJ
ap-6074	98	6	evaluating	evaluate	VERB
ap-6074	98	7	the	the	DET
ap-6074	98	8	measured	measured	ADJ
ap-6074	98	9	data	datum	NOUN
ap-6074	98	10	for	for	ADP
ap-6074	98	11	both	both	CCONJ
ap-6074	98	12	the	the	DET
ap-6074	98	13	tactile	tactile	ADJ
ap-6074	98	14	point	point	NOUN
ap-6074	98	15	-	-	PUNCT
ap-6074	98	16	to	to	ADP
ap-6074	98	17	-	-	PUNCT
ap-6074	98	18	point	point	NOUN
ap-6074	98	19	measurement	measurement	NOUN
ap-6074	98	20	and	and	CCONJ
ap-6074	98	21	the	the	DET
ap-6074	98	22	tactile	tactile	ADJ
ap-6074	98	23	scanning	scanning	NOUN
ap-6074	98	24	on	on	ADP
ap-6074	98	25	coordinate	coordinate	NOUN
ap-6074	98	26	a	a	DET
ap-6074	98	27	measurement	measurement	NOUN
ap-6074	98	28	machine	machine	NOUN
ap-6074	98	29	.	.	PUNCT
ap-6074	99	1	the	the	DET
ap-6074	99	2	standard	standard	NOUN
ap-6074	99	3	of	of	ADP
ap-6074	99	4	dimensions	dimension	NOUN
ap-6074	99	5	120	120	NUM
ap-6074	99	6	×	×	NOUN
ap-6074	99	7	120	120	NUM
ap-6074	99	8	×	×	NOUN
ap-6074	99	9	67	67	NUM
ap-6074	99	10	mm	mm	NOUN
ap-6074	99	11	consists	consist	VERB
ap-6074	99	12	of	of	ADP
ap-6074	99	13	a	a	DET
ap-6074	99	14	step	step	NOUN
ap-6074	99	15	-	-	PUNCT
ap-6074	99	16	squared	square	VERB
ap-6074	99	17	base	base	NOUN
ap-6074	99	18	intended	intend	VERB
ap-6074	99	19	for	for	ADP
ap-6074	99	20	clamping	clamp	VERB
ap-6074	99	21	the	the	DET
ap-6074	99	22	standard	standard	NOUN
ap-6074	99	23	on	on	ADP
ap-6074	99	24	the	the	DET
ap-6074	99	25	coordinate	coordinate	NOUN
ap-6074	99	26	measuring	measure	VERB
ap-6074	99	27	machine	machine	NOUN
ap-6074	99	28	(	(	PUNCT
ap-6074	99	29	depicted	depict	VERB
ap-6074	99	30	in	in	ADP
ap-6074	99	31	yellow	yellow	NOUN
ap-6074	99	32	in	in	ADP
ap-6074	99	33	fig	fig	NOUN
ap-6074	99	34	.	.	PUNCT
ap-6074	100	1	3	3	NUM
ap-6074	100	2	)	)	PUNCT
ap-6074	100	3	.	.	PUNCT
ap-6074	101	1	three	three	NUM
ap-6074	101	2	precise	precise	ADJ
ap-6074	101	3	reference	reference	NOUN
ap-6074	101	4	spheres	sphere	NOUN
ap-6074	101	5	(	(	PUNCT
ap-6074	101	6	red	red	PROPN
ap-6074	101	7	)	)	PUNCT
ap-6074	101	8	with	with	ADP
ap-6074	101	9	a	a	DET
ap-6074	101	10	radius	radius	NOUN
ap-6074	101	11	equal	equal	ADJ
ap-6074	101	12	to	to	ADP
ap-6074	101	13	8	8	NUM
ap-6074	101	14	mm	mm	NOUN
ap-6074	101	15	are	be	AUX
ap-6074	101	16	glued	glue	VERB
ap-6074	101	17	into	into	ADP
ap-6074	101	18	the	the	DET
ap-6074	101	19	three	three	NUM
ap-6074	101	20	of	of	ADP
ap-6074	101	21	the	the	DET
ap-6074	101	22	four	four	NUM
ap-6074	101	23	spherical	spherical	ADJ
ap-6074	101	24	holes	hole	NOUN
ap-6074	101	25	on	on	ADP
ap-6074	101	26	the	the	DET
ap-6074	101	27	standard	standard	NOUN
ap-6074	101	28	.	.	PUNCT
ap-6074	102	1	these	these	DET
ap-6074	102	2	spheres	sphere	NOUN
ap-6074	102	3	serve	serve	VERB
ap-6074	102	4	for	for	ADP
ap-6074	102	5	s	s	NOUN
ap-6074	102	6	workpiece	workpiece	NOUN
ap-6074	102	7	coordinate	coordinate	NOUN
ap-6074	102	8	system	system	NOUN
ap-6074	102	9	definition	definition	NOUN
ap-6074	102	10	.	.	PUNCT
ap-6074	103	1	the	the	DET
ap-6074	103	2	surface	surface	NOUN
ap-6074	103	3	of	of	ADP
ap-6074	103	4	hyperbolic	hyperbolic	ADJ
ap-6074	103	5	paraboloid	paraboloid	NOUN
ap-6074	103	6	(	(	PUNCT
ap-6074	103	7	green	green	ADJ
ap-6074	103	8	)	)	PUNCT
ap-6074	103	9	is	be	AUX
ap-6074	103	10	trimmed	trim	VERB
ap-6074	103	11	by	by	ADP
ap-6074	103	12	the	the	DET
ap-6074	103	13	cylindrical	cylindrical	ADJ
ap-6074	103	14	surface	surface	NOUN
ap-6074	103	15	(	(	PUNCT
ap-6074	103	16	blue	blue	NOUN
ap-6074	103	17	)	)	PUNCT
ap-6074	103	18	with	with	ADP
ap-6074	103	19	an	an	DET
ap-6074	103	20	axis	axis	NOUN
ap-6074	103	21	parallel	parallel	NOUN
ap-6074	103	22	to	to	ADP
ap-6074	103	23	z	z	NOUN
ap-6074	103	24	-	-	PUNCT
ap-6074	103	25	axis	axis	NOUN
ap-6074	103	26	and	and	CCONJ
ap-6074	103	27	radius	radius	NOUN
ap-6074	103	28	equal	equal	ADJ
ap-6074	103	29	to	to	ADP
ap-6074	103	30	40	40	NUM
ap-6074	103	31	mm	mm	NOUN
ap-6074	103	32	.	.	PUNCT
ap-6074	104	1	the	the	DET
ap-6074	104	2	common	common	ADJ
ap-6074	104	3	boundary	boundary	NOUN
ap-6074	104	4	between	between	ADP
ap-6074	104	5	the	the	DET
ap-6074	104	6	upper	upper	ADJ
ap-6074	104	7	squared	squared	ADJ
ap-6074	104	8	face	face	NOUN
ap-6074	104	9	and	and	CCONJ
ap-6074	104	10	the	the	DET
ap-6074	104	11	cylinder	cylinder	NOUN
ap-6074	104	12	is	be	AUX
ap-6074	104	13	filled	fill	VERB
ap-6074	104	14	with	with	ADP
ap-6074	104	15	a	a	DET
ap-6074	104	16	radius	radius	NOUN
ap-6074	104	17	of	of	ADP
ap-6074	104	18	4	4	NUM
ap-6074	104	19	mm	mm	NOUN
ap-6074	104	20	,	,	PUNCT
ap-6074	104	21	i.e.	i.e.	X
ap-6074	104	22	the	the	DET
ap-6074	104	23	transition	transition	NOUN
ap-6074	104	24	surface	surface	NOUN
ap-6074	104	25	is	be	AUX
ap-6074	104	26	created	create	VERB
ap-6074	104	27	by	by	ADP
ap-6074	104	28	a	a	DET
ap-6074	104	29	part	part	NOUN
ap-6074	104	30	of	of	ADP
ap-6074	104	31	torus	torus	NOUN
ap-6074	104	32	(	(	PUNCT
ap-6074	104	33	magenta	magenta	PROPN
ap-6074	104	34	)	)	PUNCT
ap-6074	104	35	.	.	PUNCT
ap-6074	105	1	the	the	DET
ap-6074	105	2	surface	surface	NOUN
ap-6074	105	3	of	of	ADP
ap-6074	105	4	hyperbolic	hyperbolic	ADJ
ap-6074	105	5	paraboloid	paraboloid	NOUN
ap-6074	105	6	used	use	VERB
ap-6074	105	7	in	in	ADP
ap-6074	105	8	the	the	DET
ap-6074	105	9	freeform	freeform	ADJ
ap-6074	105	10	standard	standard	ADJ
ap-6074	105	11	hyperbolic	hyperbolic	ADJ
ap-6074	105	12	paraboloid	paraboloid	NOUN
ap-6074	105	13	allows	allow	VERB
ap-6074	105	14	to	to	PART
ap-6074	105	15	measure	measure	VERB
ap-6074	105	16	the	the	DET
ap-6074	105	17	following	following	ADJ
ap-6074	105	18	curves	curve	NOUN
ap-6074	105	19	.	.	PUNCT
ap-6074	106	1	hyperbolas	hyperbola	NOUN
ap-6074	106	2	.	.	PUNCT
ap-6074	107	1	the	the	DET
ap-6074	107	2	hyperbolic	hyperbolic	ADJ
ap-6074	107	3	sections	section	NOUN
ap-6074	107	4	(	(	PUNCT
ap-6074	107	5	21	21	NUM
ap-6074	107	6	)	)	PUNCT
ap-6074	107	7	of	of	ADP
ap-6074	107	8	the	the	DET
ap-6074	107	9	hyperbolic	hyperbolic	ADJ
ap-6074	107	10	paraboloid	paraboloid	NOUN
ap-6074	107	11	by	by	ADP
ap-6074	107	12	planes	plane	NOUN
ap-6074	107	13	parallel	parallel	NOUN
ap-6074	107	14	with	with	ADP
ap-6074	107	15	(	(	PUNCT
ap-6074	107	16	x	x	NOUN
ap-6074	107	17	,	,	PUNCT
ap-6074	107	18	y	y	NOUN
ap-6074	107	19	)	)	PUNCT
ap-6074	107	20	plane	plane	NOUN
ap-6074	107	21	are	be	AUX
ap-6074	107	22	depicted	depict	VERB
ap-6074	107	23	in	in	ADP
ap-6074	107	24	fig	fig	NOUN
ap-6074	107	25	.	.	PUNCT
ap-6074	108	1	3	3	NUM
ap-6074	108	2	b	b	NOUN
ap-6074	108	3	)	)	PUNCT
ap-6074	108	4	.	.	PUNCT
ap-6074	109	1	straight	straight	ADJ
ap-6074	109	2	lines	line	NOUN
ap-6074	109	3	.	.	PUNCT
ap-6074	110	1	the	the	DET
ap-6074	110	2	linear	linear	PROPN
ap-6074	110	3	sections	section	NOUN
ap-6074	110	4	(	(	PUNCT
ap-6074	110	5	16	16	NUM
ap-6074	110	6	)	)	PUNCT
ap-6074	110	7	and	and	CCONJ
ap-6074	110	8	(	(	PUNCT
ap-6074	110	9	17	17	NUM
ap-6074	110	10	)	)	PUNCT
ap-6074	110	11	of	of	ADP
ap-6074	110	12	the	the	DET
ap-6074	110	13	hyperbolic	hyperbolic	ADJ
ap-6074	110	14	paraboloid	paraboloid	NOUN
ap-6074	110	15	by	by	ADP
ap-6074	110	16	planes	plane	NOUN
ap-6074	110	17	parallel	parallel	NOUN
ap-6074	110	18	with	with	ADP
ap-6074	110	19	(	(	PUNCT
ap-6074	110	20	x	x	NOUN
ap-6074	110	21	,	,	PUNCT
ap-6074	110	22	z	z	NOUN
ap-6074	110	23	)	)	PUNCT
ap-6074	110	24	and	and	CCONJ
ap-6074	110	25	(	(	PUNCT
ap-6074	110	26	y	y	PROPN
ap-6074	110	27	,	,	PUNCT
ap-6074	110	28	z	z	NOUN
ap-6074	110	29	)	)	PUNCT
ap-6074	110	30	planes	plane	NOUN
ap-6074	110	31	are	be	AUX
ap-6074	110	32	depicted	depict	VERB
ap-6074	110	33	in	in	ADP
ap-6074	110	34	fig	fig	NOUN
ap-6074	110	35	.	.	PUNCT
ap-6074	111	1	3	3	NUM
ap-6074	111	2	c	c	NOUN
ap-6074	111	3	)	)	PUNCT
ap-6074	111	4	and	and	CCONJ
ap-6074	111	5	fig	fig	NOUN
ap-6074	111	6	.	.	PUNCT
ap-6074	112	1	3	3	NUM
ap-6074	112	2	d	d	NOUN
ap-6074	112	3	)	)	PUNCT
ap-6074	112	4	in	in	ADP
ap-6074	112	5	the	the	DET
ap-6074	112	6	given	give	VERB
ap-6074	112	7	order	order	NOUN
ap-6074	112	8	.	.	PUNCT
ap-6074	113	1	parabolas	parabola	NOUN
ap-6074	113	2	.	.	PUNCT
ap-6074	114	1	the	the	DET
ap-6074	114	2	parabolic	parabolic	ADJ
ap-6074	114	3	sections	section	NOUN
ap-6074	114	4	(	(	PUNCT
ap-6074	114	5	19	19	NUM
ap-6074	114	6	)	)	PUNCT
ap-6074	114	7	and	and	CCONJ
ap-6074	114	8	(	(	PUNCT
ap-6074	114	9	20	20	NUM
ap-6074	114	10	)	)	PUNCT
ap-6074	114	11	of	of	ADP
ap-6074	114	12	the	the	DET
ap-6074	114	13	hyperbolic	hyperbolic	ADJ
ap-6074	114	14	paraboloid	paraboloid	NOUN
ap-6074	114	15	by	by	ADP
ap-6074	114	16	planes	plane	NOUN
ap-6074	114	17	parallel	parallel	NOUN
ap-6074	114	18	with	with	ADP
ap-6074	114	19	the	the	DET
ap-6074	114	20	plane	plane	NOUN
ap-6074	114	21	y	y	NOUN
ap-6074	114	22	=	=	PUNCT
ap-6074	114	23	x	x	PROPN
ap-6074	114	24	and	and	CCONJ
ap-6074	114	25	y	y	PROPN
ap-6074	114	26	=	=	NOUN
ap-6074	114	27	−x	−x	NOUN
ap-6074	114	28	are	be	AUX
ap-6074	114	29	depicted	depict	VERB
ap-6074	114	30	in	in	ADP
ap-6074	114	31	fig	fig	NOUN
ap-6074	114	32	.	.	PUNCT
ap-6074	115	1	3	3	NUM
ap-6074	115	2	e	e	NOUN
ap-6074	115	3	)	)	PUNCT
ap-6074	115	4	and	and	CCONJ
ap-6074	115	5	fig	fig	NOUN
ap-6074	115	6	.	.	PUNCT
ap-6074	116	1	3	3	NUM
ap-6074	116	2	f	f	X
ap-6074	116	3	)	)	PUNCT
ap-6074	116	4	in	in	ADP
ap-6074	116	5	the	the	DET
ap-6074	116	6	given	give	VERB
ap-6074	116	7	order	order	NOUN
ap-6074	116	8	.	.	PUNCT
ap-6074	117	1	2.2	2.2	NUM
ap-6074	117	2	.	.	PUNCT
ap-6074	117	3	physical	physical	ADJ
ap-6074	117	4	freeform	freeform	PROPN
ap-6074	117	5	standard	standard	ADJ
ap-6074	117	6	hyperbolic	hyperbolic	ADJ
ap-6074	117	7	paraboloid	paraboloid	NOUN
ap-6074	117	8	the	the	DET
ap-6074	117	9	standard	standard	NOUN
ap-6074	117	10	has	have	AUX
ap-6074	117	11	been	be	AUX
ap-6074	117	12	manufactured	manufacture	VERB
ap-6074	117	13	by	by	ADP
ap-6074	117	14	3	3	NUM
ap-6074	117	15	-	-	PUNCT
ap-6074	117	16	axis	axis	NOUN
ap-6074	117	17	milling	milling	NOUN
ap-6074	117	18	on	on	ADP
ap-6074	117	19	numerically	numerically	ADV
ap-6074	117	20	controlled	control	VERB
ap-6074	117	21	milling	milling	NOUN
ap-6074	117	22	machine	machine	NOUN
ap-6074	117	23	us20	us20	PROPN
ap-6074	117	24	by	by	ADP
ap-6074	117	25	high	high	ADJ
ap-6074	117	26	speed	speed	NOUN
ap-6074	117	27	cutting	cutting	NOUN
ap-6074	117	28	from	from	ADP
ap-6074	117	29	steel	steel	NOUN
ap-6074	117	30	en	en	ADP
ap-6074	117	31	x10crni18-9.the	x10crni18-9.the	DET
ap-6074	117	32	calibration	calibration	NOUN
ap-6074	117	33	of	of	ADP
ap-6074	117	34	the	the	DET
ap-6074	117	35	standard	standard	NOUN
ap-6074	117	36	on	on	ADP
ap-6074	117	37	the	the	DET
ap-6074	117	38	coordinate	coordinate	NOUN
ap-6074	117	39	measuring	measure	VERB
ap-6074	117	40	machine	machine	NOUN
ap-6074	117	41	is	be	AUX
ap-6074	117	42	shown	show	VERB
ap-6074	117	43	in	in	ADP
ap-6074	117	44	fig	fig	NOUN
ap-6074	117	45	.	.	PUNCT
ap-6074	118	1	4	4	NUM
ap-6074	118	2	.	.	X
ap-6074	118	3	3	3	NUM
ap-6074	118	4	.	.	NOUN
ap-6074	118	5	solid	solid	ADJ
ap-6074	118	6	of	of	ADP
ap-6074	118	7	hyperbolic	hyperbolic	ADJ
ap-6074	118	8	paraboloid	paraboloid	NOUN
ap-6074	118	9	the	the	DET
ap-6074	118	10	solid	solid	NOUN
ap-6074	118	11	of	of	ADP
ap-6074	118	12	the	the	DET
ap-6074	118	13	hyperbolic	hyperbolic	ADJ
ap-6074	118	14	paraboloid	paraboloid	NOUN
ap-6074	118	15	represents	represent	VERB
ap-6074	118	16	an	an	DET
ap-6074	118	17	extension	extension	NOUN
ap-6074	118	18	of	of	ADP
ap-6074	118	19	linear	linear	ADJ
ap-6074	118	20	interpolation	interpolation	NOUN
ap-6074	118	21	among	among	ADP
ap-6074	118	22	eight	eight	NUM
ap-6074	118	23	points	point	NOUN
ap-6074	118	24	in	in	ADP
ap-6074	118	25	three	three	NUM
ap-6074	118	26	-	-	PUNCT
ap-6074	118	27	dimensional	dimensional	ADJ
ap-6074	118	28	space	space	NOUN
ap-6074	118	29	.	.	PUNCT
ap-6074	119	1	considering	consider	VERB
ap-6074	119	2	the	the	DET
ap-6074	119	3	following	follow	VERB
ap-6074	119	4	figure	figure	NOUN
ap-6074	119	5	4	4	NUM
ap-6074	119	6	.	.	PUNCT
ap-6074	119	7	calibration	calibration	NOUN
ap-6074	119	8	of	of	ADP
ap-6074	119	9	freeform	freeform	ADJ
ap-6074	119	10	standard	standard	ADJ
ap-6074	119	11	hyperbolic	hyperbolic	ADJ
ap-6074	119	12	paraboloid	paraboloid	NOUN
ap-6074	119	13	on	on	ADP
ap-6074	119	14	coordinate	coordinate	NOUN
ap-6074	119	15	measurement	measurement	NOUN
ap-6074	119	16	machine	machine	NOUN
ap-6074	119	17	.	.	PUNCT
ap-6074	120	1	000	000	NUM
ap-6074	121	1	y	y	PROPN
ap-6074	121	2	z	z	PROPN
ap-6074	121	3	101	101	NUM
ap-6074	121	4	v	v	ADP
ap-6074	121	5	p	p	X
ap-6074	121	6	p	p	NOUN
ap-6074	121	7	111	111	NUM
ap-6074	121	8	p	p	NOUN
ap-6074	121	9	p	p	NOUN
ap-6074	121	10	010	010	NUM
ap-6074	121	11	001	001	NUM
ap-6074	121	12	p	p	NOUN
ap-6074	121	13	p	p	VERB
ap-6074	121	14	110	110	NUM
ap-6074	121	15	p	p	NOUN
ap-6074	121	16	x	x	X
ap-6074	121	17	p	p	NOUN
ap-6074	121	18	100	100	NUM
ap-6074	121	19	011	011	NUM
ap-6074	121	20	u	u	NOUN
ap-6074	121	21	t	t	NOUN
ap-6074	121	22	figure	figure	NOUN
ap-6074	121	23	5	5	NUM
ap-6074	121	24	.	.	NOUN
ap-6074	121	25	solid	solid	ADJ
ap-6074	121	26	of	of	ADP
ap-6074	121	27	hyperbolic	hyperbolic	ADJ
ap-6074	121	28	paraboloid	paraboloid	NOUN
ap-6074	121	29	.	.	PUNCT
ap-6074	122	1	control	control	NOUN
ap-6074	122	2	points	point	NOUN
ap-6074	123	1	p000	p000	PROPN
ap-6074	123	2	=	=	SYM
ap-6074	123	3	(	(	PUNCT
ap-6074	123	4	x000	x000	PROPN
ap-6074	123	5	,	,	PUNCT
ap-6074	123	6	y000	y000	NUM
ap-6074	123	7	,	,	PUNCT
ap-6074	123	8	z000	z000	NUM
ap-6074	123	9	)	)	PUNCT
ap-6074	123	10	,	,	PUNCT
ap-6074	123	11	p010	p010	PROPN
ap-6074	123	12	=	=	SYM
ap-6074	123	13	(	(	PUNCT
ap-6074	123	14	x010	x010	PROPN
ap-6074	123	15	,	,	PUNCT
ap-6074	123	16	y010	y010	PROPN
ap-6074	123	17	,	,	PUNCT
ap-6074	123	18	z010	z010	NUM
ap-6074	123	19	)	)	PUNCT
ap-6074	123	20	,	,	PUNCT
ap-6074	123	21	p100	p100	PROPN
ap-6074	123	22	=	=	PRON
ap-6074	123	23	(	(	PUNCT
ap-6074	123	24	x100	x100	PROPN
ap-6074	123	25	,	,	PUNCT
ap-6074	123	26	y100	y100	PROPN
ap-6074	123	27	,	,	PUNCT
ap-6074	123	28	z100	z100	NUM
ap-6074	123	29	)	)	PUNCT
ap-6074	123	30	,	,	PUNCT
ap-6074	123	31	p110	p110	PROPN
ap-6074	123	32	=	=	SYM
ap-6074	123	33	(	(	PUNCT
ap-6074	123	34	x110	x110	PROPN
ap-6074	123	35	,	,	PUNCT
ap-6074	123	36	y110	y110	PROPN
ap-6074	123	37	,	,	PUNCT
ap-6074	123	38	z110	z110	PROPN
ap-6074	123	39	)	)	PUNCT
ap-6074	123	40	,	,	PUNCT
ap-6074	123	41	p001	p001	PROPN
ap-6074	123	42	=	=	SYM
ap-6074	123	43	(	(	PUNCT
ap-6074	123	44	x001	x001	PROPN
ap-6074	123	45	,	,	PUNCT
ap-6074	123	46	y001	y001	PROPN
ap-6074	123	47	,	,	PUNCT
ap-6074	123	48	z001	z001	NUM
ap-6074	123	49	)	)	PUNCT
ap-6074	123	50	,	,	PUNCT
ap-6074	123	51	p011	p011	PROPN
ap-6074	123	52	=	=	SYM
ap-6074	123	53	(	(	PUNCT
ap-6074	123	54	x011	x011	PROPN
ap-6074	123	55	,	,	PUNCT
ap-6074	123	56	y011	y011	NUM
ap-6074	123	57	,	,	PUNCT
ap-6074	123	58	z011	z011	NUM
ap-6074	123	59	)	)	PUNCT
ap-6074	123	60	,	,	PUNCT
ap-6074	123	61	p101	p101	PROPN
ap-6074	123	62	=	=	PUNCT
ap-6074	123	63	(	(	PUNCT
ap-6074	123	64	x101	x101	PROPN
ap-6074	123	65	,	,	PUNCT
ap-6074	123	66	y101	y101	PROPN
ap-6074	123	67	,	,	PUNCT
ap-6074	123	68	z101	z101	PROPN
ap-6074	123	69	)	)	PUNCT
ap-6074	123	70	,	,	PUNCT
ap-6074	123	71	p111	p111	PROPN
ap-6074	123	72	=	=	SYM
ap-6074	123	73	(	(	PUNCT
ap-6074	123	74	x111	x111	PROPN
ap-6074	123	75	,	,	PUNCT
ap-6074	123	76	y111	y111	PROPN
ap-6074	123	77	,	,	PUNCT
ap-6074	123	78	z111	z111	PROPN
ap-6074	123	79	)	)	PUNCT
ap-6074	123	80	,	,	PUNCT
ap-6074	123	81	the	the	DET
ap-6074	123	82	trilinear	trilinear	ADJ
ap-6074	123	83	uniform	uniform	NOUN
ap-6074	123	84	clamped	clamp	VERB
ap-6074	123	85	b	b	NUM
ap-6074	123	86	-	-	PUNCT
ap-6074	123	87	spline	spline	NOUN
ap-6074	123	88	solid	solid	ADJ
ap-6074	123	89	defined	define	VERB
ap-6074	123	90	on	on	ADP
ap-6074	123	91	a	a	DET
ap-6074	123	92	normalised	normalise	VERB
ap-6074	123	93	domain	domain	NOUN
ap-6074	123	94	of	of	ADP
ap-6074	123	95	parameterization	parameterization	NOUN
ap-6074	123	96	(	(	PUNCT
ap-6074	123	97	u	u	NOUN
ap-6074	123	98	,	,	PUNCT
ap-6074	123	99	v	v	PROPN
ap-6074	123	100	,	,	PUNCT
ap-6074	123	101	t	t	PROPN
ap-6074	123	102	)	)	PUNCT
ap-6074	123	103	∈	∈	PROPN
ap-6074	124	1	[	[	X
ap-6074	124	2	0	0	NUM
ap-6074	124	3	,	,	PUNCT
ap-6074	124	4	1]3	1]3	NUM
ap-6074	124	5	is	be	AUX
ap-6074	124	6	given	give	VERB
ap-6074	124	7	by	by	ADP
ap-6074	124	8	b(u	b(u	PROPN
ap-6074	124	9	,	,	PUNCT
ap-6074	124	10	v	v	PROPN
ap-6074	124	11	,	,	PUNCT
ap-6074	124	12	t	t	PROPN
ap-6074	124	13	)	)	PUNCT
ap-6074	124	14	=	=	PUNCT
ap-6074	125	1	1∑	1∑	PROPN
ap-6074	125	2	i=0	i=0	PROPN
ap-6074	125	3	1∑	1∑	PROPN
ap-6074	125	4	j=0	j=0	PROPN
ap-6074	125	5	1∑	1∑	NUM
ap-6074	125	6	k=0	k=0	PROPN
ap-6074	125	7	ni,1(u)nj,1(v)nk1(t)pijk	ni,1(u)nj,1(v)nk1(t)pijk	PROPN
ap-6074	125	8	,	,	PUNCT
ap-6074	125	9	(	(	PUNCT
ap-6074	125	10	23	23	NUM
ap-6074	125	11	)	)	PUNCT
ap-6074	125	12	see	see	VERB
ap-6074	125	13	example	example	NOUN
ap-6074	125	14	in	in	ADP
ap-6074	125	15	fig	fig	NOUN
ap-6074	125	16	.	.	PUNCT
ap-6074	126	1	5	5	X
ap-6074	126	2	.	.	X
ap-6074	127	1	if	if	SCONJ
ap-6074	127	2	one	one	NUM
ap-6074	127	3	of	of	ADP
ap-6074	127	4	the	the	DET
ap-6074	127	5	parameters	parameter	NOUN
ap-6074	127	6	in	in	ADP
ap-6074	127	7	(	(	PUNCT
ap-6074	127	8	23	23	NUM
ap-6074	127	9	)	)	PUNCT
ap-6074	127	10	is	be	AUX
ap-6074	127	11	constant	constant	ADJ
ap-6074	127	12	,	,	PUNCT
ap-6074	127	13	a	a	DET
ap-6074	127	14	parametric	parametric	ADJ
ap-6074	127	15	surface	surface	NOUN
ap-6074	127	16	of	of	ADP
ap-6074	127	17	the	the	DET
ap-6074	127	18	solid	solid	ADJ
ap-6074	127	19	is	be	AUX
ap-6074	127	20	obtained	obtain	VERB
ap-6074	127	21	.	.	PUNCT
ap-6074	128	1	for	for	ADP
ap-6074	128	2	u	u	NOUN
ap-6074	128	3	=	=	SYM
ap-6074	128	4	α	α	PROPN
ap-6074	128	5	,	,	PUNCT
ap-6074	128	6	v	v	NOUN
ap-6074	128	7	=	=	SYM
ap-6074	128	8	β	β	X
ap-6074	128	9	and	and	CCONJ
ap-6074	128	10	t	t	PROPN
ap-6074	128	11	=	=	SYM
ap-6074	128	12	γ	γ	X
ap-6074	128	13	,	,	PUNCT
ap-6074	128	14	α	α	PROPN
ap-6074	128	15	,	,	PUNCT
ap-6074	128	16	β	β	X
ap-6074	128	17	,	,	PUNCT
ap-6074	128	18	γ	γ	PROPN
ap-6074	128	19	∈	∈	PROPN
ap-6074	129	1	[	[	X
ap-6074	129	2	0	0	NUM
ap-6074	129	3	,	,	PUNCT
ap-6074	129	4	1	1	NUM
ap-6074	129	5	]	]	PUNCT
ap-6074	129	6	,	,	PUNCT
ap-6074	129	7	there	there	PRON
ap-6074	129	8	are	be	VERB
ap-6074	129	9	three	three	NUM
ap-6074	129	10	systems	system	NOUN
ap-6074	129	11	of	of	ADP
ap-6074	129	12	parametric	parametric	ADJ
ap-6074	129	13	surfaces	surface	NOUN
ap-6074	129	14	b(u	b(u	PROPN
ap-6074	129	15	,	,	PUNCT
ap-6074	129	16	v	v	NOUN
ap-6074	129	17	,	,	PUNCT
ap-6074	129	18	γ	γ	NOUN
ap-6074	129	19	)	)	PUNCT
ap-6074	129	20	=	=	PUNCT
ap-6074	130	1	1∑	1∑	PROPN
ap-6074	130	2	i=0	i=0	PROPN
ap-6074	130	3	1∑	1∑	PROPN
ap-6074	130	4	j=0	j=0	PROPN
ap-6074	130	5	1∑	1∑	NUM
ap-6074	130	6	k=0	k=0	PROPN
ap-6074	130	7	ni,1(u)nj,1(v)nk,1(γ)pijk	ni,1(u)nj,1(v)nk,1(γ)pijk	PROPN
ap-6074	130	8	,	,	PUNCT
ap-6074	130	9	103	103	NUM
ap-6074	130	10	ivana	ivana	PROPN
ap-6074	130	11	linkeová	linkeová	PROPN
ap-6074	130	12	,	,	PUNCT
ap-6074	130	13	vít	vít	PROPN
ap-6074	130	14	zelený	zelený	PROPN
ap-6074	130	15	acta	acta	PROPN
ap-6074	130	16	polytechnica	polytechnica	PROPN
ap-6074	130	17	figure	figure	NOUN
ap-6074	130	18	6	6	NUM
ap-6074	130	19	.	.	PUNCT
ap-6074	130	20	parametric	parametric	ADJ
ap-6074	130	21	surfaces	surface	NOUN
ap-6074	130	22	in	in	ADP
ap-6074	130	23	solid	solid	ADJ
ap-6074	130	24	of	of	ADP
ap-6074	130	25	hyperbolic	hyperbolic	ADJ
ap-6074	130	26	paraboloid	paraboloid	NOUN
ap-6074	130	27	.	.	PUNCT
ap-6074	131	1	b(u	b(u	PROPN
ap-6074	131	2	,	,	PUNCT
ap-6074	131	3	β	β	X
ap-6074	131	4	,	,	PUNCT
ap-6074	131	5	t	t	PROPN
ap-6074	131	6	)	)	PUNCT
ap-6074	131	7	=	=	PUNCT
ap-6074	132	1	1∑	1∑	PROPN
ap-6074	132	2	i=0	i=0	PROPN
ap-6074	132	3	1∑	1∑	PROPN
ap-6074	132	4	j=0	j=0	PROPN
ap-6074	132	5	1∑	1∑	NUM
ap-6074	132	6	k=0	k=0	PROPN
ap-6074	132	7	ni,1(u)nj,1(β)nk,1(t)pijk	ni,1(u)nj,1(β)nk,1(t)pijk	PROPN
ap-6074	132	8	,	,	PUNCT
ap-6074	132	9	b(α	b(α	PROPN
ap-6074	132	10	,	,	PUNCT
ap-6074	132	11	v	v	NOUN
ap-6074	132	12	,	,	PUNCT
ap-6074	132	13	t	t	PROPN
ap-6074	132	14	)	)	PUNCT
ap-6074	132	15	=	=	PUNCT
ap-6074	133	1	1∑	1∑	PROPN
ap-6074	133	2	i=0	i=0	PROPN
ap-6074	133	3	1∑	1∑	PROPN
ap-6074	133	4	j=0	j=0	PROPN
ap-6074	133	5	1∑	1∑	NUM
ap-6074	133	6	k=0	k=0	PROPN
ap-6074	133	7	ni,1(α)nj,1(v)nk,1(t)pijk	ni,1(α)nj,1(v)nk,1(t)pijk	PROPN
ap-6074	133	8	.	.	PUNCT
ap-6074	134	1	obviously	obviously	ADV
ap-6074	134	2	,	,	PUNCT
ap-6074	134	3	all	all	DET
ap-6074	134	4	three	three	NUM
ap-6074	134	5	systems	system	NOUN
ap-6074	134	6	of	of	ADP
ap-6074	134	7	parametric	parametric	ADJ
ap-6074	134	8	surfaces	surface	NOUN
ap-6074	134	9	of	of	ADP
ap-6074	134	10	the	the	DET
ap-6074	134	11	solid	solid	ADJ
ap-6074	134	12	are	be	AUX
ap-6074	134	13	created	create	VERB
ap-6074	134	14	by	by	ADP
ap-6074	134	15	surfaces	surface	NOUN
ap-6074	134	16	of	of	ADP
ap-6074	134	17	hyperbolic	hyperbolic	ADJ
ap-6074	134	18	paraboloid	paraboloid	NOUN
ap-6074	134	19	.	.	PUNCT
ap-6074	135	1	consequently	consequently	ADV
ap-6074	135	2	,	,	PUNCT
ap-6074	135	3	the	the	DET
ap-6074	135	4	parametric	parametric	ADJ
ap-6074	135	5	curves	curve	NOUN
ap-6074	135	6	of	of	ADP
ap-6074	135	7	the	the	DET
ap-6074	135	8	solid	solid	ADJ
ap-6074	135	9	are	be	AUX
ap-6074	135	10	straight	straight	ADJ
ap-6074	135	11	lines	line	NOUN
ap-6074	135	12	(	(	PUNCT
ap-6074	135	13	fig	fig	NOUN
ap-6074	135	14	.	.	PUNCT
ap-6074	136	1	6	6	NUM
ap-6074	136	2	)	)	PUNCT
ap-6074	136	3	.	.	PUNCT
ap-6074	137	1	3.1	3.1	NUM
ap-6074	137	2	.	.	PUNCT
ap-6074	138	1	spatial	spatial	ADJ
ap-6074	138	2	hyperbolic	hyperbolic	ADJ
ap-6074	138	3	paraboloid	paraboloid	ADJ
ap-6074	138	4	standard	standard	PROPN
ap-6074	138	5	spatial	spatial	ADJ
ap-6074	138	6	hyperbolic	hyperbolic	ADJ
ap-6074	138	7	paraboloid	paraboloid	ADJ
ap-6074	138	8	standard	standard	NOUN
ap-6074	138	9	with	with	ADP
ap-6074	138	10	cavities	cavity	NOUN
ap-6074	138	11	has	have	AUX
ap-6074	138	12	been	be	AUX
ap-6074	138	13	developed	develop	VERB
ap-6074	138	14	so	so	SCONJ
ap-6074	138	15	that	that	SCONJ
ap-6074	138	16	the	the	DET
ap-6074	138	17	standard	standard	NOUN
ap-6074	138	18	can	can	AUX
ap-6074	138	19	be	be	AUX
ap-6074	138	20	calibrated	calibrate	VERB
ap-6074	138	21	by	by	ADP
ap-6074	138	22	the	the	DET
ap-6074	138	23	point	point	NOUN
ap-6074	138	24	-	-	PUNCT
ap-6074	138	25	to	to	ADP
ap-6074	138	26	-	-	PUNCT
ap-6074	138	27	point	point	NOUN
ap-6074	138	28	tactile	tactile	ADJ
ap-6074	138	29	measurement	measurement	NOUN
ap-6074	138	30	and	and	CCONJ
ap-6074	138	31	then	then	ADV
ap-6074	138	32	measured	measure	VERB
ap-6074	138	33	by	by	ADP
ap-6074	138	34	means	mean	NOUN
ap-6074	138	35	of	of	ADP
ap-6074	138	36	various	various	ADJ
ap-6074	138	37	metrology	metrology	NOUN
ap-6074	138	38	technologies	technology	NOUN
ap-6074	138	39	(	(	PUNCT
ap-6074	138	40	tactile	tactile	ADJ
ap-6074	138	41	scanning	scanning	NOUN
ap-6074	138	42	,	,	PUNCT
ap-6074	138	43	optical	optical	ADJ
ap-6074	138	44	scanning	scanning	NOUN
ap-6074	138	45	,	,	PUNCT
ap-6074	138	46	computer	computer	NOUN
ap-6074	138	47	tomography	tomography	NOUN
ap-6074	138	48	,	,	PUNCT
ap-6074	138	49	etc	etc	X
ap-6074	138	50	.	.	X
ap-6074	138	51	)	)	PUNCT
ap-6074	138	52	.	.	PUNCT
ap-6074	139	1	the	the	DET
ap-6074	139	2	solid	solid	NOUN
ap-6074	139	3	of	of	ADP
ap-6074	139	4	hyperbolic	hyperbolic	ADJ
ap-6074	139	5	paraboloid	paraboloid	NOUN
ap-6074	139	6	(	(	PUNCT
ap-6074	139	7	23	23	NUM
ap-6074	139	8	)	)	PUNCT
ap-6074	139	9	represents	represent	VERB
ap-6074	139	10	the	the	DET
ap-6074	139	11	freeform	freeform	ADJ
ap-6074	139	12	functional	functional	ADJ
ap-6074	139	13	figure	figure	NOUN
ap-6074	139	14	on	on	ADP
ap-6074	139	15	this	this	DET
ap-6074	139	16	standard	standard	NOUN
ap-6074	139	17	,	,	PUNCT
ap-6074	139	18	see	see	VERB
ap-6074	139	19	fig	fig	NOUN
ap-6074	139	20	.	.	PUNCT
ap-6074	140	1	7	7	NUM
ap-6074	140	2	,	,	PUNCT
ap-6074	140	3	where	where	SCONJ
ap-6074	140	4	the	the	DET
ap-6074	140	5	cad	cad	PROPN
ap-6074	140	6	model	model	NOUN
ap-6074	140	7	of	of	ADP
ap-6074	140	8	the	the	DET
ap-6074	140	9	standard	standard	NOUN
ap-6074	140	10	is	be	AUX
ap-6074	140	11	depicted	depict	VERB
ap-6074	140	12	.	.	PUNCT
ap-6074	141	1	the	the	DET
ap-6074	141	2	standard	standard	NOUN
ap-6074	141	3	of	of	ADP
ap-6074	141	4	dimensions	dimension	NOUN
ap-6074	141	5	100×	100×	PROPN
ap-6074	142	1	100×	100×	PROPN
ap-6074	142	2	100	100	NUM
ap-6074	142	3	mm	mm	NOUN
ap-6074	142	4	consists	consist	VERB
ap-6074	142	5	of	of	ADP
ap-6074	142	6	squared	square	VERB
ap-6074	142	7	box	box	NOUN
ap-6074	142	8	base	base	NOUN
ap-6074	142	9	intended	intend	VERB
ap-6074	142	10	for	for	ADP
ap-6074	142	11	clamping	clamp	VERB
ap-6074	142	12	the	the	DET
ap-6074	142	13	standard	standard	NOUN
ap-6074	142	14	to	to	ADP
ap-6074	142	15	the	the	DET
ap-6074	142	16	coordinate	coordinate	NOUN
ap-6074	142	17	measuring	measure	VERB
ap-6074	142	18	machine	machine	NOUN
ap-6074	142	19	.	.	PUNCT
ap-6074	143	1	the	the	DET
ap-6074	143	2	centre	centre	NOUN
ap-6074	143	3	upper	upper	ADJ
ap-6074	143	4	squared	square	VERB
ap-6074	143	5	face	face	NOUN
ap-6074	143	6	of	of	ADP
ap-6074	143	7	the	the	DET
ap-6074	143	8	base	base	NOUN
ap-6074	143	9	lies	lie	VERB
ap-6074	143	10	at	at	ADP
ap-6074	143	11	the	the	DET
ap-6074	143	12	origin	origin	NOUN
ap-6074	143	13	of	of	ADP
ap-6074	143	14	the	the	DET
ap-6074	143	15	coordinate	coordinate	NOUN
ap-6074	143	16	system	system	NOUN
ap-6074	143	17	.	.	PUNCT
ap-6074	144	1	freeform	freeform	ADJ
ap-6074	144	2	faces	face	NOUN
ap-6074	144	3	of	of	ADP
ap-6074	144	4	the	the	DET
ap-6074	144	5	standard	standard	NOUN
ap-6074	144	6	are	be	AUX
ap-6074	144	7	the	the	DET
ap-6074	144	8	boundary	boundary	ADJ
ap-6074	144	9	surfaces	surface	NOUN
ap-6074	144	10	of	of	ADP
ap-6074	144	11	the	the	DET
ap-6074	144	12	solid	solid	NOUN
ap-6074	144	13	of	of	ADP
ap-6074	144	14	hyperbolic	hyperbolic	ADJ
ap-6074	144	15	paraboloid	paraboloid	NOUN
ap-6074	144	16	.	.	PUNCT
ap-6074	145	1	the	the	DET
ap-6074	145	2	cavity	cavity	NOUN
ap-6074	145	3	of	of	ADP
ap-6074	145	4	the	the	DET
ap-6074	145	5	standard	standard	NOUN
ap-6074	145	6	is	be	AUX
ap-6074	145	7	created	create	VERB
ap-6074	145	8	by	by	ADP
ap-6074	145	9	non	non	ADJ
ap-6074	145	10	-	-	ADJ
ap-6074	145	11	coaxial	coaxial	ADJ
ap-6074	145	12	cylindrical	cylindrical	ADJ
ap-6074	145	13	holes	hole	NOUN
ap-6074	145	14	serving	serve	VERB
ap-6074	145	15	for	for	ADP
ap-6074	145	16	orientation	orientation	NOUN
ap-6074	145	17	when	when	SCONJ
ap-6074	145	18	measuring	measure	VERB
ap-6074	145	19	the	the	DET
ap-6074	145	20	standard	standard	NOUN
ap-6074	145	21	by	by	ADP
ap-6074	145	22	a	a	DET
ap-6074	145	23	computer	computer	NOUN
ap-6074	145	24	tomography	tomography	NOUN
ap-6074	145	25	technology	technology	NOUN
ap-6074	145	26	.	.	PUNCT
ap-6074	146	1	3.1.1	3.1.1	X
ap-6074	146	2	.	.	PUNCT
ap-6074	147	1	physical	physical	ADJ
ap-6074	147	2	spatial	spatial	ADJ
ap-6074	147	3	hyperbolic	hyperbolic	ADJ
ap-6074	147	4	paraboloid	paraboloid	NOUN
ap-6074	147	5	standard	standard	NOUN
ap-6074	147	6	the	the	DET
ap-6074	147	7	standard	standard	NOUN
ap-6074	147	8	has	have	AUX
ap-6074	147	9	been	be	AUX
ap-6074	147	10	manufactured	manufacture	VERB
ap-6074	147	11	from	from	ADP
ap-6074	147	12	aluminium	aluminium	NOUN
ap-6074	147	13	alloy	alloy	NOUN
ap-6074	147	14	certal	certal	NOUN
ap-6074	147	15	en	en	ADP
ap-6074	147	16	aw	aw	INTJ
ap-6074	147	17	7022	7022	NUM
ap-6074	147	18	[	[	X
ap-6074	147	19	alzn5mg3cu	alzn5mg3cu	X
ap-6074	147	20	]	]	PUNCT
ap-6074	147	21	by	by	ADP
ap-6074	147	22	numerically	numerically	ADV
ap-6074	147	23	controlled	control	VERB
ap-6074	147	24	machining	machining	NOUN
ap-6074	147	25	and	and	CCONJ
ap-6074	147	26	polished	polished	ADJ
ap-6074	147	27	.	.	PUNCT
ap-6074	148	1	the	the	DET
ap-6074	148	2	calibration	calibration	NOUN
ap-6074	148	3	of	of	ADP
ap-6074	148	4	the	the	DET
ap-6074	148	5	standard	standard	NOUN
ap-6074	148	6	on	on	ADP
ap-6074	148	7	coordinate	coordinate	NOUN
ap-6074	148	8	measuring	measure	VERB
ap-6074	148	9	machine	machine	NOUN
ap-6074	148	10	is	be	AUX
ap-6074	148	11	shown	show	VERB
ap-6074	148	12	in	in	ADP
ap-6074	148	13	fig	fig	NOUN
ap-6074	148	14	.	.	PUNCT
ap-6074	149	1	8	8	NUM
ap-6074	149	2	figure	figure	NOUN
ap-6074	149	3	7	7	NUM
ap-6074	149	4	.	.	PUNCT
ap-6074	149	5	cad	cad	PROPN
ap-6074	149	6	model	model	NOUN
ap-6074	149	7	of	of	ADP
ap-6074	149	8	spatial	spatial	ADJ
ap-6074	149	9	hyperbolic	hyperbolic	ADJ
ap-6074	149	10	paraboloid	paraboloid	ADJ
ap-6074	149	11	standar	standar	NOUN
ap-6074	149	12	figure	figure	NOUN
ap-6074	149	13	8	8	NUM
ap-6074	149	14	.	.	PUNCT
ap-6074	150	1	calibration	calibration	NOUN
ap-6074	150	2	of	of	ADP
ap-6074	150	3	spatial	spatial	ADJ
ap-6074	150	4	hyperbolic	hyperbolic	ADJ
ap-6074	150	5	paraboloid	paraboloid	ADJ
ap-6074	150	6	standard	standard	NOUN
ap-6074	150	7	.	.	PUNCT
ap-6074	151	1	4	4	X
ap-6074	151	2	.	.	NUM
ap-6074	151	3	surfaces	surface	NOUN
ap-6074	151	4	generated	generate	VERB
ap-6074	151	5	by	by	ADP
ap-6074	151	6	motion	motion	NOUN
ap-6074	151	7	of	of	ADP
ap-6074	151	8	a	a	DET
ap-6074	151	9	circle	circle	NOUN
ap-6074	151	10	involute	involute	ADJ
ap-6074	151	11	involute	involute	ADJ
ap-6074	151	12	e	e	NOUN
ap-6074	151	13	of	of	ADP
ap-6074	151	14	a	a	DET
ap-6074	151	15	curve	curve	NOUN
ap-6074	151	16	c	c	NOUN
ap-6074	151	17	is	be	AUX
ap-6074	151	18	the	the	DET
ap-6074	151	19	trajectory	trajectory	NOUN
ap-6074	151	20	of	of	ADP
ap-6074	151	21	a	a	DET
ap-6074	151	22	free	free	ADJ
ap-6074	151	23	endpoint	endpoint	NOUN
ap-6074	151	24	of	of	ADP
ap-6074	151	25	the	the	DET
ap-6074	151	26	tangent	tangent	ADJ
ap-6074	151	27	line	line	NOUN
ap-6074	151	28	of	of	ADP
ap-6074	151	29	the	the	DET
ap-6074	151	30	curve	curve	NOUN
ap-6074	151	31	c	c	AUX
ap-6074	151	32	rolling	roll	VERB
ap-6074	151	33	along	along	ADP
ap-6074	151	34	the	the	DET
ap-6074	151	35	curve	curve	NOUN
ap-6074	151	36	c.	c.	NOUN
ap-6074	151	37	in	in	ADP
ap-6074	151	38	other	other	ADJ
ap-6074	151	39	words	word	NOUN
ap-6074	151	40	,	,	PUNCT
ap-6074	151	41	the	the	DET
ap-6074	151	42	normal	normal	ADJ
ap-6074	151	43	line	line	NOUN
ap-6074	151	44	at	at	ADP
ap-6074	151	45	each	each	DET
ap-6074	151	46	point	point	NOUN
ap-6074	151	47	of	of	ADP
ap-6074	151	48	the	the	DET
ap-6074	151	49	involute	involute	ADJ
ap-6074	151	50	e	e	NOUN
ap-6074	151	51	is	be	AUX
ap-6074	151	52	the	the	DET
ap-6074	151	53	tangent	tangent	ADJ
ap-6074	151	54	line	line	NOUN
ap-6074	151	55	to	to	ADP
ap-6074	151	56	the	the	DET
ap-6074	151	57	curve	curve	NOUN
ap-6074	151	58	c.	c.	PROPN
ap-6074	151	59	in	in	ADP
ap-6074	151	60	technical	technical	ADJ
ap-6074	151	61	practice	practice	NOUN
ap-6074	151	62	,	,	PUNCT
ap-6074	151	63	a	a	DET
ap-6074	151	64	circle	circle	NOUN
ap-6074	151	65	involute	involute	NOUN
ap-6074	151	66	(	(	PUNCT
ap-6074	151	67	hereinafter	hereinafter	NOUN
ap-6074	151	68	referred	refer	VERB
ap-6074	151	69	to	to	ADP
ap-6074	151	70	as	as	ADP
ap-6074	151	71	the	the	DET
ap-6074	151	72	"	"	PUNCT
ap-6074	151	73	involute	involute	NOUN
ap-6074	151	74	"	"	PUNCT
ap-6074	151	75	)	)	PUNCT
ap-6074	151	76	,	,	PUNCT
ap-6074	151	77	see	see	VERB
ap-6074	151	78	fig	fig	NOUN
ap-6074	151	79	.	.	PUNCT
ap-6074	152	1	9	9	NUM
ap-6074	152	2	,	,	PUNCT
ap-6074	152	3	has	have	VERB
ap-6074	152	4	a	a	DET
ap-6074	152	5	special	special	ADJ
ap-6074	152	6	meaning	meaning	NOUN
ap-6074	152	7	.	.	PUNCT
ap-6074	153	1	it	it	PRON
ap-6074	153	2	is	be	AUX
ap-6074	153	3	well	well	ADV
ap-6074	153	4	known	know	VERB
ap-6074	153	5	that	that	SCONJ
ap-6074	153	6	a	a	DET
ap-6074	153	7	flank	flank	NOUN
ap-6074	153	8	surface	surface	NOUN
ap-6074	153	9	of	of	ADP
ap-6074	153	10	involute	involute	ADJ
ap-6074	153	11	spur	spur	NOUN
ap-6074	153	12	gears	gear	NOUN
ap-6074	153	13	is	be	AUX
ap-6074	153	14	an	an	DET
ap-6074	153	15	involute	involute	ADJ
ap-6074	153	16	ruled	rule	VERB
ap-6074	153	17	surface	surface	NOUN
ap-6074	153	18	(	(	PUNCT
ap-6074	153	19	i.e.	i.e.	X
ap-6074	153	20	,	,	PUNCT
ap-6074	153	21	the	the	DET
ap-6074	153	22	surface	surface	NOUN
ap-6074	153	23	generated	generate	VERB
ap-6074	153	24	by	by	ADP
ap-6074	153	25	a	a	DET
ap-6074	153	26	translation	translation	NOUN
ap-6074	153	27	of	of	ADP
ap-6074	153	28	the	the	DET
ap-6074	153	29	involute	involute	NOUN
ap-6074	153	30	along	along	ADP
ap-6074	153	31	a	a	DET
ap-6074	153	32	straight	straight	ADJ
ap-6074	153	33	line	line	NOUN
ap-6074	153	34	)	)	PUNCT
ap-6074	153	35	and	and	CCONJ
ap-6074	153	36	a	a	DET
ap-6074	153	37	flank	flank	NOUN
ap-6074	153	38	surface	surface	NOUN
ap-6074	153	39	of	of	ADP
ap-6074	153	40	involute	involute	ADJ
ap-6074	153	41	helical	helical	ADJ
ap-6074	153	42	gears	gear	NOUN
ap-6074	153	43	is	be	AUX
ap-6074	153	44	an	an	DET
ap-6074	153	45	involute	involute	ADJ
ap-6074	153	46	helicoidal	helicoidal	ADJ
ap-6074	153	47	surface	surface	NOUN
ap-6074	153	48	(	(	PUNCT
ap-6074	153	49	i.e.	i.e.	X
ap-6074	153	50	,	,	PUNCT
ap-6074	153	51	the	the	DET
ap-6074	153	52	surface	surface	NOUN
ap-6074	153	53	generated	generate	VERB
ap-6074	153	54	by	by	ADP
ap-6074	153	55	screw	screw	VERB
ap-6074	153	56	motion	motion	NOUN
ap-6074	153	57	of	of	ADP
ap-6074	153	58	the	the	DET
ap-6074	153	59	involute	involute	NOUN
ap-6074	153	60	)	)	PUNCT
ap-6074	153	61	.	.	PUNCT
ap-6074	154	1	what	what	PRON
ap-6074	154	2	is	be	AUX
ap-6074	154	3	not	not	PART
ap-6074	154	4	so	so	ADV
ap-6074	154	5	obvious	obvious	ADJ
ap-6074	154	6	is	be	AUX
ap-6074	154	7	that	that	SCONJ
ap-6074	154	8	the	the	DET
ap-6074	154	9	involute	involute	ADJ
ap-6074	154	10	helicoidal	helicoidal	ADJ
ap-6074	154	11	surface	surface	NOUN
ap-6074	154	12	and	and	CCONJ
ap-6074	154	13	tangent	tangent	NOUN
ap-6074	154	14	surface	surface	NOUN
ap-6074	154	15	of	of	ADP
ap-6074	154	16	the	the	DET
ap-6074	154	17	helix	helix	NOUN
ap-6074	154	18	have	have	VERB
ap-6074	154	19	the	the	DET
ap-6074	154	20	same	same	ADJ
ap-6074	154	21	shape	shape	NOUN
ap-6074	154	22	(	(	PUNCT
ap-6074	154	23	if	if	SCONJ
ap-6074	154	24	certain	certain	ADJ
ap-6074	154	25	geometrical	geometrical	ADJ
ap-6074	154	26	conditions	condition	NOUN
ap-6074	154	27	are	be	AUX
ap-6074	154	28	met	meet	VERB
ap-6074	154	29	)	)	PUNCT
ap-6074	154	30	.	.	PUNCT
ap-6074	155	1	consequently	consequently	ADV
ap-6074	155	2	,	,	PUNCT
ap-6074	155	3	the	the	DET
ap-6074	155	4	flank	flank	NOUN
ap-6074	155	5	surface	surface	NOUN
ap-6074	155	6	of	of	ADP
ap-6074	155	7	involute	involute	ADJ
ap-6074	155	8	helical	helical	ADJ
ap-6074	155	9	gears	gear	NOUN
ap-6074	155	10	104	104	NUM
ap-6074	155	11	vol	vol	NOUN
ap-6074	155	12	.	.	PUNCT
ap-6074	156	1	61	61	NUM
ap-6074	156	2	special	special	ADJ
ap-6074	156	3	issue/2021	issue/2021	NOUN
ap-6074	156	4	application	application	NOUN
ap-6074	156	5	of	of	ADP
ap-6074	156	6	ruled	rule	VERB
ap-6074	156	7	surfaces	surface	NOUN
ap-6074	156	8	in	in	ADP
ap-6074	156	9	freeform	freeform	NOUN
ap-6074	156	10	and	and	CCONJ
ap-6074	156	11	gear	gear	NOUN
ap-6074	156	12	metrology	metrology	NOUN
ap-6074	156	13	c	c	PROPN
ap-6074	156	14	e	e	NOUN
ap-6074	156	15	figure	figure	NOUN
ap-6074	156	16	9	9	NUM
ap-6074	156	17	.	.	PUNCT
ap-6074	156	18	circle	circle	NOUN
ap-6074	156	19	involute	involute	NOUN
ap-6074	156	20	.	.	PUNCT
ap-6074	157	1	can	can	AUX
ap-6074	157	2	be	be	AUX
ap-6074	157	3	expressed	express	VERB
ap-6074	157	4	as	as	ADP
ap-6074	157	5	a	a	DET
ap-6074	157	6	tangent	tangent	ADJ
ap-6074	157	7	surface	surface	NOUN
ap-6074	157	8	of	of	ADP
ap-6074	157	9	the	the	DET
ap-6074	157	10	base	base	NOUN
ap-6074	157	11	helix	helix	NOUN
ap-6074	157	12	,	,	PUNCT
ap-6074	157	13	which	which	PRON
ap-6074	157	14	is	be	AUX
ap-6074	157	15	mathematically	mathematically	ADV
ap-6074	157	16	simpler	simple	ADJ
ap-6074	157	17	than	than	ADP
ap-6074	157	18	an	an	DET
ap-6074	157	19	expression	expression	NOUN
ap-6074	157	20	of	of	ADP
ap-6074	157	21	an	an	DET
ap-6074	157	22	involute	involute	ADJ
ap-6074	157	23	helicoidal	helicoidal	ADJ
ap-6074	157	24	surface	surface	NOUN
ap-6074	158	1	[	[	X
ap-6074	158	2	6	6	NUM
ap-6074	158	3	]	]	PUNCT
ap-6074	158	4	.	.	PUNCT
ap-6074	159	1	in	in	ADP
ap-6074	159	2	this	this	DET
ap-6074	159	3	section	section	NOUN
ap-6074	159	4	,	,	PUNCT
ap-6074	159	5	the	the	DET
ap-6074	159	6	helix	helix	NOUN
ap-6074	159	7	,	,	PUNCT
ap-6074	159	8	as	as	ADP
ap-6074	159	9	a	a	DET
ap-6074	159	10	trajectory	trajectory	NOUN
ap-6074	159	11	of	of	ADP
ap-6074	159	12	a	a	DET
ap-6074	159	13	point	point	NOUN
ap-6074	159	14	under	under	ADP
ap-6074	159	15	screw	screw	ADJ
ap-6074	159	16	motion	motion	NOUN
ap-6074	159	17	,	,	PUNCT
ap-6074	159	18	is	be	AUX
ap-6074	159	19	described	describe	VERB
ap-6074	159	20	firstly	firstly	ADV
ap-6074	159	21	.	.	PUNCT
ap-6074	160	1	after	after	ADP
ap-6074	160	2	that	that	PRON
ap-6074	160	3	,	,	PUNCT
ap-6074	160	4	the	the	DET
ap-6074	160	5	tangent	tangent	ADJ
ap-6074	160	6	surface	surface	NOUN
ap-6074	160	7	of	of	ADP
ap-6074	160	8	the	the	DET
ap-6074	160	9	helix	helix	NOUN
ap-6074	160	10	,	,	PUNCT
ap-6074	160	11	involute	involute	ADJ
ap-6074	160	12	helicoidal	helicoidal	ADJ
ap-6074	160	13	surface	surface	NOUN
ap-6074	160	14	and	and	CCONJ
ap-6074	160	15	ruled	rule	VERB
ap-6074	160	16	surface	surface	NOUN
ap-6074	160	17	are	be	AUX
ap-6074	160	18	mentioned	mention	VERB
ap-6074	160	19	together	together	ADV
ap-6074	160	20	with	with	ADP
ap-6074	160	21	their	their	PRON
ap-6074	160	22	properties	property	NOUN
ap-6074	160	23	.	.	PUNCT
ap-6074	161	1	finally	finally	ADV
ap-6074	161	2	,	,	PUNCT
ap-6074	161	3	an	an	DET
ap-6074	161	4	example	example	NOUN
ap-6074	161	5	of	of	ADP
ap-6074	161	6	an	an	DET
ap-6074	161	7	application	application	NOUN
ap-6074	161	8	of	of	ADP
ap-6074	161	9	these	these	DET
ap-6074	161	10	surfaces	surface	NOUN
ap-6074	161	11	in	in	ADP
ap-6074	161	12	metrology	metrology	NOUN
ap-6074	161	13	practice	practice	NOUN
ap-6074	161	14	is	be	AUX
ap-6074	161	15	given	give	VERB
ap-6074	161	16	.	.	PUNCT
ap-6074	162	1	4.1	4.1	NUM
ap-6074	162	2	.	.	PUNCT
ap-6074	162	3	tangent	tangent	PROPN
ap-6074	162	4	surface	surface	NOUN
ap-6074	162	5	of	of	ADP
ap-6074	162	6	a	a	DET
ap-6074	162	7	cylindrical	cylindrical	ADJ
ap-6074	162	8	helix	helix	NOUN
ap-6074	162	9	the	the	DET
ap-6074	162	10	tangent	tangent	ADJ
ap-6074	162	11	surface	surface	NOUN
ap-6074	162	12	of	of	ADP
ap-6074	162	13	a	a	DET
ap-6074	162	14	cylindrical	cylindrical	ADJ
ap-6074	162	15	helix	helix	NOUN
ap-6074	162	16	is	be	AUX
ap-6074	162	17	very	very	ADV
ap-6074	162	18	important	important	ADJ
ap-6074	162	19	in	in	ADP
ap-6074	162	20	gear	gear	NOUN
ap-6074	162	21	geometry	geometry	NOUN
ap-6074	162	22	because	because	SCONJ
ap-6074	162	23	an	an	DET
ap-6074	162	24	unmodified	unmodified	ADJ
ap-6074	162	25	involute	involute	ADJ
ap-6074	162	26	helical	helical	ADJ
ap-6074	162	27	tooth	tooth	NOUN
ap-6074	162	28	flank	flank	NOUN
ap-6074	162	29	is	be	AUX
ap-6074	162	30	a	a	DET
ap-6074	162	31	tangent	tangent	ADJ
ap-6074	162	32	surface	surface	NOUN
ap-6074	162	33	of	of	ADP
ap-6074	162	34	the	the	DET
ap-6074	162	35	base	base	NOUN
ap-6074	162	36	helix	helix	NOUN
ap-6074	162	37	[	[	X
ap-6074	162	38	7	7	NUM
ap-6074	162	39	]	]	PUNCT
ap-6074	162	40	,	,	PUNCT
ap-6074	162	41	i.e.	i.e.	X
ap-6074	162	42	,	,	PUNCT
ap-6074	162	43	the	the	DET
ap-6074	162	44	helix	helix	NOUN
ap-6074	162	45	located	locate	VERB
ap-6074	162	46	on	on	ADP
ap-6074	162	47	the	the	DET
ap-6074	162	48	gear	gear	NOUN
ap-6074	162	49	base	base	NOUN
ap-6074	162	50	cylinder	cylinder	NOUN
ap-6074	162	51	.	.	PUNCT
ap-6074	163	1	helix	helix	NOUN
ap-6074	163	2	is	be	AUX
ap-6074	163	3	a	a	DET
ap-6074	163	4	spatial	spatial	ADJ
ap-6074	163	5	curve	curve	NOUN
ap-6074	163	6	generated	generate	VERB
ap-6074	163	7	by	by	ADP
ap-6074	163	8	screw	screw	VERB
ap-6074	163	9	motion	motion	NOUN
ap-6074	163	10	of	of	ADP
ap-6074	163	11	a	a	DET
ap-6074	163	12	generating	generating	NOUN
ap-6074	163	13	point	point	NOUN
ap-6074	163	14	.	.	PUNCT
ap-6074	164	1	a	a	DET
ap-6074	164	2	screw	screw	ADJ
ap-6074	164	3	motion	motion	NOUN
ap-6074	164	4	is	be	AUX
ap-6074	164	5	a	a	DET
ap-6074	164	6	combination	combination	NOUN
ap-6074	164	7	of	of	ADP
ap-6074	164	8	revolution	revolution	NOUN
ap-6074	164	9	about	about	ADP
ap-6074	164	10	axis	axis	ADJ
ap-6074	164	11	o	o	NOUN
ap-6074	164	12	of	of	ADP
ap-6074	164	13	the	the	DET
ap-6074	164	14	screw	screw	ADJ
ap-6074	164	15	motion	motion	NOUN
ap-6074	164	16	and	and	CCONJ
ap-6074	164	17	a	a	DET
ap-6074	164	18	translation	translation	NOUN
ap-6074	164	19	along	along	ADP
ap-6074	164	20	axis	axis	NOUN
ap-6074	164	21	o.	o.	NOUN
ap-6074	164	22	the	the	DET
ap-6074	164	23	helix	helix	NOUN
ap-6074	164	24	is	be	AUX
ap-6074	164	25	called	call	VERB
ap-6074	164	26	cylindrical	cylindrical	ADJ
ap-6074	164	27	if	if	SCONJ
ap-6074	164	28	the	the	DET
ap-6074	164	29	angle	angle	NOUN
ap-6074	164	30	of	of	ADP
ap-6074	164	31	revolution	revolution	NOUN
ap-6074	164	32	is	be	AUX
ap-6074	164	33	directly	directly	ADV
ap-6074	164	34	proportional	proportional	ADJ
ap-6074	164	35	to	to	ADP
ap-6074	164	36	the	the	DET
ap-6074	164	37	length	length	NOUN
ap-6074	164	38	of	of	ADP
ap-6074	164	39	translation	translation	NOUN
ap-6074	164	40	and	and	CCONJ
ap-6074	164	41	the	the	DET
ap-6074	164	42	distance	distance	NOUN
ap-6074	164	43	of	of	ADP
ap-6074	164	44	the	the	DET
ap-6074	164	45	generating	generate	VERB
ap-6074	164	46	point	point	NOUN
ap-6074	164	47	from	from	ADP
ap-6074	164	48	the	the	DET
ap-6074	164	49	axis	axis	NOUN
ap-6074	164	50	o	o	NOUN
ap-6074	164	51	is	be	AUX
ap-6074	164	52	constant	constant	ADJ
ap-6074	164	53	.	.	PUNCT
ap-6074	165	1	the	the	DET
ap-6074	165	2	cylindrical	cylindrical	ADJ
ap-6074	165	3	helix	helix	NOUN
ap-6074	165	4	(	(	PUNCT
ap-6074	165	5	hereinafter	hereinafter	NOUN
ap-6074	165	6	referred	refer	VERB
ap-6074	165	7	to	to	ADP
ap-6074	165	8	as	as	SCONJ
ap-6074	165	9	the	the	DET
ap-6074	165	10	"	"	PUNCT
ap-6074	165	11	helix	helix	NOUN
ap-6074	165	12	"	"	PUNCT
ap-6074	165	13	)	)	PUNCT
ap-6074	165	14	is	be	AUX
ap-6074	165	15	a	a	DET
ap-6074	165	16	curve	curve	NOUN
ap-6074	165	17	of	of	ADP
ap-6074	165	18	a	a	DET
ap-6074	165	19	constant	constant	ADJ
ap-6074	165	20	slope	slope	NOUN
ap-6074	165	21	,	,	PUNCT
ap-6074	165	22	i.e.	i.e.	X
ap-6074	165	23	the	the	DET
ap-6074	165	24	angle	angle	NOUN
ap-6074	165	25	formed	form	VERB
ap-6074	165	26	by	by	ADP
ap-6074	165	27	the	the	DET
ap-6074	165	28	tangent	tangent	ADJ
ap-6074	165	29	line	line	NOUN
ap-6074	165	30	to	to	ADP
ap-6074	165	31	the	the	DET
ap-6074	165	32	helix	helix	NOUN
ap-6074	165	33	and	and	CCONJ
ap-6074	165	34	any	any	DET
ap-6074	165	35	plane	plane	NOUN
ap-6074	165	36	perpendicular	perpendicular	NOUN
ap-6074	165	37	to	to	PART
ap-6074	165	38	axis	axis	VERB
ap-6074	165	39	o	o	NOUN
ap-6074	165	40	is	be	AUX
ap-6074	165	41	constant	constant	ADJ
ap-6074	165	42	.	.	PUNCT
ap-6074	166	1	the	the	DET
ap-6074	166	2	development	development	NOUN
ap-6074	166	3	of	of	ADP
ap-6074	166	4	the	the	DET
ap-6074	166	5	helix	helix	NOUN
ap-6074	166	6	(	(	PUNCT
ap-6074	166	7	flattening	flatten	VERB
ap-6074	166	8	onto	onto	ADP
ap-6074	166	9	a	a	DET
ap-6074	166	10	plane	plane	NOUN
ap-6074	166	11	)	)	PUNCT
ap-6074	166	12	is	be	AUX
ap-6074	166	13	a	a	DET
ap-6074	166	14	directly	directly	ADV
ap-6074	166	15	proportional	proportional	ADJ
ap-6074	166	16	graph	graph	NOUN
ap-6074	166	17	with	with	ADP
ap-6074	166	18	the	the	DET
ap-6074	166	19	revolution	revolution	NOUN
ap-6074	166	20	(	(	PUNCT
ap-6074	166	21	measured	measure	VERB
ap-6074	166	22	in	in	ADP
ap-6074	166	23	the	the	DET
ap-6074	166	24	length	length	NOUN
ap-6074	166	25	of	of	ADP
ap-6074	166	26	arc	arc	NOUN
ap-6074	166	27	)	)	PUNCT
ap-6074	166	28	on	on	ADP
ap-6074	166	29	horizontal	horizontal	ADJ
ap-6074	166	30	axis	axis	NOUN
ap-6074	166	31	and	and	CCONJ
ap-6074	166	32	translation	translation	NOUN
ap-6074	166	33	of	of	ADP
ap-6074	166	34	vertical	vertical	ADJ
ap-6074	166	35	axis	axis	NOUN
ap-6074	166	36	.	.	PUNCT
ap-6074	167	1	the	the	DET
ap-6074	167	2	slope	slope	NOUN
ap-6074	167	3	of	of	ADP
ap-6074	167	4	the	the	DET
ap-6074	167	5	graph	graph	NOUN
ap-6074	167	6	is	be	AUX
ap-6074	167	7	identical	identical	ADJ
ap-6074	167	8	to	to	ADP
ap-6074	167	9	the	the	DET
ap-6074	167	10	slope	slope	NOUN
ap-6074	167	11	of	of	ADP
ap-6074	167	12	the	the	DET
ap-6074	167	13	helix	helix	NOUN
ap-6074	167	14	.	.	PUNCT
ap-6074	168	1	the	the	DET
ap-6074	168	2	tangent	tangent	ADJ
ap-6074	168	3	surface	surface	NOUN
ap-6074	168	4	of	of	ADP
ap-6074	168	5	the	the	DET
ap-6074	168	6	helix	helix	NOUN
ap-6074	168	7	is	be	AUX
ap-6074	168	8	a	a	DET
ap-6074	168	9	developable	developable	ADJ
ap-6074	168	10	surface	surface	NOUN
ap-6074	168	11	[	[	X
ap-6074	168	12	8	8	NUM
ap-6074	168	13	]	]	PUNCT
ap-6074	168	14	(	(	PUNCT
ap-6074	168	15	it	it	PRON
ap-6074	168	16	is	be	AUX
ap-6074	168	17	possible	possible	ADJ
ap-6074	168	18	to	to	PART
ap-6074	168	19	unfold	unfold	VERB
ap-6074	168	20	it	it	PRON
ap-6074	168	21	into	into	ADP
ap-6074	168	22	a	a	DET
ap-6074	168	23	plane	plane	NOUN
ap-6074	168	24	without	without	ADP
ap-6074	168	25	any	any	DET
ap-6074	168	26	distortion	distortion	NOUN
ap-6074	168	27	)	)	PUNCT
ap-6074	168	28	.	.	PUNCT
ap-6074	169	1	to	to	PART
ap-6074	169	2	derive	derive	VERB
ap-6074	169	3	a	a	DET
ap-6074	169	4	mathematical	mathematical	ADJ
ap-6074	169	5	model	model	NOUN
ap-6074	169	6	of	of	ADP
ap-6074	169	7	the	the	DET
ap-6074	169	8	tangent	tangent	ADJ
ap-6074	169	9	surface	surface	NOUN
ap-6074	169	10	of	of	ADP
ap-6074	169	11	the	the	DET
ap-6074	169	12	helix	helix	NOUN
ap-6074	169	13	,	,	PUNCT
ap-6074	169	14	consider	consider	VERB
ap-6074	169	15	the	the	DET
ap-6074	169	16	cylinder	cylinder	NOUN
ap-6074	169	17	(	(	PUNCT
ap-6074	169	18	axis	axis	ADJ
ap-6074	169	19	identical	identical	ADJ
ap-6074	169	20	to	to	PART
ap-6074	169	21	coordinate	coordinate	VERB
ap-6074	169	22	z	z	NOUN
ap-6074	169	23	axis	axis	NOUN
ap-6074	169	24	,	,	PUNCT
ap-6074	169	25	radius	radius	NOUN
ap-6074	169	26	rb	rb	NOUN
ap-6074	169	27	,	,	PUNCT
ap-6074	169	28	height	height	NOUN
ap-6074	169	29	equal	equal	ADJ
ap-6074	169	30	to	to	ADP
ap-6074	169	31	the	the	DET
ap-6074	169	32	lead	lead	ADJ
ap-6074	169	33	pz	pz	NOUN
ap-6074	169	34	)	)	PUNCT
ap-6074	169	35	and	and	CCONJ
ap-6074	169	36	one	one	NUM
ap-6074	169	37	thread	thread	NOUN
ap-6074	169	38	of	of	ADP
ap-6074	169	39	right	right	ADJ
ap-6074	169	40	hand	hand	NOUN
ap-6074	169	41	helix	helix	NOUN
ap-6074	169	42	hb	hb	PROPN
ap-6074	169	43	generated	generate	VERB
ap-6074	169	44	by	by	ADP
ap-6074	169	45	a	a	DET
ap-6074	169	46	screw	screw	ADJ
ap-6074	169	47	motion	motion	NOUN
ap-6074	169	48	of	of	ADP
ap-6074	169	49	point	point	NOUN
ap-6074	169	50	b	b	NOUN
ap-6074	169	51	located	locate	VERB
ap-6074	169	52	on	on	ADP
ap-6074	169	53	coordinate	coordinate	NOUN
ap-6074	169	54	x	x	PUNCT
ap-6074	169	55	axis	axis	NOUN
ap-6074	169	56	,	,	PUNCT
ap-6074	169	57	b	b	NOUN
ap-6074	169	58	=	=	SYM
ap-6074	169	59	(	(	PUNCT
ap-6074	169	60	xb	xb	PROPN
ap-6074	169	61	,	,	PUNCT
ap-6074	169	62	yb	yb	PROPN
ap-6074	169	63	,	,	PUNCT
ap-6074	169	64	zb	zb	PROPN
ap-6074	169	65	,	,	PUNCT
ap-6074	169	66	1	1	NUM
ap-6074	169	67	)	)	PUNCT
ap-6074	169	68	=	=	SYM
ap-6074	169	69	(	(	PUNCT
ap-6074	169	70	rb	rb	PROPN
ap-6074	169	71	,	,	PUNCT
ap-6074	169	72	0	0	NUM
ap-6074	169	73	,	,	PUNCT
ap-6074	169	74	0	0	NUM
ap-6074	169	75	,	,	PUNCT
ap-6074	169	76	1	1	NUM
ap-6074	169	77	)	)	PUNCT
ap-6074	169	78	(	(	PUNCT
ap-6074	169	79	in	in	ADP
ap-6074	169	80	homogeneous	homogeneous	ADJ
ap-6074	169	81	coordinates	coordinate	NOUN
ap-6074	169	82	)	)	PUNCT
ap-6074	169	83	,	,	PUNCT
ap-6074	169	84	see	see	VERB
ap-6074	169	85	fig	fig	NOUN
ap-6074	169	86	.	.	PUNCT
ap-6074	170	1	10	10	NUM
ap-6074	170	2	.	.	PUNCT
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ap-6074	170	4	z	z	PROPN
ap-6074	170	5	b	b	PROPN
ap-6074	170	6	b	b	PROPN
ap-6074	170	7	t	t	PROPN
ap-6074	170	8	z	z	NOUN
ap-6074	170	9	h	h	NOUN
ap-6074	170	10	v	v	PROPN
ap-6074	170	11	σ	σ	X
ap-6074	170	12	y	y	PROPN
ap-6074	171	1	x	x	X
ap-6074	171	2	p	p	X
ap-6074	171	3	u	u	PRON
ap-6074	171	4	figure	figure	NOUN
ap-6074	171	5	10	10	NUM
ap-6074	171	6	.	.	PUNCT
ap-6074	172	1	tangent	tangent	PROPN
ap-6074	172	2	surface	surface	PROPN
ap-6074	172	3	of	of	ADP
ap-6074	172	4	cylindrical	cylindrical	ADJ
ap-6074	172	5	helix	helix	NOUN
ap-6074	172	6	.	.	PUNCT
ap-6074	173	1	p	p	X
ap-6074	173	2	2	2	NUM
ap-6074	173	3	r	r	NOUN
ap-6074	173	4	b	b	PROPN
ap-6074	173	5	β	β	X
ap-6074	173	6	b	b	NUM
ap-6074	173	7	developed	develop	VERB
ap-6074	173	8	helix	helix	NOUN
ap-6074	173	9	h	h	NOUN
ap-6074	173	10	π	π	PROPN
ap-6074	173	11	γ	γ	X
ap-6074	173	12	b	b	PROPN
ap-6074	173	13	r	r	NOUN
ap-6074	173	14	b	b	PROPN
ap-6074	173	15	0	0	NUM
ap-6074	173	16	b	b	PROPN
ap-6074	173	17	p	p	NOUN
ap-6074	173	18	z	z	NOUN
ap-6074	173	19	figure	figure	NOUN
ap-6074	173	20	11	11	NUM
ap-6074	173	21	.	.	PUNCT
ap-6074	174	1	development	development	NOUN
ap-6074	174	2	of	of	ADP
ap-6074	174	3	the	the	DET
ap-6074	174	4	helix	helix	NOUN
ap-6074	174	5	.	.	PUNCT
ap-6074	175	1	the	the	DET
ap-6074	175	2	development	development	NOUN
ap-6074	175	3	of	of	ADP
ap-6074	175	4	the	the	DET
ap-6074	175	5	cylinder	cylinder	NOUN
ap-6074	175	6	is	be	AUX
ap-6074	175	7	the	the	DET
ap-6074	175	8	rectangle	rectangle	NOUN
ap-6074	175	9	(	(	PUNCT
ap-6074	175	10	width	width	VERB
ap-6074	175	11	2πrb	2πrb	NOUN
ap-6074	175	12	,	,	PUNCT
ap-6074	175	13	height	height	NOUN
ap-6074	175	14	pz	pz	NOUN
ap-6074	175	15	)	)	PUNCT
ap-6074	175	16	,	,	PUNCT
ap-6074	175	17	the	the	DET
ap-6074	175	18	development	development	NOUN
ap-6074	175	19	of	of	ADP
ap-6074	175	20	the	the	DET
ap-6074	175	21	helix	helix	NOUN
ap-6074	175	22	is	be	AUX
ap-6074	175	23	the	the	DET
ap-6074	175	24	diagonal	diagonal	ADJ
ap-6074	175	25	of	of	ADP
ap-6074	175	26	this	this	DET
ap-6074	175	27	rectangle	rectangle	NOUN
ap-6074	175	28	,	,	PUNCT
ap-6074	175	29	see	see	VERB
ap-6074	175	30	fig	fig	NOUN
ap-6074	175	31	.	.	PUNCT
ap-6074	176	1	11	11	NUM
ap-6074	176	2	.	.	X
ap-6074	177	1	direction	direction	NOUN
ap-6074	177	2	vector	vector	NOUN
ap-6074	177	3	b	b	PROPN
ap-6074	177	4	of	of	ADP
ap-6074	177	5	tangent	tangent	NOUN
ap-6074	177	6	line	line	PROPN
ap-6074	177	7	t	t	PROPN
ap-6074	177	8	is	be	AUX
ap-6074	177	9	given	give	VERB
ap-6074	177	10	by	by	ADP
ap-6074	177	11	b	b	NOUN
ap-6074	177	12	=	=	SYM
ap-6074	177	13	(	(	PUNCT
ap-6074	177	14	b1	b1	PROPN
ap-6074	177	15	,	,	PUNCT
ap-6074	177	16	b2	b2	NOUN
ap-6074	177	17	,	,	PUNCT
ap-6074	177	18	b3	b3	NOUN
ap-6074	177	19	,	,	PUNCT
ap-6074	177	20	0	0	NUM
ap-6074	177	21	)	)	PUNCT
ap-6074	177	22	=	=	SYM
ap-6074	177	23	(	(	PUNCT
ap-6074	177	24	0	0	NUM
ap-6074	177	25	,	,	PUNCT
ap-6074	177	26	rb	rb	NOUN
ap-6074	177	27	,	,	PUNCT
ap-6074	177	28	p0	p0	NOUN
ap-6074	177	29	,	,	PUNCT
ap-6074	177	30	0	0	NUM
ap-6074	177	31	)	)	PUNCT
ap-6074	177	32	where	where	SCONJ
ap-6074	177	33	p0	p0	NOUN
ap-6074	177	34	=	=	SYM
ap-6074	177	35	pz/2π	pz/2π	PROPN
ap-6074	177	36	is	be	AUX
ap-6074	177	37	called	call	VERB
ap-6074	177	38	the	the	DET
ap-6074	177	39	parameter	parameter	NOUN
ap-6074	177	40	of	of	ADP
ap-6074	177	41	the	the	DET
ap-6074	177	42	screw	screw	ADJ
ap-6074	177	43	motion	motion	NOUN
ap-6074	177	44	(	(	PUNCT
ap-6074	177	45	translation	translation	NOUN
ap-6074	177	46	directly	directly	ADV
ap-6074	177	47	proportional	proportional	ADJ
ap-6074	177	48	to	to	ADP
ap-6074	177	49	the	the	DET
ap-6074	177	50	revolution	revolution	NOUN
ap-6074	177	51	about	about	ADP
ap-6074	177	52	one	one	NUM
ap-6074	177	53	radian	radian	NOUN
ap-6074	177	54	)	)	PUNCT
ap-6074	177	55	.	.	PUNCT
ap-6074	178	1	the	the	DET
ap-6074	178	2	vector	vector	NOUN
ap-6074	178	3	equation	equation	NOUN
ap-6074	178	4	of	of	ADP
ap-6074	178	5	tangent	tangent	NOUN
ap-6074	178	6	line	line	PROPN
ap-6074	178	7	t	t	PROPN
ap-6074	178	8	:	:	PUNCT
ap-6074	178	9	t(v	t(v	NUM
ap-6074	178	10	)	)	PUNCT
ap-6074	178	11	=	=	PRON
ap-6074	178	12	(	(	PUNCT
ap-6074	178	13	x(v	x(v	PROPN
ap-6074	178	14	)	)	PUNCT
ap-6074	178	15	,	,	PUNCT
ap-6074	178	16	y(v	y(v	PROPN
ap-6074	178	17	)	)	PUNCT
ap-6074	178	18	,	,	PUNCT
ap-6074	178	19	z(v	z(v	PROPN
ap-6074	178	20	)	)	PUNCT
ap-6074	178	21	,	,	PUNCT
ap-6074	178	22	1	1	NUM
ap-6074	178	23	)	)	PUNCT
ap-6074	178	24	to	to	ADP
ap-6074	178	25	the	the	DET
ap-6074	178	26	helix	helix	NOUN
ap-6074	178	27	hb	hb	NOUN
ap-6074	178	28	passing	pass	VERB
ap-6074	178	29	through	through	ADP
ap-6074	178	30	point	point	NOUN
ap-6074	178	31	b	b	PROPN
ap-6074	178	32	is	be	AUX
ap-6074	178	33	given	give	VERB
ap-6074	178	34	by	by	ADP
ap-6074	178	35	t(v	t(v	PROPN
ap-6074	178	36	)	)	PUNCT
ap-6074	178	37	=(	=(	NOUN
ap-6074	178	38	xb	xb	PROPN
ap-6074	179	1	+	+	CCONJ
ap-6074	179	2	b1v	b1v	X
ap-6074	179	3	,	,	PUNCT
ap-6074	179	4	yb	yb	PROPN
ap-6074	179	5	+	+	PROPN
ap-6074	179	6	b2v	b2v	PROPN
ap-6074	179	7	,	,	PUNCT
ap-6074	179	8	zb	zb	X
ap-6074	179	9	+	+	CCONJ
ap-6074	179	10	b3v	b3v	PROPN
ap-6074	179	11	,	,	PUNCT
ap-6074	179	12	1	1	X
ap-6074	179	13	)	)	PUNCT
ap-6074	179	14	=	=	SYM
ap-6074	179	15	=(	=(	X
ap-6074	179	16	rb	rb	PROPN
ap-6074	179	17	,	,	PUNCT
ap-6074	179	18	rbv	rbv	NOUN
ap-6074	179	19	,	,	PUNCT
ap-6074	179	20	p0v	p0v	NOUN
ap-6074	179	21	,	,	PUNCT
ap-6074	179	22	1	1	NUM
ap-6074	179	23	)	)	PUNCT
ap-6074	179	24	,	,	PUNCT
ap-6074	179	25	v	v	X
ap-6074	179	26	∈	∈	PROPN
ap-6074	179	27	r.	r.	NOUN
ap-6074	179	28	(	(	PUNCT
ap-6074	179	29	24	24	NUM
ap-6074	179	30	)	)	PUNCT
ap-6074	179	31	the	the	DET
ap-6074	179	32	transformation	transformation	NOUN
ap-6074	179	33	matrix	matrix	NOUN
ap-6074	179	34	of	of	ADP
ap-6074	179	35	the	the	DET
ap-6074	179	36	right	right	ADJ
ap-6074	179	37	hand	hand	NOUN
ap-6074	179	38	screw	screw	VERB
ap-6074	179	39	motion	motion	NOUN
ap-6074	179	40	is	be	AUX
ap-6074	179	41	given	give	VERB
ap-6074	179	42	by	by	ADP
ap-6074	179	43	gr(u	gr(u	NOUN
ap-6074	179	44	)	)	PUNCT
ap-6074	180	1	=	=	SYM
ap-6074	180	2			PROPN
ap-6074	180	3	cosu	cosu	VERB
ap-6074	180	4	sin	sin	VERB
ap-6074	180	5	u	u	NOUN
ap-6074	180	6	0	0	NUM
ap-6074	180	7	0	0	NUM
ap-6074	180	8	−	−	PROPN
ap-6074	180	9	sin	sin	NOUN
ap-6074	180	10	u	u	NOUN
ap-6074	180	11	cosu	cosu	VERB
ap-6074	180	12	0	0	NUM
ap-6074	180	13	0	0	NUM
ap-6074	180	14	0	0	NUM
ap-6074	180	15	0	0	NUM
ap-6074	181	1	1	1	NUM
ap-6074	181	2	0	0	NUM
ap-6074	181	3	0	0	NUM
ap-6074	181	4	0	0	NUM
ap-6074	181	5	p0u	p0u	NOUN
ap-6074	181	6	1	1	NUM
ap-6074	181	7			NOUN
ap-6074	181	8	,	,	PUNCT
ap-6074	181	9	u	u	NOUN
ap-6074	181	10	∈	∈	PROPN
ap-6074	181	11	r	r	PROPN
ap-6074	181	12	,	,	PUNCT
ap-6074	181	13	(	(	PUNCT
ap-6074	181	14	25	25	NUM
ap-6074	181	15	)	)	PUNCT
ap-6074	181	16	where	where	SCONJ
ap-6074	181	17	u	u	NOUN
ap-6074	181	18	is	be	AUX
ap-6074	181	19	the	the	DET
ap-6074	181	20	angle	angle	NOUN
ap-6074	181	21	parameter	parameter	NOUN
ap-6074	181	22	in	in	ADP
ap-6074	181	23	radians	radian	NOUN
ap-6074	181	24	.	.	PUNCT
ap-6074	182	1	the	the	DET
ap-6074	182	2	first	first	ADJ
ap-6074	182	3	three	three	NUM
ap-6074	182	4	rows	row	NOUN
ap-6074	182	5	of	of	ADP
ap-6074	182	6	matrix	matrix	NOUN
ap-6074	182	7	(	(	PUNCT
ap-6074	182	8	25	25	NUM
ap-6074	182	9	)	)	PUNCT
ap-6074	182	10	correspond	correspond	VERB
ap-6074	182	11	to	to	ADP
ap-6074	182	12	the	the	DET
ap-6074	182	13	revolution	revolution	NOUN
ap-6074	182	14	105	105	NUM
ap-6074	182	15	ivana	ivana	PROPN
ap-6074	182	16	linkeová	linkeová	PROPN
ap-6074	182	17	,	,	PUNCT
ap-6074	182	18	vít	vít	PROPN
ap-6074	182	19	zelený	zelený	PROPN
ap-6074	182	20	acta	acta	PROPN
ap-6074	182	21	polytechnica	polytechnica	PROPN
ap-6074	183	1	e	e	PROPN
ap-6074	183	2	p	p	PROPN
ap-6074	183	3	t	t	PROPN
ap-6074	183	4	z	z	PROPN
ap-6074	183	5	bh	bh	PROPN
ap-6074	183	6	σ	σ	PROPN
ap-6074	183	7	rb	rb	PROPN
ap-6074	183	8	o	o	X
ap-6074	183	9	z	z	NOUN
ap-6074	183	10	x	x	SYM
ap-6074	183	11	y	y	PROPN
ap-6074	183	12	b	b	PROPN
ap-6074	183	13	figure	figure	NOUN
ap-6074	183	14	12	12	NUM
ap-6074	183	15	.	.	PUNCT
ap-6074	184	1	involute	involute	ADJ
ap-6074	184	2	section	section	NOUN
ap-6074	184	3	e	e	NOUN
ap-6074	184	4	of	of	ADP
ap-6074	184	5	tangent	tangent	ADJ
ap-6074	184	6	surface	surface	NOUN
ap-6074	184	7	of	of	ADP
ap-6074	184	8	the	the	DET
ap-6074	184	9	helix	helix	NOUN
ap-6074	184	10	.	.	PUNCT
ap-6074	185	1	about	about	ADP
ap-6074	185	2	z	z	NOUN
ap-6074	185	3	axis	axis	NOUN
ap-6074	185	4	and	and	CCONJ
ap-6074	185	5	the	the	DET
ap-6074	185	6	fourth	fourth	ADJ
ap-6074	185	7	row	row	NOUN
ap-6074	185	8	corresponds	correspond	VERB
ap-6074	185	9	to	to	ADP
ap-6074	185	10	the	the	DET
ap-6074	185	11	translation	translation	NOUN
ap-6074	185	12	along	along	ADP
ap-6074	185	13	z	z	PROPN
ap-6074	185	14	axis	axis	NOUN
ap-6074	185	15	.	.	PUNCT
ap-6074	186	1	tangent	tangent	PROPN
ap-6074	186	2	surface	surface	PROPN
ap-6074	186	3	σ	σ	PROPN
ap-6074	186	4	:	:	PUNCT
ap-6074	186	5	s(u	s(u	PROPN
ap-6074	186	6	,	,	PUNCT
ap-6074	186	7	v	v	NOUN
ap-6074	186	8	)	)	PUNCT
ap-6074	186	9	=	=	SYM
ap-6074	186	10	(	(	PUNCT
ap-6074	186	11	x(u	x(u	PROPN
ap-6074	186	12	,	,	PUNCT
ap-6074	186	13	v	v	NOUN
ap-6074	186	14	)	)	PUNCT
ap-6074	186	15	,	,	PUNCT
ap-6074	186	16	y(u	y(u	PROPN
ap-6074	186	17	,	,	PUNCT
ap-6074	186	18	v	v	NOUN
ap-6074	186	19	)	)	PUNCT
ap-6074	186	20	,	,	PUNCT
ap-6074	186	21	z(u	z(u	PROPN
ap-6074	186	22	,	,	PUNCT
ap-6074	186	23	v	v	NOUN
ap-6074	186	24	)	)	PUNCT
ap-6074	186	25	,	,	PUNCT
ap-6074	186	26	1	1	X
ap-6074	186	27	)	)	PUNCT
ap-6074	186	28	of	of	ADP
ap-6074	186	29	the	the	DET
ap-6074	186	30	right	right	ADJ
ap-6074	186	31	hand	hand	NOUN
ap-6074	186	32	helix	helix	NOUN
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ap-6074	186	35	by	by	ADP
ap-6074	186	36	s(u	s(u	PROPN
ap-6074	186	37	,	,	PUNCT
ap-6074	186	38	v	v	NOUN
ap-6074	186	39	)	)	PUNCT
ap-6074	186	40	=	=	SYM
ap-6074	186	41	t(v	t(v	PROPN
ap-6074	186	42	)	)	PUNCT
ap-6074	186	43	·	·	PUNCT
ap-6074	186	44	gr(u	gr(u	X
ap-6074	186	45	)	)	PUNCT
ap-6074	186	46	=	=	SYM
ap-6074	186	47	=(	=(	NOUN
ap-6074	186	48	rb(cosu−	rb(cosu−	PROPN
ap-6074	186	49	v	v	ADP
ap-6074	186	50	sin	sin	NOUN
ap-6074	186	51	u	u	NOUN
ap-6074	186	52	)	)	PUNCT
ap-6074	186	53	,	,	PUNCT
ap-6074	186	54	rb(sin	rb(sin	NOUN
ap-6074	186	55	u+	u+	NOUN
ap-6074	186	56	v	v	NUM
ap-6074	186	57	cosu	cosu	PROPN
ap-6074	186	58	)	)	PUNCT
ap-6074	186	59	,	,	PUNCT
ap-6074	186	60	p0(v	p0(v	PROPN
ap-6074	186	61	+	+	CCONJ
ap-6074	186	62	u	u	NOUN
ap-6074	186	63	)	)	PUNCT
ap-6074	186	64	,	,	PUNCT
ap-6074	186	65	1	1	NUM
ap-6074	186	66	)	)	PUNCT
ap-6074	186	67	.	.	PUNCT
ap-6074	187	1	(	(	PUNCT
ap-6074	187	2	26	26	NUM
ap-6074	187	3	)	)	PUNCT
ap-6074	187	4	there	there	PRON
ap-6074	187	5	are	be	VERB
ap-6074	187	6	three	three	NUM
ap-6074	187	7	types	type	NOUN
ap-6074	187	8	of	of	ADP
ap-6074	187	9	curves	curve	NOUN
ap-6074	187	10	on	on	ADP
ap-6074	187	11	the	the	DET
ap-6074	187	12	surface	surface	NOUN
ap-6074	187	13	(	(	PUNCT
ap-6074	187	14	26	26	NUM
ap-6074	187	15	):	):	PUNCT
ap-6074	187	16	two	two	NUM
ap-6074	187	17	systems	system	NOUN
ap-6074	187	18	of	of	ADP
ap-6074	187	19	parametric	parametric	ADJ
ap-6074	187	20	curves	curve	NOUN
ap-6074	187	21	,	,	PUNCT
ap-6074	187	22	i.e.	i.e.	X
ap-6074	187	23	helices	helix	NOUN
ap-6074	187	24	and	and	CCONJ
ap-6074	187	25	straight	straight	ADJ
ap-6074	187	26	lines	line	NOUN
ap-6074	187	27	,	,	PUNCT
ap-6074	187	28	see	see	VERB
ap-6074	187	29	fig	fig	NOUN
ap-6074	187	30	.	.	PUNCT
ap-6074	188	1	10	10	NUM
ap-6074	188	2	,	,	PUNCT
ap-6074	188	3	and	and	CCONJ
ap-6074	188	4	involute	involute	ADJ
ap-6074	188	5	curves	curve	NOUN
ap-6074	188	6	,	,	PUNCT
ap-6074	188	7	see	see	VERB
ap-6074	188	8	fig	fig	NOUN
ap-6074	188	9	.	.	PUNCT
ap-6074	189	1	12	12	NUM
ap-6074	189	2	.	.	PUNCT
ap-6074	190	1	two	two	NUM
ap-6074	190	2	parametric	parametric	ADJ
ap-6074	190	3	curves	curve	NOUN
ap-6074	190	4	,	,	PUNCT
ap-6074	190	5	each	each	PRON
ap-6074	190	6	of	of	ADP
ap-6074	190	7	them	they	PRON
ap-6074	190	8	from	from	ADP
ap-6074	190	9	a	a	DET
ap-6074	190	10	different	different	ADJ
ap-6074	190	11	system	system	NOUN
ap-6074	190	12	,	,	PUNCT
ap-6074	190	13	have	have	VERB
ap-6074	190	14	a	a	DET
ap-6074	190	15	common	common	ADJ
ap-6074	190	16	point	point	NOUN
ap-6074	190	17	located	locate	VERB
ap-6074	190	18	on	on	ADP
ap-6074	190	19	the	the	DET
ap-6074	190	20	surface	surface	NOUN
ap-6074	190	21	,	,	PUNCT
ap-6074	190	22	parametric	parametric	ADJ
ap-6074	190	23	coordinates	coordinate	NOUN
ap-6074	190	24	of	of	ADP
ap-6074	190	25	this	this	DET
ap-6074	190	26	point	point	NOUN
ap-6074	190	27	correspond	correspond	ADV
ap-6074	190	28	to	to	ADP
ap-6074	190	29	the	the	DET
ap-6074	190	30	constant	constant	ADJ
ap-6074	190	31	values	value	NOUN
ap-6074	190	32	of	of	ADP
ap-6074	190	33	parameters	parameter	NOUN
ap-6074	190	34	u	u	NOUN
ap-6074	190	35	and	and	CCONJ
ap-6074	190	36	v.	v.	ADP
ap-6074	190	37	parametric	parametric	PROPN
ap-6074	190	38	u	u	NOUN
ap-6074	190	39	-	-	NOUN
ap-6074	190	40	curves	curve	NOUN
ap-6074	190	41	are	be	AUX
ap-6074	190	42	helices	helix	NOUN
ap-6074	190	43	obtained	obtain	VERB
ap-6074	190	44	by	by	ADP
ap-6074	190	45	the	the	DET
ap-6074	190	46	substitution	substitution	NOUN
ap-6074	190	47	of	of	ADP
ap-6074	190	48	constant	constant	ADJ
ap-6074	190	49	value	value	NOUN
ap-6074	190	50	v	v	NOUN
ap-6074	190	51	=	=	SYM
ap-6074	190	52	vc	vc	NOUN
ap-6074	190	53	,	,	PUNCT
ap-6074	190	54	vc	vc	PROPN
ap-6074	190	55	∈	∈	PROPN
ap-6074	190	56	r	r	NOUN
ap-6074	190	57	in	in	ADP
ap-6074	190	58	(	(	PUNCT
ap-6074	190	59	26	26	NUM
ap-6074	190	60	)	)	PUNCT
ap-6074	190	61	.	.	PUNCT
ap-6074	191	1	parametric	parametric	ADJ
ap-6074	191	2	v	v	NOUN
ap-6074	191	3	-	-	PUNCT
ap-6074	191	4	curves	curve	NOUN
ap-6074	191	5	are	be	AUX
ap-6074	191	6	tangent	tangent	ADJ
ap-6074	191	7	lines	line	NOUN
ap-6074	191	8	to	to	ADP
ap-6074	191	9	the	the	DET
ap-6074	191	10	helix	helix	NOUN
ap-6074	191	11	obtained	obtain	VERB
ap-6074	191	12	by	by	ADP
ap-6074	191	13	the	the	DET
ap-6074	191	14	substitution	substitution	NOUN
ap-6074	191	15	of	of	ADP
ap-6074	191	16	constant	constant	ADJ
ap-6074	191	17	value	value	NOUN
ap-6074	191	18	u	u	NOUN
ap-6074	191	19	=	=	PROPN
ap-6074	191	20	uc	uc	PROPN
ap-6074	191	21	,	,	PUNCT
ap-6074	191	22	uc	uc	PROPN
ap-6074	191	23	∈	∈	PROPN
ap-6074	191	24	r	r	NOUN
ap-6074	191	25	in	in	ADP
ap-6074	191	26	(	(	PUNCT
ap-6074	191	27	26	26	NUM
ap-6074	191	28	)	)	PUNCT
ap-6074	191	29	.	.	PUNCT
ap-6074	192	1	the	the	DET
ap-6074	192	2	involute	involute	ADJ
ap-6074	192	3	curve	curve	NOUN
ap-6074	192	4	is	be	AUX
ap-6074	192	5	the	the	DET
ap-6074	192	6	intersection	intersection	NOUN
ap-6074	192	7	of	of	ADP
ap-6074	192	8	the	the	DET
ap-6074	192	9	tangent	tangent	ADJ
ap-6074	192	10	surface	surface	NOUN
ap-6074	192	11	of	of	ADP
ap-6074	192	12	the	the	DET
ap-6074	192	13	helix	helix	NOUN
ap-6074	192	14	and	and	CCONJ
ap-6074	192	15	any	any	DET
ap-6074	192	16	plane	plane	NOUN
ap-6074	192	17	perpendicular	perpendicular	NOUN
ap-6074	192	18	to	to	ADP
ap-6074	192	19	z	z	PROPN
ap-6074	192	20	axis	axis	NOUN
ap-6074	192	21	.	.	PUNCT
ap-6074	193	1	to	to	PART
ap-6074	193	2	derive	derive	VERB
ap-6074	193	3	the	the	DET
ap-6074	193	4	equation	equation	NOUN
ap-6074	193	5	of	of	ADP
ap-6074	193	6	the	the	DET
ap-6074	193	7	involute	involute	ADJ
ap-6074	193	8	curve	curve	NOUN
ap-6074	193	9	from	from	ADP
ap-6074	193	10	(	(	PUNCT
ap-6074	193	11	26	26	NUM
ap-6074	193	12	)	)	PUNCT
ap-6074	193	13	,	,	PUNCT
ap-6074	193	14	the	the	DET
ap-6074	193	15	solution	solution	NOUN
ap-6074	193	16	of	of	ADP
ap-6074	193	17	equation	equation	NOUN
ap-6074	193	18	z(u	z(u	PROPN
ap-6074	193	19	,	,	PUNCT
ap-6074	193	20	v	v	NOUN
ap-6074	193	21	)	)	PUNCT
ap-6074	193	22	=	=	SYM
ap-6074	193	23	zc	zc	X
ap-6074	193	24	,	,	PUNCT
ap-6074	193	25	zc	zc	PROPN
ap-6074	193	26	∈	∈	PROPN
ap-6074	193	27	r	r	NOUN
ap-6074	193	28	has	have	VERB
ap-6074	193	29	to	to	PART
ap-6074	193	30	be	be	AUX
ap-6074	193	31	substituted	substitute	VERB
ap-6074	193	32	in	in	ADP
ap-6074	193	33	(	(	PUNCT
ap-6074	193	34	26	26	NUM
ap-6074	193	35	)	)	PUNCT
ap-6074	193	36	.	.	PUNCT
ap-6074	194	1	considering	consider	VERB
ap-6074	194	2	zc	zc	X
ap-6074	194	3	=	=	SYM
ap-6074	194	4	0	0	NUM
ap-6074	194	5	,	,	PUNCT
ap-6074	194	6	i.e.	i.e.	X
ap-6074	194	7	,	,	PUNCT
ap-6074	194	8	the	the	DET
ap-6074	194	9	intersection	intersection	NOUN
ap-6074	194	10	of	of	ADP
ap-6074	194	11	the	the	DET
ap-6074	194	12	tangent	tangent	ADJ
ap-6074	194	13	surface	surface	NOUN
ap-6074	194	14	of	of	ADP
ap-6074	194	15	the	the	DET
ap-6074	194	16	helix	helix	NOUN
ap-6074	194	17	and	and	CCONJ
ap-6074	194	18	coordinate	coordinate	NOUN
ap-6074	194	19	plane	plane	NOUN
ap-6074	194	20	(	(	PUNCT
ap-6074	194	21	x	x	NOUN
ap-6074	194	22	,	,	PUNCT
ap-6074	194	23	y	y	PROPN
ap-6074	194	24	)	)	PUNCT
ap-6074	194	25	,	,	PUNCT
ap-6074	194	26	the	the	DET
ap-6074	194	27	condition	condition	NOUN
ap-6074	194	28	p0(u+	p0(u+	PROPN
ap-6074	194	29	v	v	NOUN
ap-6074	194	30	)	)	PUNCT
ap-6074	194	31	=	=	SYM
ap-6074	194	32	0	0	NUM
ap-6074	194	33	is	be	AUX
ap-6074	194	34	met	meet	VERB
ap-6074	194	35	if	if	SCONJ
ap-6074	194	36	v	v	ADP
ap-6074	194	37	=	=	PUNCT
ap-6074	194	38	−u	−u	NOUN
ap-6074	194	39	or	or	CCONJ
ap-6074	194	40	u	u	NOUN
ap-6074	194	41	=	=	NOUN
ap-6074	194	42	−v	−v	NOUN
ap-6074	194	43	.	.	PUNCT
ap-6074	195	1	these	these	DET
ap-6074	195	2	solutions	solution	NOUN
ap-6074	195	3	are	be	AUX
ap-6074	195	4	identical	identical	ADJ
ap-6074	195	5	from	from	ADP
ap-6074	195	6	the	the	DET
ap-6074	195	7	geometrical	geometrical	ADJ
ap-6074	195	8	point	point	NOUN
ap-6074	195	9	of	of	ADP
ap-6074	195	10	view	view	NOUN
ap-6074	195	11	,	,	PUNCT
ap-6074	195	12	because	because	SCONJ
ap-6074	195	13	the	the	DET
ap-6074	195	14	shape	shape	NOUN
ap-6074	195	15	of	of	ADP
ap-6074	195	16	involute	involute	ADJ
ap-6074	195	17	curves	curve	NOUN
ap-6074	195	18	obtained	obtain	VERB
ap-6074	195	19	by	by	ADP
ap-6074	195	20	substituting	substitute	VERB
ap-6074	195	21	v	v	ADP
ap-6074	195	22	=	=	SYM
ap-6074	195	23	−u	−u	PROPN
ap-6074	195	24	as	as	ADV
ap-6074	195	25	well	well	ADV
ap-6074	195	26	as	as	ADP
ap-6074	195	27	u	u	NOUN
ap-6074	195	28	=	=	NOUN
ap-6074	195	29	−v	−v	NOUN
ap-6074	195	30	in	in	ADP
ap-6074	195	31	(	(	PUNCT
ap-6074	195	32	26	26	NUM
ap-6074	195	33	)	)	PUNCT
ap-6074	195	34	is	be	AUX
ap-6074	195	35	the	the	DET
ap-6074	195	36	same	same	ADJ
ap-6074	195	37	.	.	PUNCT
ap-6074	196	1	however	however	ADV
ap-6074	196	2	,	,	PUNCT
ap-6074	196	3	from	from	ADP
ap-6074	196	4	mathematical	mathematical	ADJ
ap-6074	196	5	point	point	NOUN
ap-6074	196	6	of	of	ADP
ap-6074	196	7	view	view	NOUN
ap-6074	196	8	,	,	PUNCT
ap-6074	196	9	the	the	DET
ap-6074	196	10	later	later	ADJ
ap-6074	196	11	solution	solution	NOUN
ap-6074	196	12	and	and	CCONJ
ap-6074	196	13	the	the	DET
ap-6074	196	14	interchange	interchange	NOUN
ap-6074	196	15	of	of	ADP
ap-6074	196	16	parameters	parameter	NOUN
ap-6074	196	17	u	u	NOUN
ap-6074	196	18	and	and	CCONJ
ap-6074	196	19	v	v	NOUN
ap-6074	196	20	is	be	AUX
ap-6074	196	21	preferable	preferable	ADJ
ap-6074	196	22	.	.	PUNCT
ap-6074	197	1	thus	thus	ADV
ap-6074	197	2	,	,	PUNCT
ap-6074	197	3	the	the	DET
ap-6074	197	4	involute	involute	NOUN
ap-6074	197	5	e	e	NOUN
ap-6074	197	6	obtained	obtain	VERB
ap-6074	197	7	by	by	ADP
ap-6074	197	8	substituting	substitute	VERB
ap-6074	197	9	u	u	NOUN
ap-6074	197	10	=	=	PROPN
ap-6074	197	11	v	v	NOUN
ap-6074	197	12	in	in	ADP
ap-6074	197	13	(	(	PUNCT
ap-6074	197	14	26	26	NUM
ap-6074	197	15	)	)	PUNCT
ap-6074	197	16	e	e	NOUN
ap-6074	197	17	:	:	PUNCT
ap-6074	197	18	e(v	e(v	NOUN
ap-6074	197	19	)	)	PUNCT
ap-6074	197	20	=	=	SYM
ap-6074	197	21	(	(	PUNCT
ap-6074	197	22	xe(v	xe(v	NOUN
ap-6074	197	23	)	)	PUNCT
ap-6074	197	24	,	,	PUNCT
ap-6074	197	25	ye(v	ye(v	NOUN
ap-6074	197	26	)	)	PUNCT
ap-6074	197	27	,	,	PUNCT
ap-6074	197	28	ze(v	ze(v	NOUN
ap-6074	197	29	)	)	PUNCT
ap-6074	197	30	,	,	PUNCT
ap-6074	197	31	1	1	X
ap-6074	197	32	)	)	PUNCT
ap-6074	197	33	x	x	X
ap-6074	197	34	z	z	PUNCT
ap-6074	197	35	r	r	NOUN
ap-6074	197	36	σ	σ	PROPN
ap-6074	197	37	b	b	PROPN
ap-6074	197	38	e	e	X
ap-6074	197	39	b	b	PROPN
ap-6074	197	40	s	s	PROPN
ap-6074	197	41	b	b	X
ap-6074	197	42	o	o	X
ap-6074	197	43	u	u	NOUN
ap-6074	197	44	v	v	ADP
ap-6074	197	45	y	y	PROPN
ap-6074	197	46	k	k	PROPN
ap-6074	197	47	figure	figure	NOUN
ap-6074	197	48	13	13	NUM
ap-6074	197	49	.	.	PUNCT
ap-6074	197	50	ruled	rule	VERB
ap-6074	197	51	involute	involute	ADJ
ap-6074	197	52	surface	surface	NOUN
ap-6074	197	53	.	.	PUNCT
ap-6074	197	54	is	be	AUX
ap-6074	197	55	given	give	VERB
ap-6074	197	56	by	by	ADP
ap-6074	197	57	e(v	e(v	NOUN
ap-6074	197	58	)	)	PUNCT
ap-6074	197	59	=(	=(	NOUN
ap-6074	197	60	rb(cos	rb(cos	PROPN
ap-6074	197	61	v	v	PROPN
ap-6074	197	62	+	+	NUM
ap-6074	197	63	v	v	ADP
ap-6074	197	64	sin	sin	NOUN
ap-6074	197	65	v	v	NOUN
ap-6074	197	66	)	)	PUNCT
ap-6074	197	67	,	,	PUNCT
ap-6074	197	68	rb(sin	rb(sin	VERB
ap-6074	197	69	v	v	ADP
ap-6074	197	70	−	−	PROPN
ap-6074	197	71	v	v	PROPN
ap-6074	197	72	cos	cos	PROPN
ap-6074	197	73	v	v	NOUN
ap-6074	197	74	)	)	PUNCT
ap-6074	197	75	,	,	PUNCT
ap-6074	197	76	0	0	NUM
ap-6074	197	77	,	,	PUNCT
ap-6074	197	78	1	1	NUM
ap-6074	197	79	)	)	PUNCT
ap-6074	197	80	,	,	PUNCT
ap-6074	197	81	v	v	PART
ap-6074	197	82	≥	≥	NOUN
ap-6074	197	83	0	0	NUM
ap-6074	197	84	(	(	PUNCT
ap-6074	197	85	27	27	NUM
ap-6074	197	86	)	)	PUNCT
ap-6074	197	87	note	note	NOUN
ap-6074	197	88	that	that	SCONJ
ap-6074	197	89	the	the	DET
ap-6074	197	90	flank	flank	NOUN
ap-6074	197	91	surface	surface	NOUN
ap-6074	197	92	of	of	ADP
ap-6074	197	93	a	a	DET
ap-6074	197	94	helical	helical	ADJ
ap-6074	197	95	gear	gear	NOUN
ap-6074	197	96	can	can	AUX
ap-6074	197	97	be	be	AUX
ap-6074	197	98	generated	generate	VERB
ap-6074	197	99	by	by	ADP
ap-6074	197	100	a	a	DET
ap-6074	197	101	screw	screw	ADJ
ap-6074	197	102	motion	motion	NOUN
ap-6074	197	103	of	of	ADP
ap-6074	197	104	the	the	DET
ap-6074	197	105	involute	involute	ADJ
ap-6074	197	106	profile	profile	NOUN
ap-6074	197	107	,	,	PUNCT
ap-6074	197	108	too	too	ADV
ap-6074	197	109	.	.	PUNCT
ap-6074	198	1	4.2	4.2	NUM
ap-6074	198	2	.	.	PUNCT
ap-6074	198	3	involute	involute	PROPN
ap-6074	198	4	ruled	rule	VERB
ap-6074	198	5	surface	surface	NOUN
ap-6074	198	6	the	the	DET
ap-6074	198	7	surface	surface	NOUN
ap-6074	198	8	of	of	ADP
ap-6074	198	9	the	the	DET
ap-6074	198	10	involute	involute	ADJ
ap-6074	198	11	spur	spur	NOUN
ap-6074	198	12	tooth	tooth	NOUN
ap-6074	198	13	flank	flank	NOUN
ap-6074	198	14	σs	σs	ADP
ap-6074	198	15	:	:	PUNCT
ap-6074	198	16	ss(u	ss(u	ADJ
ap-6074	198	17	,	,	PUNCT
ap-6074	198	18	v	v	NOUN
ap-6074	198	19	)	)	PUNCT
ap-6074	198	20	is	be	AUX
ap-6074	198	21	generated	generate	VERB
ap-6074	198	22	by	by	ADP
ap-6074	198	23	a	a	DET
ap-6074	198	24	translation	translation	NOUN
ap-6074	198	25	of	of	ADP
ap-6074	198	26	involute	involute	ADJ
ap-6074	198	27	e	e	NOUN
ap-6074	198	28	given	give	VERB
ap-6074	198	29	by	by	ADP
ap-6074	198	30	(	(	PUNCT
ap-6074	198	31	27	27	NUM
ap-6074	198	32	)	)	PUNCT
ap-6074	198	33	along	along	ADP
ap-6074	198	34	a	a	DET
ap-6074	198	35	straight	straight	ADJ
ap-6074	198	36	line	line	NOUN
ap-6074	198	37	k	k	PROPN
ap-6074	198	38	‖	‖	PROPN
ap-6074	198	39	z	z	PROPN
ap-6074	198	40	ss(u	ss(u	PROPN
ap-6074	198	41	,	,	PUNCT
ap-6074	198	42	v	v	NOUN
ap-6074	198	43	)	)	PUNCT
ap-6074	198	44	=	=	SYM
ap-6074	199	1	(	(	PUNCT
ap-6074	199	2	rb(cos	rb(cos	PROPN
ap-6074	199	3	v+	v+	X
ap-6074	199	4	v	v	ADP
ap-6074	199	5	sin	sin	NOUN
ap-6074	199	6	v	v	NOUN
ap-6074	199	7	)	)	PUNCT
ap-6074	200	1	,	,	PUNCT
ap-6074	200	2	rb(sin	rb(sin	NOUN
ap-6074	200	3	v−	v−	PROPN
ap-6074	200	4	v	v	PROPN
ap-6074	200	5	cos	cos	PROPN
ap-6074	200	6	v	v	NOUN
ap-6074	200	7	)	)	PUNCT
ap-6074	200	8	,	,	PUNCT
ap-6074	200	9	u	u	NOUN
ap-6074	200	10	,	,	PUNCT
ap-6074	200	11	1	1	NUM
ap-6074	200	12	)	)	PUNCT
ap-6074	200	13	,	,	PUNCT
ap-6074	200	14	see	see	VERB
ap-6074	200	15	fig	fig	NOUN
ap-6074	200	16	.	.	PUNCT
ap-6074	201	1	13	13	NUM
ap-6074	201	2	.	.	X
ap-6074	202	1	parametric	parametric	PROPN
ap-6074	202	2	u	u	NOUN
ap-6074	202	3	-	-	NOUN
ap-6074	202	4	curves	curve	NOUN
ap-6074	202	5	are	be	AUX
ap-6074	202	6	straight	straight	ADJ
ap-6074	202	7	lines	line	NOUN
ap-6074	202	8	parallel	parallel	ADJ
ap-6074	202	9	with	with	ADP
ap-6074	202	10	z	z	NOUN
ap-6074	202	11	axis	axis	NOUN
ap-6074	202	12	,	,	PUNCT
ap-6074	202	13	parametric	parametric	ADJ
ap-6074	202	14	v	v	NOUN
ap-6074	202	15	-	-	PUNCT
ap-6074	202	16	curves	curve	NOUN
ap-6074	202	17	are	be	AUX
ap-6074	202	18	involutes	involute	NOUN
ap-6074	202	19	(	(	PUNCT
ap-6074	202	20	27	27	NUM
ap-6074	202	21	)	)	PUNCT
ap-6074	202	22	lying	lie	VERB
ap-6074	202	23	in	in	ADP
ap-6074	202	24	planes	plane	NOUN
ap-6074	202	25	perpendicular	perpendicular	NOUN
ap-6074	202	26	to	to	ADP
ap-6074	202	27	z	z	PROPN
ap-6074	202	28	axis	axis	NOUN
ap-6074	202	29	.	.	PUNCT
ap-6074	203	1	4.3	4.3	NUM
ap-6074	203	2	.	.	PUNCT
ap-6074	203	3	smart	smart	ADJ
ap-6074	203	4	gear	gear	NOUN
ap-6074	203	5	measurement	measurement	NOUN
ap-6074	203	6	standard	standard	NOUN
ap-6074	203	7	in	in	ADP
ap-6074	203	8	gear	gear	NOUN
ap-6074	203	9	metrology	metrology	NOUN
ap-6074	203	10	,	,	PUNCT
ap-6074	203	11	precise	precise	ADJ
ap-6074	203	12	gear	gear	NOUN
ap-6074	203	13	measurement	measurement	NOUN
ap-6074	203	14	standards	standard	NOUN
ap-6074	203	15	of	of	ADP
ap-6074	203	16	various	various	ADJ
ap-6074	203	17	designs	design	NOUN
ap-6074	203	18	and	and	CCONJ
ap-6074	203	19	purposes	purpose	NOUN
ap-6074	203	20	are	be	AUX
ap-6074	203	21	developed	develop	VERB
ap-6074	203	22	,	,	PUNCT
ap-6074	203	23	manufactured	manufacture	VERB
ap-6074	203	24	and	and	CCONJ
ap-6074	203	25	calibrated	calibrate	VERB
ap-6074	203	26	.	.	PUNCT
ap-6074	204	1	for	for	ADP
ap-6074	204	2	example	example	NOUN
ap-6074	204	3	,	,	PUNCT
ap-6074	204	4	for	for	ADP
ap-6074	204	5	a	a	DET
ap-6074	204	6	profile	profile	NOUN
ap-6074	204	7	and	and	CCONJ
ap-6074	204	8	helix	helix	ADJ
ap-6074	204	9	inspection	inspection	NOUN
ap-6074	204	10	,	,	PUNCT
ap-6074	204	11	the	the	DET
ap-6074	204	12	internal	internal	ADJ
ap-6074	204	13	involute	involute	ADJ
ap-6074	204	14	scanning	scanning	NOUN
ap-6074	204	15	measurement	measurement	NOUN
ap-6074	204	16	standards	standard	NOUN
ap-6074	204	17	developed	develop	VERB
ap-6074	204	18	by	by	ADP
ap-6074	204	19	physikalischtechnische	physikalischtechnische	PROPN
ap-6074	204	20	bundesanstalt	bundesanstalt	PROPN
ap-6074	204	21	(	(	PUNCT
ap-6074	204	22	ptb	ptb	PROPN
ap-6074	204	23	)	)	PUNCT
ap-6074	204	24	contains	contain	VERB
ap-6074	204	25	both	both	CCONJ
ap-6074	204	26	the	the	DET
ap-6074	204	27	precise	precise	ADJ
ap-6074	204	28	internal	internal	ADJ
ap-6074	204	29	and	and	CCONJ
ap-6074	204	30	external	external	ADJ
ap-6074	204	31	involute	involute	ADJ
ap-6074	204	32	profiles	profile	NOUN
ap-6074	204	33	[	[	X
ap-6074	204	34	9	9	NUM
ap-6074	204	35	]	]	PUNCT
ap-6074	204	36	and	and	CCONJ
ap-6074	204	37	profiles	profile	NOUN
ap-6074	204	38	with	with	ADP
ap-6074	204	39	a	a	DET
ap-6074	204	40	certain	certain	ADJ
ap-6074	204	41	waviness	waviness	NOUN
ap-6074	204	42	superposed	superpose	VERB
ap-6074	204	43	[	[	PUNCT
ap-6074	204	44	10	10	NUM
ap-6074	204	45	]	]	PUNCT
ap-6074	204	46	,	,	PUNCT
ap-6074	204	47	which	which	PRON
ap-6074	204	48	enable	enable	VERB
ap-6074	204	49	to	to	PART
ap-6074	204	50	characterise	characterise	VERB
ap-6074	204	51	the	the	DET
ap-6074	204	52	dynamic	dynamic	ADJ
ap-6074	204	53	behaviour	behaviour	NOUN
ap-6074	204	54	of	of	ADP
ap-6074	204	55	the	the	DET
ap-6074	204	56	probing	probe	VERB
ap-6074	204	57	system	system	NOUN
ap-6074	204	58	.	.	PUNCT
ap-6074	205	1	the	the	DET
ap-6074	205	2	large	large	ADJ
ap-6074	205	3	gear	gear	NOUN
ap-6074	205	4	measurement	measurement	NOUN
ap-6074	205	5	standard	standard	NOUN
ap-6074	205	6	(	(	PUNCT
ap-6074	205	7	ptb	ptb	PROPN
ap-6074	205	8	)	)	PUNCT
ap-6074	205	9	is	be	AUX
ap-6074	205	10	designed	design	VERB
ap-6074	205	11	as	as	ADP
ap-6074	205	12	a	a	DET
ap-6074	205	13	segment	segment	NOUN
ap-6074	205	14	of	of	ADP
ap-6074	205	15	a	a	DET
ap-6074	205	16	complete	complete	ADJ
ap-6074	205	17	gear	gear	NOUN
ap-6074	205	18	[	[	X
ap-6074	205	19	11	11	NUM
ap-6074	205	20	]	]	PUNCT
ap-6074	205	21	and	and	CCONJ
ap-6074	205	22	large	large	ADJ
ap-6074	205	23	ring	ring	NOUN
ap-6074	205	24	gear	gear	NOUN
ap-6074	205	25	measurement	measurement	NOUN
ap-6074	205	26	standard	standard	NOUN
ap-6074	205	27	(	(	PUNCT
ap-6074	205	28	ptb	ptb	PROPN
ap-6074	205	29	)	)	PUNCT
ap-6074	205	30	embodies	embody	VERB
ap-6074	205	31	three	three	NUM
ap-6074	205	32	different	different	ADJ
ap-6074	205	33	internal	internal	ADJ
ap-6074	205	34	and	and	CCONJ
ap-6074	205	35	external	external	ADJ
ap-6074	205	36	gearing	gearing	NOUN
ap-6074	205	37	,	,	PUNCT
ap-6074	205	38	each	each	DET
ap-6074	205	39	one	one	NUM
ap-6074	205	40	with	with	ADP
ap-6074	205	41	helix	helix	ADJ
ap-6074	205	42	angles	angle	NOUN
ap-6074	205	43	of	of	ADP
ap-6074	205	44	0	0	NUM
ap-6074	205	45	°	°	NOUN
ap-6074	205	46	(	(	PUNCT
ap-6074	205	47	spur	spur	VERB
ap-6074	205	48	gearing	gearing	NOUN
ap-6074	205	49	)	)	PUNCT
ap-6074	205	50	,	,	PUNCT
ap-6074	205	51	10	10	NUM
ap-6074	205	52	°	°	NUM
ap-6074	205	53	and	and	CCONJ
ap-6074	205	54	20	20	NUM
ap-6074	205	55	°	°	NOUN
ap-6074	206	1	[	[	X
ap-6074	206	2	12	12	NUM
ap-6074	206	3	]	]	PUNCT
ap-6074	206	4	.	.	PUNCT
ap-6074	207	1	all	all	DET
ap-6074	207	2	the	the	DET
ap-6074	207	3	specially	specially	ADV
ap-6074	207	4	designed	design	VERB
ap-6074	207	5	or	or	CCONJ
ap-6074	207	6	commercially	commercially	ADV
ap-6074	207	7	produced	produce	VERB
ap-6074	207	8	gear	gear	NOUN
ap-6074	207	9	measurement	measurement	NOUN
ap-6074	207	10	standards	standard	NOUN
ap-6074	207	11	for	for	ADP
ap-6074	207	12	the	the	DET
ap-6074	207	13	profile	profile	NOUN
ap-6074	207	14	and	and	CCONJ
ap-6074	207	15	helix	helix	ADJ
ap-6074	207	16	inspection	inspection	NOUN
ap-6074	207	17	contain	contain	VERB
ap-6074	207	18	separate	separate	ADJ
ap-6074	207	19	geometry	geometry	NOUN
ap-6074	207	20	for	for	ADP
ap-6074	207	21	each	each	DET
ap-6074	207	22	type	type	NOUN
ap-6074	207	23	of	of	ADP
ap-6074	207	24	gearing	gearing	NOUN
ap-6074	207	25	.	.	PUNCT
ap-6074	208	1	106	106	NUM
ap-6074	208	2	vol	vol	NOUN
ap-6074	208	3	.	.	PUNCT
ap-6074	209	1	61	61	NUM
ap-6074	209	2	special	special	ADJ
ap-6074	209	3	issue/2021	issue/2021	NOUN
ap-6074	209	4	application	application	NOUN
ap-6074	209	5	of	of	ADP
ap-6074	209	6	ruled	rule	VERB
ap-6074	209	7	surfaces	surface	NOUN
ap-6074	209	8	in	in	ADP
ap-6074	209	9	freeform	freeform	NOUN
ap-6074	209	10	and	and	CCONJ
ap-6074	209	11	gear	gear	NOUN
ap-6074	209	12	metrology	metrology	NOUN
ap-6074	209	13	figure	figure	NOUN
ap-6074	209	14	14	14	NUM
ap-6074	209	15	.	.	PUNCT
ap-6074	210	1	cad	cad	PROPN
ap-6074	210	2	model	model	NOUN
ap-6074	210	3	of	of	ADP
ap-6074	210	4	smart	smart	ADJ
ap-6074	210	5	gear	gear	NOUN
ap-6074	210	6	standard	standard	NOUN
ap-6074	210	7	.	.	PUNCT
ap-6074	211	1	the	the	DET
ap-6074	211	2	contrary	contrary	NOUN
ap-6074	211	3	,	,	PUNCT
ap-6074	211	4	the	the	DET
ap-6074	211	5	flank	flank	NOUN
ap-6074	211	6	surface	surface	NOUN
ap-6074	211	7	of	of	ADP
ap-6074	211	8	the	the	DET
ap-6074	211	9	smart	smart	ADJ
ap-6074	211	10	gear	gear	NOUN
ap-6074	211	11	measurement	measurement	NOUN
ap-6074	211	12	standard	standard	NOUN
ap-6074	211	13	(	(	PUNCT
ap-6074	211	14	developed	develop	VERB
ap-6074	211	15	by	by	ADP
ap-6074	211	16	the	the	DET
ap-6074	211	17	cmi	cmi	NOUN
ap-6074	211	18	in	in	ADP
ap-6074	211	19	cooperation	cooperation	NOUN
ap-6074	211	20	with	with	ADP
ap-6074	211	21	ctu	ctu	NOUN
ap-6074	211	22	)	)	PUNCT
ap-6074	211	23	is	be	AUX
ap-6074	211	24	represented	represent	VERB
ap-6074	211	25	by	by	ADP
ap-6074	211	26	a	a	DET
ap-6074	211	27	tangent	tangent	ADJ
ap-6074	211	28	surface	surface	NOUN
ap-6074	211	29	of	of	ADP
ap-6074	211	30	the	the	DET
ap-6074	211	31	helix	helix	NOUN
ap-6074	211	32	on	on	ADP
ap-6074	211	33	which	which	PRON
ap-6074	211	34	all	all	DET
ap-6074	211	35	three	three	NUM
ap-6074	211	36	types	type	NOUN
ap-6074	211	37	of	of	ADP
ap-6074	211	38	curves	curve	NOUN
ap-6074	211	39	(	(	PUNCT
ap-6074	211	40	straight	straight	ADJ
ap-6074	211	41	lines	line	NOUN
ap-6074	211	42	,	,	PUNCT
ap-6074	211	43	involutes	involute	NOUN
ap-6074	211	44	and	and	CCONJ
ap-6074	211	45	helices	helix	NOUN
ap-6074	211	46	)	)	PUNCT
ap-6074	211	47	important	important	ADJ
ap-6074	211	48	in	in	ADP
ap-6074	211	49	gear	gear	NOUN
ap-6074	211	50	profile	profile	NOUN
ap-6074	211	51	and	and	CCONJ
ap-6074	211	52	helix	helix	ADJ
ap-6074	211	53	inspection	inspection	NOUN
ap-6074	211	54	are	be	AUX
ap-6074	211	55	located	locate	VERB
ap-6074	211	56	.	.	PUNCT
ap-6074	212	1	consequently	consequently	ADV
ap-6074	212	2	,	,	PUNCT
ap-6074	212	3	it	it	PRON
ap-6074	212	4	is	be	AUX
ap-6074	212	5	possible	possible	ADJ
ap-6074	212	6	to	to	PART
ap-6074	212	7	measure	measure	VERB
ap-6074	212	8	profile	profile	NOUN
ap-6074	212	9	and	and	CCONJ
ap-6074	212	10	helix	helix	ADJ
ap-6074	212	11	deviations	deviation	NOUN
ap-6074	212	12	of	of	ADP
ap-6074	212	13	different	different	ADJ
ap-6074	212	14	gearings	gearing	NOUN
ap-6074	212	15	on	on	ADP
ap-6074	212	16	one	one	NUM
ap-6074	212	17	geometry	geometry	NOUN
ap-6074	212	18	.	.	PUNCT
ap-6074	213	1	the	the	DET
ap-6074	213	2	cad	cad	PROPN
ap-6074	213	3	model	model	NOUN
ap-6074	213	4	of	of	ADP
ap-6074	213	5	the	the	DET
ap-6074	213	6	smart	smart	ADJ
ap-6074	213	7	gear	gear	NOUN
ap-6074	213	8	measurement	measurement	NOUN
ap-6074	213	9	standard	standard	NOUN
ap-6074	213	10	is	be	AUX
ap-6074	213	11	shown	show	VERB
ap-6074	213	12	in	in	ADP
ap-6074	213	13	(	(	PUNCT
ap-6074	213	14	fig	fig	NOUN
ap-6074	213	15	.	.	PUNCT
ap-6074	214	1	14	14	NUM
ap-6074	214	2	)	)	PUNCT
ap-6074	214	3	.	.	PUNCT
ap-6074	215	1	note	note	VERB
ap-6074	215	2	that	that	SCONJ
ap-6074	215	3	both	both	CCONJ
ap-6074	215	4	the	the	DET
ap-6074	215	5	helix	helix	NOUN
ap-6074	215	6	and	and	CCONJ
ap-6074	215	7	involute	involute	ADJ
ap-6074	215	8	are	be	AUX
ap-6074	215	9	transcendental	transcendental	ADJ
ap-6074	215	10	curves	curve	NOUN
ap-6074	215	11	,	,	PUNCT
ap-6074	215	12	i.e.	i.e.	X
ap-6074	215	13	,	,	PUNCT
ap-6074	215	14	they	they	PRON
ap-6074	215	15	have	have	VERB
ap-6074	215	16	neither	neither	CCONJ
ap-6074	215	17	polynomial	polynomial	ADJ
ap-6074	215	18	nor	nor	CCONJ
ap-6074	215	19	rational	rational	ADJ
ap-6074	215	20	parameterisation	parameterisation	NOUN
ap-6074	215	21	.	.	PUNCT
ap-6074	216	1	consequently	consequently	ADV
ap-6074	216	2	,	,	PUNCT
ap-6074	216	3	it	it	PRON
ap-6074	216	4	is	be	AUX
ap-6074	216	5	impossible	impossible	ADJ
ap-6074	216	6	to	to	PART
ap-6074	216	7	express	express	VERB
ap-6074	216	8	them	they	PRON
ap-6074	216	9	by	by	ADP
ap-6074	216	10	nurbs	nurb	NOUN
ap-6074	216	11	(	(	PUNCT
ap-6074	216	12	non	non	ADJ
ap-6074	216	13	-	-	ADJ
ap-6074	216	14	uniform	uniform	ADJ
ap-6074	216	15	b	b	NOUN
ap-6074	216	16	-	-	PUNCT
ap-6074	216	17	spline	spline	NOUN
ap-6074	216	18	)	)	PUNCT
ap-6074	216	19	representation	representation	NOUN
ap-6074	216	20	,	,	PUNCT
ap-6074	216	21	which	which	PRON
ap-6074	216	22	is	be	AUX
ap-6074	216	23	the	the	DET
ap-6074	216	24	theoretical	theoretical	ADJ
ap-6074	216	25	basis	basis	NOUN
ap-6074	216	26	of	of	ADP
ap-6074	216	27	cad	cad	PROPN
ap-6074	216	28	systems	system	NOUN
ap-6074	216	29	.	.	PUNCT
ap-6074	217	1	thus	thus	ADV
ap-6074	217	2	,	,	PUNCT
ap-6074	217	3	their	their	PRON
ap-6074	217	4	precise	precise	ADJ
ap-6074	217	5	cad	cad	NOUN
ap-6074	217	6	model	model	NOUN
ap-6074	217	7	can	can	AUX
ap-6074	217	8	not	not	PART
ap-6074	217	9	be	be	AUX
ap-6074	217	10	created	create	VERB
ap-6074	217	11	.	.	PUNCT
ap-6074	218	1	usually	usually	ADV
ap-6074	218	2	,	,	PUNCT
ap-6074	218	3	more	more	ADJ
ap-6074	218	4	or	or	CCONJ
ap-6074	218	5	less	less	ADV
ap-6074	218	6	accurate	accurate	ADJ
ap-6074	218	7	approximation	approximation	NOUN
ap-6074	218	8	by	by	ADP
ap-6074	218	9	means	mean	NOUN
ap-6074	218	10	of	of	ADP
ap-6074	218	11	b	b	NOUN
ap-6074	218	12	-	-	PUNCT
ap-6074	218	13	spline	spline	NOUN
ap-6074	218	14	curves	curve	NOUN
ap-6074	218	15	is	be	AUX
ap-6074	218	16	used	use	VERB
ap-6074	218	17	in	in	ADP
ap-6074	218	18	cad	cad	PROPN
ap-6074	218	19	systems	system	NOUN
ap-6074	218	20	[	[	X
ap-6074	218	21	13	13	NUM
ap-6074	218	22	]	]	PUNCT
ap-6074	218	23	.	.	PUNCT
ap-6074	219	1	involute	involute	ADJ
ap-6074	219	2	is	be	AUX
ap-6074	219	3	not	not	PART
ap-6074	219	4	implemented	implement	VERB
ap-6074	219	5	in	in	ADP
ap-6074	219	6	cad	cad	PROPN
ap-6074	219	7	systems	system	NOUN
ap-6074	219	8	yet	yet	ADV
ap-6074	219	9	.	.	PUNCT
ap-6074	220	1	the	the	DET
ap-6074	220	2	standard	standard	NOUN
ap-6074	220	3	has	have	VERB
ap-6074	220	4	a	a	DET
ap-6074	220	5	box	box	NOUN
ap-6074	220	6	base	base	NOUN
ap-6074	220	7	140	140	NUM
ap-6074	220	8	×	×	NOUN
ap-6074	220	9	140	140	NUM
ap-6074	220	10	×	×	NOUN
ap-6074	220	11	10	10	NUM
ap-6074	220	12	mm	mm	NOUN
ap-6074	220	13	(	(	PUNCT
ap-6074	220	14	drawn	draw	VERB
ap-6074	220	15	in	in	ADP
ap-6074	220	16	grey	grey	PROPN
ap-6074	220	17	in	in	ADP
ap-6074	220	18	fig	fig	NOUN
ap-6074	220	19	.	.	PUNCT
ap-6074	221	1	14	14	NUM
ap-6074	221	2	)	)	PUNCT
ap-6074	221	3	.	.	PUNCT
ap-6074	222	1	the	the	DET
ap-6074	222	2	origin	origin	NOUN
ap-6074	222	3	of	of	ADP
ap-6074	222	4	the	the	DET
ap-6074	222	5	coordinate	coordinate	NOUN
ap-6074	222	6	system	system	NOUN
ap-6074	222	7	lying	lie	VERB
ap-6074	222	8	in	in	ADP
ap-6074	222	9	the	the	DET
ap-6074	222	10	upper	upper	ADJ
ap-6074	222	11	face	face	NOUN
ap-6074	222	12	of	of	ADP
ap-6074	222	13	the	the	DET
ap-6074	222	14	box	box	NOUN
ap-6074	222	15	is	be	AUX
ap-6074	222	16	determined	determine	VERB
ap-6074	222	17	by	by	ADP
ap-6074	222	18	the	the	DET
ap-6074	222	19	centre	centre	NOUN
ap-6074	222	20	of	of	ADP
ap-6074	222	21	a	a	DET
ap-6074	222	22	cylindrical	cylindrical	ADJ
ap-6074	222	23	hole	hole	NOUN
ap-6074	222	24	with	with	ADP
ap-6074	222	25	the	the	DET
ap-6074	222	26	base	base	NOUN
ap-6074	222	27	diameter	diameter	NOUN
ap-6074	222	28	db	db	PROPN
ap-6074	222	29	(	(	PUNCT
ap-6074	222	30	cyan	cyan	PROPN
ap-6074	222	31	)	)	PUNCT
ap-6074	222	32	.	.	PUNCT
ap-6074	223	1	the	the	DET
ap-6074	223	2	direction	direction	NOUN
ap-6074	223	3	of	of	ADP
ap-6074	223	4	y	y	NOUN
ap-6074	223	5	-	-	PUNCT
ap-6074	223	6	axis	axis	NOUN
ap-6074	223	7	is	be	AUX
ap-6074	223	8	defined	define	VERB
ap-6074	223	9	by	by	ADP
ap-6074	223	10	the	the	DET
ap-6074	223	11	centre	centre	NOUN
ap-6074	223	12	of	of	ADP
ap-6074	223	13	the	the	DET
ap-6074	223	14	cylindrical	cylindrical	ADJ
ap-6074	223	15	hole	hole	NOUN
ap-6074	223	16	diameter	diameter	NOUN
ap-6074	223	17	of	of	ADP
ap-6074	223	18	10	10	NUM
ap-6074	223	19	mm	mm	NOUN
ap-6074	223	20	(	(	PUNCT
ap-6074	223	21	yellow	yellow	PROPN
ap-6074	223	22	)	)	PUNCT
ap-6074	223	23	.	.	PUNCT
ap-6074	224	1	the	the	DET
ap-6074	224	2	upper	upper	ADJ
ap-6074	224	3	face	face	NOUN
ap-6074	224	4	of	of	ADP
ap-6074	224	5	the	the	DET
ap-6074	224	6	box	box	NOUN
ap-6074	224	7	defines	define	NOUN
ap-6074	224	8	(	(	PUNCT
ap-6074	224	9	x	x	NOUN
ap-6074	224	10	,	,	PUNCT
ap-6074	224	11	y	y	NOUN
ap-6074	224	12	)	)	PUNCT
ap-6074	224	13	plane	plane	NOUN
ap-6074	224	14	,	,	PUNCT
ap-6074	224	15	z	z	NOUN
ap-6074	224	16	axis	axis	NOUN
ap-6074	224	17	is	be	AUX
ap-6074	224	18	perpendicular	perpendicular	ADJ
ap-6074	224	19	to	to	ADP
ap-6074	224	20	it	it	PRON
ap-6074	224	21	.	.	PUNCT
ap-6074	225	1	the	the	DET
ap-6074	225	2	10	10	NUM
ap-6074	225	3	mm	mm	INTJ
ap-6074	225	4	high	high	ADJ
ap-6074	225	5	involute	involute	NOUN
ap-6074	225	6	ruled	rule	VERB
ap-6074	225	7	surface	surface	NOUN
ap-6074	225	8	placed	place	VERB
ap-6074	225	9	on	on	ADP
ap-6074	225	10	the	the	DET
ap-6074	225	11	upper	upper	ADJ
ap-6074	225	12	face	face	NOUN
ap-6074	225	13	of	of	ADP
ap-6074	225	14	the	the	DET
ap-6074	225	15	box	box	NOUN
ap-6074	225	16	represents	represent	VERB
ap-6074	225	17	the	the	DET
ap-6074	225	18	external	external	ADJ
ap-6074	225	19	and	and	CCONJ
ap-6074	225	20	internal	internal	ADJ
ap-6074	225	21	spur	spur	NOUN
ap-6074	225	22	involute	involute	ADJ
ap-6074	225	23	flank	flank	NOUN
ap-6074	225	24	surface	surface	NOUN
ap-6074	225	25	(	(	PUNCT
ap-6074	225	26	magenta	magenta	NOUN
ap-6074	225	27	and	and	CCONJ
ap-6074	225	28	red	red	ADJ
ap-6074	225	29	)	)	PUNCT
ap-6074	225	30	.	.	PUNCT
ap-6074	226	1	the	the	DET
ap-6074	226	2	external	external	ADJ
ap-6074	226	3	and	and	CCONJ
ap-6074	226	4	internal	internal	ADJ
ap-6074	226	5	helical	helical	ADJ
ap-6074	226	6	involute	involute	ADJ
ap-6074	226	7	flank	flank	NOUN
ap-6074	226	8	surface	surface	NOUN
ap-6074	226	9	(	(	PUNCT
ap-6074	226	10	green	green	ADJ
ap-6074	226	11	and	and	CCONJ
ap-6074	226	12	blue	blue	ADJ
ap-6074	226	13	)	)	PUNCT
ap-6074	226	14	is	be	AUX
ap-6074	226	15	represented	represent	VERB
ap-6074	226	16	by	by	ADP
ap-6074	226	17	the	the	DET
ap-6074	226	18	tangent	tangent	ADJ
ap-6074	226	19	surface	surface	NOUN
ap-6074	226	20	of	of	ADP
ap-6074	226	21	the	the	DET
ap-6074	226	22	base	base	NOUN
ap-6074	226	23	helix	helix	NOUN
ap-6074	226	24	trimmed	trim	VERB
ap-6074	226	25	by	by	ADP
ap-6074	226	26	planes	plane	NOUN
ap-6074	226	27	z	z	NOUN
ap-6074	226	28	=	=	SYM
ap-6074	226	29	10	10	NUM
ap-6074	226	30	and	and	CCONJ
ap-6074	226	31	z	z	NOUN
ap-6074	226	32	=	=	SYM
ap-6074	226	33	50	50	NUM
ap-6074	226	34	mm	mm	INTJ
ap-6074	226	35	(	(	PUNCT
ap-6074	226	36	violet	violet	NOUN
ap-6074	226	37	)	)	PUNCT
ap-6074	226	38	.	.	PUNCT
ap-6074	227	1	the	the	DET
ap-6074	227	2	most	most	ADV
ap-6074	227	3	important	important	ADJ
ap-6074	227	4	shape	shape	NOUN
ap-6074	227	5	figure	figure	NOUN
ap-6074	227	6	included	include	VERB
ap-6074	227	7	in	in	ADP
ap-6074	227	8	the	the	DET
ap-6074	227	9	tangent	tangent	ADJ
ap-6074	227	10	surface	surface	NOUN
ap-6074	227	11	of	of	ADP
ap-6074	227	12	the	the	DET
ap-6074	227	13	base	base	NOUN
ap-6074	227	14	helix	helix	NOUN
ap-6074	227	15	corresponds	correspond	NOUN
ap-6074	227	16	to	to	ADP
ap-6074	227	17	the	the	DET
ap-6074	227	18	real	real	ADJ
ap-6074	227	19	helical	helical	ADJ
ap-6074	227	20	gear	gear	NOUN
ap-6074	227	21	with	with	ADP
ap-6074	227	22	parameters	parameter	NOUN
ap-6074	227	23	given	give	VERB
ap-6074	227	24	in	in	ADP
ap-6074	227	25	tab	tab	NOUN
ap-6074	227	26	.	.	PUNCT
ap-6074	228	1	1	1	X
ap-6074	228	2	.	.	PUNCT
ap-6074	229	1	this	this	DET
ap-6074	229	2	gear	gear	NOUN
ap-6074	229	3	,	,	PUNCT
ap-6074	229	4	together	together	ADV
ap-6074	229	5	with	with	ADP
ap-6074	229	6	its	its	PRON
ap-6074	229	7	spur	spur	NOUN
ap-6074	229	8	variant	variant	NOUN
ap-6074	229	9	(	(	PUNCT
ap-6074	229	10	with	with	ADP
ap-6074	229	11	(	(	PUNCT
ap-6074	229	12	β	β	NOUN
ap-6074	229	13	=	=	SYM
ap-6074	229	14	0	0	NUM
ap-6074	229	15	◦	◦	NOUN
ap-6074	229	16	)	)	PUNCT
ap-6074	229	17	and	and	CCONJ
ap-6074	229	18	the	the	DET
ap-6074	229	19	other	other	ADJ
ap-6074	229	20	parameters	parameter	NOUN
ap-6074	229	21	the	the	DET
ap-6074	229	22	same	same	ADJ
ap-6074	229	23	as	as	SCONJ
ap-6074	229	24	is	be	AUX
ap-6074	229	25	given	give	VERB
ap-6074	229	26	in	in	ADP
ap-6074	229	27	tab	tab	NOUN
ap-6074	229	28	.	.	PUNCT
ap-6074	229	29	1	1	NUM
ap-6074	229	30	)	)	PUNCT
ap-6074	229	31	,	,	PUNCT
ap-6074	229	32	is	be	AUX
ap-6074	229	33	shown	show	VERB
ap-6074	229	34	in	in	ADP
ap-6074	229	35	fig	fig	NOUN
ap-6074	229	36	.	.	PUNCT
ap-6074	230	1	15	15	NUM
ap-6074	230	2	.	.	PUNCT
ap-6074	230	3	parameter	parameter	NOUN
ap-6074	230	4	symbol	symbol	NOUN
ap-6074	230	5	value	value	NOUN
ap-6074	230	6	helix	helix	NOUN
ap-6074	230	7	angle	angle	NOUN
ap-6074	230	8	β	β	X
ap-6074	230	9	(	(	PUNCT
ap-6074	230	10	°	°	PROPN
ap-6074	230	11	)	)	PUNCT
ap-6074	230	12	10	10	NUM
ap-6074	230	13	normal	normal	ADJ
ap-6074	230	14	module	module	NOUN
ap-6074	230	15	mn	mn	PROPN
ap-6074	230	16	(	(	PUNCT
ap-6074	230	17	mm	mm	PROPN
ap-6074	230	18	)	)	PUNCT
ap-6074	230	19	3.54	3.54	NUM
ap-6074	230	20	teeth	tooth	NOUN
ap-6074	230	21	number	number	NOUN
ap-6074	230	22	z	z	PROPN
ap-6074	230	23	(	(	PUNCT
ap-6074	230	24	-	-	PUNCT
ap-6074	230	25	)	)	PUNCT
ap-6074	230	26	6	6	NUM
ap-6074	230	27	reference	reference	NOUN
ap-6074	230	28	circle	circle	NOUN
ap-6074	230	29	diameter	diameter	NOUN
ap-6074	231	1	d	d	PROPN
ap-6074	231	2	(	(	PUNCT
ap-6074	231	3	mm	mm	PROPN
ap-6074	231	4	)	)	PUNCT
ap-6074	231	5	21.324	21.324	NUM
ap-6074	231	6	tip	tip	NOUN
ap-6074	231	7	circle	circle	NOUN
ap-6074	231	8	diameter	diameter	NOUN
ap-6074	231	9	da	da	PROPN
ap-6074	231	10	(	(	PUNCT
ap-6074	231	11	mm	mm	NOUN
ap-6074	231	12	)	)	PUNCT
ap-6074	231	13	28.324	28.324	NUM
ap-6074	231	14	normal	normal	ADJ
ap-6074	231	15	angle	angle	NOUN
ap-6074	231	16	αn	αn	NOUN
ap-6074	231	17	(	(	PUNCT
ap-6074	231	18	°	°	PROPN
ap-6074	231	19	)	)	PUNCT
ap-6074	231	20	20	20	NUM
ap-6074	231	21	transverse	transverse	NOUN
ap-6074	231	22	angle	angle	NOUN
ap-6074	231	23	αt	αt	PROPN
ap-6074	231	24	(	(	PUNCT
ap-6074	231	25	°	°	PROPN
ap-6074	231	26	)	)	PUNCT
ap-6074	231	27	20.284	20.284	NUM
ap-6074	231	28	base	base	NOUN
ap-6074	231	29	circle	circle	NOUN
ap-6074	231	30	diameter	diameter	NOUN
ap-6074	231	31	db	db	PROPN
ap-6074	231	32	(	(	PUNCT
ap-6074	231	33	mm	mm	PROPN
ap-6074	231	34	)	)	PUNCT
ap-6074	231	35	20.002	20.002	NUM
ap-6074	231	36	lead	lead	NOUN
ap-6074	231	37	pz	pz	NOUN
ap-6074	231	38	(	(	PUNCT
ap-6074	231	39	mm	mm	NOUN
ap-6074	231	40	)	)	PUNCT
ap-6074	231	41	379.926	379.926	NUM
ap-6074	231	42	table	table	NOUN
ap-6074	231	43	1	1	NUM
ap-6074	231	44	.	.	PUNCT
ap-6074	231	45	gear	gear	NOUN
ap-6074	231	46	parameters	parameter	NOUN
ap-6074	231	47	of	of	ADP
ap-6074	231	48	smart	smart	ADJ
ap-6074	231	49	gear	gear	NOUN
ap-6074	231	50	measurement	measurement	NOUN
ap-6074	231	51	standard	standard	PROPN
ap-6074	231	52	.	.	PUNCT
ap-6074	232	1	figure	figure	NOUN
ap-6074	232	2	15	15	NUM
ap-6074	232	3	.	.	PUNCT
ap-6074	233	1	spur	spur	NOUN
ap-6074	233	2	(	(	PUNCT
ap-6074	233	3	magenta	magenta	NOUN
ap-6074	233	4	)	)	PUNCT
ap-6074	233	5	and	and	CCONJ
ap-6074	233	6	helical	helical	ADJ
ap-6074	233	7	(	(	PUNCT
ap-6074	233	8	cyan	cyan	ADJ
ap-6074	233	9	)	)	PUNCT
ap-6074	233	10	gear	gear	NOUN
ap-6074	233	11	included	include	VERB
ap-6074	233	12	in	in	ADP
ap-6074	233	13	smart	smart	ADJ
ap-6074	233	14	gear	gear	NOUN
ap-6074	233	15	measurement	measurement	NOUN
ap-6074	233	16	standard	standard	NOUN
ap-6074	233	17	.	.	PUNCT
ap-6074	234	1	the	the	DET
ap-6074	234	2	tangent	tangent	ADJ
ap-6074	234	3	surface	surface	NOUN
ap-6074	234	4	of	of	ADP
ap-6074	234	5	the	the	DET
ap-6074	234	6	base	base	NOUN
ap-6074	234	7	helix	helix	NOUN
ap-6074	234	8	used	use	VERB
ap-6074	234	9	in	in	ADP
ap-6074	234	10	the	the	DET
ap-6074	234	11	smart	smart	ADJ
ap-6074	234	12	gear	gear	NOUN
ap-6074	234	13	standard	standard	NOUN
ap-6074	234	14	allows	allow	VERB
ap-6074	234	15	to	to	PART
ap-6074	234	16	measure	measure	VERB
ap-6074	234	17	the	the	DET
ap-6074	234	18	following	follow	VERB
ap-6074	234	19	curves	curve	NOUN
ap-6074	234	20	.	.	PUNCT
ap-6074	235	1	helices	helix	NOUN
ap-6074	235	2	helices	helix	NOUN
ap-6074	235	3	located	locate	VERB
ap-6074	235	4	on	on	ADP
ap-6074	235	5	the	the	DET
ap-6074	235	6	tangent	tangent	ADJ
ap-6074	235	7	surface	surface	NOUN
ap-6074	235	8	of	of	ADP
ap-6074	235	9	the	the	DET
ap-6074	235	10	helix	helix	NOUN
ap-6074	235	11	are	be	AUX
ap-6074	235	12	defined	define	VERB
ap-6074	235	13	as	as	ADP
ap-6074	235	14	intersections	intersection	NOUN
ap-6074	235	15	of	of	ADP
ap-6074	235	16	the	the	DET
ap-6074	235	17	surface	surface	NOUN
ap-6074	235	18	and	and	CCONJ
ap-6074	235	19	cylindrical	cylindrical	ADJ
ap-6074	235	20	surface	surface	NOUN
ap-6074	235	21	coaxial	coaxial	ADJ
ap-6074	235	22	with	with	ADP
ap-6074	235	23	the	the	DET
ap-6074	235	24	base	base	NOUN
ap-6074	235	25	cylinder	cylinder	NOUN
ap-6074	235	26	.	.	PUNCT
ap-6074	236	1	in	in	ADP
ap-6074	236	2	fig	fig	NOUN
ap-6074	236	3	.	.	PUNCT
ap-6074	237	1	16	16	NUM
ap-6074	237	2	,	,	PUNCT
ap-6074	237	3	the	the	DET
ap-6074	237	4	intersection	intersection	NOUN
ap-6074	237	5	with	with	ADP
ap-6074	237	6	the	the	DET
ap-6074	237	7	cylindrical	cylindrical	ADJ
ap-6074	237	8	surface	surface	NOUN
ap-6074	237	9	of	of	ADP
ap-6074	237	10	radius	radius	NOUN
ap-6074	237	11	r	r	NOUN
ap-6074	237	12	=	=	SYM
ap-6074	237	13	34.911	34.911	NUM
ap-6074	237	14	mm	mm	NOUN
ap-6074	237	15	and	and	CCONJ
ap-6074	237	16	the	the	DET
ap-6074	237	17	corresponding	corresponding	ADJ
ap-6074	237	18	angle	angle	NOUN
ap-6074	237	19	β	β	X
ap-6074	237	20	=	=	SYM
ap-6074	237	21	30	30	NUM
ap-6074	237	22	◦	◦	NOUN
ap-6074	237	23	can	can	AUX
ap-6074	237	24	be	be	AUX
ap-6074	237	25	seen	see	VERB
ap-6074	237	26	.	.	PUNCT
ap-6074	238	1	the	the	DET
ap-6074	238	2	shape	shape	NOUN
ap-6074	238	3	of	of	ADP
ap-6074	238	4	the	the	DET
ap-6074	238	5	standard	standard	ADJ
ap-6074	238	6	enables	enable	VERB
ap-6074	238	7	to	to	PART
ap-6074	238	8	measure	measure	VERB
ap-6074	238	9	the	the	DET
ap-6074	238	10	external	external	ADJ
ap-6074	238	11	helical	helical	ADJ
ap-6074	238	12	gear	gear	NOUN
ap-6074	238	13	from	from	ADP
ap-6074	238	14	β	β	X
ap-6074	238	15	=	=	SYM
ap-6074	238	16	0	0	NUM
ap-6074	238	17	◦	◦	NOUN
ap-6074	238	18	(	(	PUNCT
ap-6074	238	19	spur	spur	VERB
ap-6074	238	20	gear	gear	NOUN
ap-6074	238	21	as	as	ADP
ap-6074	238	22	a	a	DET
ap-6074	238	23	special	special	ADJ
ap-6074	238	24	case	case	NOUN
ap-6074	238	25	of	of	ADP
ap-6074	238	26	the	the	DET
ap-6074	238	27	helical	helical	ADJ
ap-6074	238	28	gear	gear	NOUN
ap-6074	238	29	)	)	PUNCT
ap-6074	238	30	to	to	ADP
ap-6074	238	31	β	β	NOUN
ap-6074	238	32	=	=	SYM
ap-6074	238	33	60	60	NUM
ap-6074	238	34	◦	◦	NOUN
ap-6074	238	35	and	and	CCONJ
ap-6074	238	36	internal	internal	ADJ
ap-6074	238	37	helical	helical	ADJ
ap-6074	238	38	gear	gear	NOUN
ap-6074	238	39	from	from	ADP
ap-6074	238	40	β	β	X
ap-6074	238	41	=	=	SYM
ap-6074	238	42	0	0	NUM
ap-6074	238	43	◦	◦	NOUN
ap-6074	238	44	to	to	ADP
ap-6074	238	45	β	β	X
ap-6074	238	46	=	=	SYM
ap-6074	238	47	56	56	NUM
ap-6074	238	48	◦	◦	NOUN
ap-6074	238	49	.	.	PUNCT
ap-6074	239	1	parameters	parameter	NOUN
ap-6074	239	2	of	of	ADP
ap-6074	239	3	the	the	DET
ap-6074	239	4	selected	select	VERB
ap-6074	239	5	external	external	ADJ
ap-6074	239	6	helical	helical	ADJ
ap-6074	239	7	gear	gear	NOUN
ap-6074	239	8	helices	helix	NOUN
ap-6074	239	9	which	which	PRON
ap-6074	239	10	possible	possible	ADJ
ap-6074	239	11	to	to	PART
ap-6074	239	12	measure	measure	VERB
ap-6074	239	13	are	be	AUX
ap-6074	239	14	given	give	VERB
ap-6074	239	15	in	in	ADP
ap-6074	239	16	tab	tab	NOUN
ap-6074	239	17	.	.	PUNCT
ap-6074	240	1	2	2	X
ap-6074	240	2	.	.	X
ap-6074	240	3	the	the	DET
ap-6074	240	4	corresponding	corresponding	ADJ
ap-6074	240	5	helical	helical	ADJ
ap-6074	240	6	teeth	tooth	NOUN
ap-6074	240	7	included	include	VERB
ap-6074	240	8	in	in	ADP
ap-6074	240	9	the	the	DET
ap-6074	240	10	standard	standard	NOUN
ap-6074	240	11	are	be	AUX
ap-6074	240	12	depicted	depict	VERB
ap-6074	240	13	in	in	ADP
ap-6074	240	14	fig	fig	NOUN
ap-6074	240	15	.	.	PUNCT
ap-6074	241	1	17	17	NUM
ap-6074	241	2	together	together	ADV
ap-6074	241	3	with	with	ADP
ap-6074	241	4	their	their	PRON
ap-6074	241	5	helices	helix	NOUN
ap-6074	241	6	lying	lie	VERB
ap-6074	241	7	on	on	ADP
ap-6074	241	8	the	the	DET
ap-6074	241	9	surface	surface	NOUN
ap-6074	241	10	of	of	ADP
ap-6074	241	11	the	the	DET
ap-6074	241	12	standard	standard	NOUN
ap-6074	241	13	.	.	PUNCT
ap-6074	242	1	straight	straight	ADJ
ap-6074	242	2	lines	line	NOUN
ap-6074	242	3	straight	straight	ADJ
ap-6074	242	4	lines	line	NOUN
ap-6074	242	5	located	locate	VERB
ap-6074	242	6	on	on	ADP
ap-6074	242	7	the	the	DET
ap-6074	242	8	tangent	tangent	ADJ
ap-6074	242	9	surface	surface	NOUN
ap-6074	242	10	of	of	ADP
ap-6074	242	11	the	the	DET
ap-6074	242	12	helix	helix	NOUN
ap-6074	242	13	are	be	AUX
ap-6074	242	14	defined	define	VERB
ap-6074	242	15	by	by	ADP
ap-6074	242	16	individual	individual	ADJ
ap-6074	242	17	tangent	tangent	NOUN
ap-6074	242	18	lines	line	NOUN
ap-6074	242	19	of	of	ADP
ap-6074	242	20	the	the	DET
ap-6074	242	21	helix	helix	NOUN
ap-6074	242	22	.	.	PUNCT
ap-6074	243	1	consequently	consequently	ADV
ap-6074	243	2	,	,	PUNCT
ap-6074	243	3	these	these	DET
ap-6074	243	4	straight	straight	ADJ
ap-6074	243	5	lines	line	NOUN
ap-6074	243	6	are	be	AUX
ap-6074	243	7	obtained	obtain	VERB
ap-6074	243	8	as	as	ADP
ap-6074	243	9	intersections	intersection	NOUN
ap-6074	243	10	of	of	ADP
ap-6074	243	11	the	the	DET
ap-6074	243	12	surface	surface	NOUN
ap-6074	243	13	and	and	CCONJ
ap-6074	243	14	tangent	tangent	ADJ
ap-6074	243	15	planes	plane	NOUN
ap-6074	243	16	to	to	ADP
ap-6074	243	17	the	the	DET
ap-6074	243	18	base	base	NOUN
ap-6074	243	19	cylinder	cylinder	NOUN
ap-6074	243	20	,	,	PUNCT
ap-6074	243	21	see	see	VERB
ap-6074	243	22	fig	fig	NOUN
ap-6074	243	23	.	.	PUNCT
ap-6074	244	1	18	18	NUM
ap-6074	244	2	.	.	PUNCT
ap-6074	245	1	here	here	ADV
ap-6074	245	2	,	,	PUNCT
ap-6074	245	3	several	several	ADJ
ap-6074	245	4	section	section	NOUN
ap-6074	245	5	planes	plane	NOUN
ap-6074	245	6	perpendicular	perpendicular	NOUN
ap-6074	245	7	to	to	ADP
ap-6074	245	8	(	(	PUNCT
ap-6074	245	9	x	x	NOUN
ap-6074	245	10	,	,	PUNCT
ap-6074	245	11	y	y	NOUN
ap-6074	245	12	)	)	PUNCT
ap-6074	245	13	plane	plane	NOUN
ap-6074	245	14	with	with	ADP
ap-6074	245	15	angle	angle	NOUN
ap-6074	245	16	span	span	NOUN
ap-6074	245	17	of	of	ADP
ap-6074	245	18	45	45	NUM
ap-6074	245	19	°	°	NOUN
ap-6074	245	20	depicted	depict	VERB
ap-6074	245	21	.	.	PUNCT
ap-6074	246	1	107	107	NUM
ap-6074	246	2	ivana	ivana	PROPN
ap-6074	246	3	linkeová	linkeová	PROPN
ap-6074	246	4	,	,	PUNCT
ap-6074	246	5	vít	vít	PROPN
ap-6074	246	6	zelený	zelený	PROPN
ap-6074	246	7	acta	acta	PROPN
ap-6074	246	8	polytechnica	polytechnica	PROPN
ap-6074	246	9	β	β	X
ap-6074	246	10	(	(	PUNCT
ap-6074	246	11	◦	◦	NOUN
ap-6074	246	12	)	)	PUNCT
ap-6074	246	13	mn	mn	PROPN
ap-6074	246	14	(	(	PUNCT
ap-6074	246	15	mm	mm	NOUN
ap-6074	246	16	)	)	PUNCT
ap-6074	246	17	z	z	NOUN
ap-6074	246	18	(	(	PUNCT
ap-6074	246	19	-	-	SYM
ap-6074	246	20	)	)	PUNCT
ap-6074	246	21	d	d	NOUN
ap-6074	246	22	(	(	PUNCT
ap-6074	246	23	mm	mm	NOUN
ap-6074	246	24	)	)	PUNCT
ap-6074	246	25	10	10	NUM
ap-6074	246	26	3.5	3.5	NUM
ap-6074	246	27	6	6	NUM
ap-6074	246	28	21.324	21.324	NUM
ap-6074	246	29	15	15	NUM
ap-6074	246	30	1.49	1.49	NUM
ap-6074	246	31	21	21	NUM
ap-6074	246	32	32.404	32.404	NUM
ap-6074	246	33	20	20	NUM
ap-6074	246	34	2.76	2.76	NUM
ap-6074	246	35	15	15	NUM
ap-6074	246	36	44.016	44.016	NUM
ap-6074	246	37	25	25	NUM
ap-6074	246	38	3.01	3.01	NUM
ap-6074	246	39	17	17	NUM
ap-6074	246	40	56.392	56.392	NUM
ap-6074	246	41	30	30	NUM
ap-6074	246	42	2.02	2.02	NUM
ap-6074	246	43	30	30	NUM
ap-6074	246	44	69.821	69.821	NUM
ap-6074	246	45	35	35	NUM
ap-6074	246	46	3.02	3.02	NUM
ap-6074	246	47	23	23	NUM
ap-6074	246	48	84.679	84.679	NUM
ap-6074	246	49	40	40	NUM
ap-6074	246	50	5.98	5.98	NUM
ap-6074	246	51	13	13	NUM
ap-6074	246	52	101.476	101.476	NUM
ap-6074	246	53	45	45	NUM
ap-6074	246	54	4.50	4.50	NUM
ap-6074	246	55	19	19	NUM
ap-6074	246	56	120.934	120.934	NUM
ap-6074	246	57	table	table	NOUN
ap-6074	246	58	2	2	NUM
ap-6074	246	59	.	.	PUNCT
ap-6074	246	60	parameters	parameter	NOUN
ap-6074	246	61	of	of	ADP
ap-6074	246	62	selected	select	VERB
ap-6074	246	63	helical	helical	ADJ
ap-6074	246	64	gears	gear	NOUN
ap-6074	246	65	on	on	ADP
ap-6074	246	66	smart	smart	ADJ
ap-6074	246	67	gear	gear	NOUN
ap-6074	246	68	standard	standard	ADJ
ap-6074	246	69	figure	figure	NOUN
ap-6074	246	70	16	16	NUM
ap-6074	246	71	.	.	PUNCT
ap-6074	247	1	helical	helical	ADJ
ap-6074	247	2	sections	section	NOUN
ap-6074	247	3	on	on	ADP
ap-6074	247	4	smart	smart	ADJ
ap-6074	247	5	gear	gear	NOUN
ap-6074	247	6	measurement	measurement	NOUN
ap-6074	247	7	standard	standard	PROPN
ap-6074	247	8	.	.	PUNCT
ap-6074	248	1	figure	figure	NOUN
ap-6074	248	2	17	17	NUM
ap-6074	248	3	.	.	PUNCT
ap-6074	249	1	helical	helical	ADJ
ap-6074	249	2	teeth	tooth	NOUN
ap-6074	249	3	included	include	VERB
ap-6074	249	4	in	in	ADP
ap-6074	249	5	smart	smart	ADJ
ap-6074	249	6	gear	gear	NOUN
ap-6074	249	7	measurement	measurement	NOUN
ap-6074	249	8	standard	standard	PROPN
ap-6074	249	9	.	.	PUNCT
ap-6074	250	1	figure	figure	NOUN
ap-6074	250	2	18	18	NUM
ap-6074	250	3	.	.	PUNCT
ap-6074	251	1	line	line	NOUN
ap-6074	251	2	sections	section	NOUN
ap-6074	251	3	on	on	ADP
ap-6074	251	4	smart	smart	ADJ
ap-6074	251	5	gear	gear	NOUN
ap-6074	251	6	measurement	measurement	NOUN
ap-6074	251	7	standard	standard	PROPN
ap-6074	251	8	.	.	PUNCT
ap-6074	252	1	figure	figure	NOUN
ap-6074	252	2	19	19	NUM
ap-6074	252	3	.	.	PUNCT
ap-6074	252	4	involute	involute	ADJ
ap-6074	252	5	sections	section	NOUN
ap-6074	252	6	on	on	ADP
ap-6074	252	7	smart	smart	ADJ
ap-6074	252	8	gear	gear	NOUN
ap-6074	252	9	measurement	measurement	NOUN
ap-6074	252	10	standard	standard	NOUN
ap-6074	252	11	.	.	PUNCT
ap-6074	253	1	involutes	involute	VERB
ap-6074	253	2	involutes	involute	NOUN
ap-6074	253	3	located	locate	VERB
ap-6074	253	4	on	on	ADP
ap-6074	253	5	the	the	DET
ap-6074	253	6	tangent	tangent	ADJ
ap-6074	253	7	surface	surface	NOUN
ap-6074	253	8	of	of	ADP
ap-6074	253	9	the	the	DET
ap-6074	253	10	helix	helix	NOUN
ap-6074	253	11	are	be	AUX
ap-6074	253	12	defined	define	VERB
ap-6074	253	13	as	as	ADP
ap-6074	253	14	intersections	intersection	NOUN
ap-6074	253	15	of	of	ADP
ap-6074	253	16	the	the	DET
ap-6074	253	17	surface	surface	NOUN
ap-6074	253	18	and	and	CCONJ
ap-6074	253	19	planes	plane	NOUN
ap-6074	253	20	perpendicular	perpendicular	NOUN
ap-6074	253	21	to	to	ADP
ap-6074	253	22	the	the	DET
ap-6074	253	23	axis	axis	NOUN
ap-6074	253	24	of	of	ADP
ap-6074	253	25	the	the	DET
ap-6074	253	26	helix	helix	NOUN
ap-6074	253	27	.	.	PUNCT
ap-6074	254	1	the	the	DET
ap-6074	254	2	plane	plane	NOUN
ap-6074	254	3	z	z	NOUN
ap-6074	254	4	=	=	SYM
ap-6074	254	5	30	30	NUM
ap-6074	254	6	mm	mm	NOUN
ap-6074	254	7	is	be	AUX
ap-6074	254	8	depicted	depict	VERB
ap-6074	254	9	in	in	ADP
ap-6074	254	10	fig	fig	NOUN
ap-6074	254	11	.	.	PUNCT
ap-6074	255	1	19	19	NUM
ap-6074	255	2	.	.	X
ap-6074	256	1	4.3.1	4.3.1	X
ap-6074	256	2	.	.	PUNCT
ap-6074	257	1	physical	physical	ADJ
ap-6074	257	2	smart	smart	ADJ
ap-6074	257	3	gear	gear	NOUN
ap-6074	257	4	standard	standard	NOUN
ap-6074	257	5	the	the	DET
ap-6074	257	6	final	final	ADJ
ap-6074	257	7	shape	shape	NOUN
ap-6074	257	8	of	of	ADP
ap-6074	257	9	the	the	DET
ap-6074	257	10	smart	smart	ADJ
ap-6074	257	11	gear	gear	NOUN
ap-6074	257	12	standard	standard	NOUN
ap-6074	257	13	is	be	AUX
ap-6074	257	14	currently	currently	ADV
ap-6074	257	15	in	in	ADP
ap-6074	257	16	the	the	DET
ap-6074	257	17	research	research	NOUN
ap-6074	257	18	and	and	CCONJ
ap-6074	257	19	development	development	NOUN
ap-6074	257	20	phase	phase	NOUN
ap-6074	257	21	.	.	PUNCT
ap-6074	258	1	therefore	therefore	ADV
ap-6074	258	2	,	,	PUNCT
ap-6074	258	3	the	the	DET
ap-6074	258	4	first	first	ADJ
ap-6074	258	5	sample	sample	NOUN
ap-6074	258	6	of	of	ADP
ap-6074	258	7	this	this	DET
ap-6074	258	8	standard	standard	NOUN
ap-6074	258	9	has	have	AUX
ap-6074	258	10	been	be	AUX
ap-6074	258	11	manufactured	manufacture	VERB
ap-6074	258	12	by	by	ADP
ap-6074	258	13	3d	3d	NUM
ap-6074	258	14	printing	printing	NOUN
ap-6074	258	15	technology	technology	NOUN
ap-6074	258	16	and	and	CCONJ
ap-6074	258	17	experimental	experimental	ADJ
ap-6074	258	18	measurements	measurement	NOUN
ap-6074	258	19	have	have	AUX
ap-6074	258	20	been	be	AUX
ap-6074	258	21	realised	realise	VERB
ap-6074	258	22	.	.	PUNCT
ap-6074	259	1	based	base	VERB
ap-6074	259	2	on	on	ADP
ap-6074	259	3	the	the	DET
ap-6074	259	4	metrological	metrological	ADJ
ap-6074	259	5	experience	experience	NOUN
ap-6074	259	6	,	,	PUNCT
ap-6074	259	7	the	the	DET
ap-6074	259	8	shape	shape	NOUN
ap-6074	259	9	of	of	ADP
ap-6074	259	10	the	the	DET
ap-6074	259	11	standard	standard	NOUN
ap-6074	259	12	will	will	AUX
ap-6074	259	13	be	be	AUX
ap-6074	259	14	modified	modify	VERB
ap-6074	259	15	.	.	PUNCT
ap-6074	260	1	numerically	numerically	ADV
ap-6074	260	2	controlled	control	VERB
ap-6074	260	3	manufacturing	manufacturing	NOUN
ap-6074	260	4	technology	technology	NOUN
ap-6074	260	5	and	and	CCONJ
ap-6074	260	6	metal	metal	NOUN
ap-6074	260	7	material	material	NOUN
ap-6074	260	8	is	be	AUX
ap-6074	260	9	assumed	assume	VERB
ap-6074	260	10	for	for	ADP
ap-6074	260	11	the	the	DET
ap-6074	260	12	future	future	ADJ
ap-6074	260	13	production	production	NOUN
ap-6074	260	14	of	of	ADP
ap-6074	260	15	the	the	DET
ap-6074	260	16	standard	standard	NOUN
ap-6074	260	17	.	.	PUNCT
ap-6074	261	1	due	due	ADP
ap-6074	261	2	to	to	ADP
ap-6074	261	3	the	the	DET
ap-6074	261	4	geometrical	geometrical	ADJ
ap-6074	261	5	properties	property	NOUN
ap-6074	261	6	of	of	ADP
ap-6074	261	7	the	the	DET
ap-6074	261	8	flank	flank	NOUN
ap-6074	261	9	surfaces	surface	NOUN
ap-6074	261	10	,	,	PUNCT
ap-6074	261	11	using	use	VERB
ap-6074	261	12	the	the	DET
ap-6074	261	13	5	5	NUM
ap-6074	261	14	-	-	PUNCT
ap-6074	261	15	axis	axis	NOUN
ap-6074	261	16	flank	flank	NOUN
ap-6074	261	17	milling	mill	VERB
ap-6074	261	18	technology	technology	NOUN
ap-6074	261	19	to	to	PART
ap-6074	261	20	obtain	obtain	VERB
ap-6074	261	21	as	as	ADP
ap-6074	261	22	precise	precise	ADJ
ap-6074	261	23	model	model	NOUN
ap-6074	261	24	as	as	ADP
ap-6074	261	25	possible	possible	ADJ
ap-6074	261	26	,	,	PUNCT
ap-6074	261	27	the	the	DET
ap-6074	261	28	main	main	ADJ
ap-6074	261	29	functional	functional	ADJ
ap-6074	261	30	surface	surface	NOUN
ap-6074	261	31	of	of	ADP
ap-6074	261	32	the	the	DET
ap-6074	261	33	standard	standard	NOUN
ap-6074	261	34	will	will	AUX
ap-6074	261	35	be	be	AUX
ap-6074	261	36	possible	possible	ADJ
ap-6074	261	37	.	.	PUNCT
ap-6074	262	1	108	108	NUM
ap-6074	262	2	vol	vol	NOUN
ap-6074	262	3	.	.	PUNCT
ap-6074	262	4	61	61	NUM
ap-6074	262	5	special	special	ADJ
ap-6074	262	6	issue/2021	issue/2021	NOUN
ap-6074	262	7	application	application	NOUN
ap-6074	262	8	of	of	ADP
ap-6074	262	9	ruled	rule	VERB
ap-6074	262	10	surfaces	surface	NOUN
ap-6074	262	11	in	in	ADP
ap-6074	262	12	freeform	freeform	NOUN
ap-6074	262	13	and	and	CCONJ
ap-6074	262	14	gear	gear	NOUN
ap-6074	262	15	metrology	metrology	NOUN
ap-6074	262	16	figure	figure	NOUN
ap-6074	262	17	20	20	NUM
ap-6074	262	18	.	.	PUNCT
ap-6074	263	1	smart	smart	ADJ
ap-6074	263	2	gear	gear	NOUN
ap-6074	263	3	measurement	measurement	NOUN
ap-6074	263	4	standard	standard	NOUN
ap-6074	263	5	manufactured	manufacture	VERB
ap-6074	263	6	by	by	ADP
ap-6074	263	7	3d	3d	NUM
ap-6074	263	8	printing	printing	NOUN
ap-6074	263	9	technology	technology	NOUN
ap-6074	263	10	.	.	PUNCT
ap-6074	264	1	5	5	X
ap-6074	264	2	.	.	X
ap-6074	264	3	conclusion	conclusion	NOUN
ap-6074	264	4	two	two	NUM
ap-6074	264	5	ruled	rule	VERB
ap-6074	264	6	surfaces	surface	NOUN
ap-6074	264	7	surface	surface	NOUN
ap-6074	264	8	of	of	ADP
ap-6074	264	9	hyperbolic	hyperbolic	ADJ
ap-6074	264	10	paraboloid	paraboloid	NOUN
ap-6074	264	11	and	and	CCONJ
ap-6074	264	12	tangent	tangent	ADJ
ap-6074	264	13	surface	surface	NOUN
ap-6074	264	14	of	of	ADP
ap-6074	264	15	a	a	DET
ap-6074	264	16	cylindrical	cylindrical	ADJ
ap-6074	264	17	helix	helix	NOUN
ap-6074	264	18	are	be	AUX
ap-6074	264	19	described	describe	VERB
ap-6074	264	20	in	in	ADP
ap-6074	264	21	this	this	DET
ap-6074	264	22	paper	paper	NOUN
ap-6074	264	23	.	.	PUNCT
ap-6074	265	1	geometrical	geometrical	ADJ
ap-6074	265	2	-	-	PUNCT
ap-6074	265	3	mathematical	mathematical	ADJ
ap-6074	265	4	properties	property	NOUN
ap-6074	265	5	of	of	ADP
ap-6074	265	6	both	both	DET
ap-6074	265	7	surfaces	surface	NOUN
ap-6074	265	8	are	be	AUX
ap-6074	265	9	summarised	summarise	VERB
ap-6074	265	10	and	and	CCONJ
ap-6074	265	11	their	their	PRON
ap-6074	265	12	application	application	NOUN
ap-6074	265	13	in	in	ADP
ap-6074	265	14	freeform	freeform	NOUN
ap-6074	265	15	and	and	CCONJ
ap-6074	265	16	gear	gear	NOUN
ap-6074	265	17	metrology	metrology	NOUN
ap-6074	265	18	is	be	AUX
ap-6074	265	19	shown	show	VERB
ap-6074	265	20	.	.	PUNCT
ap-6074	266	1	two	two	NUM
ap-6074	266	2	freeform	freeform	ADJ
ap-6074	266	3	metrological	metrological	ADJ
ap-6074	266	4	standards	standard	NOUN
ap-6074	266	5	freeform	freeform	VERB
ap-6074	266	6	standard	standard	ADJ
ap-6074	266	7	hyperbolic	hyperbolic	ADJ
ap-6074	266	8	paraboloid	paraboloid	NOUN
ap-6074	266	9	and	and	CCONJ
ap-6074	266	10	spatial	spatial	ADJ
ap-6074	266	11	hyperbolic	hyperbolic	ADJ
ap-6074	266	12	paraboloid	paraboloid	ADJ
ap-6074	266	13	standard	standard	NOUN
ap-6074	266	14	and	and	CCONJ
ap-6074	266	15	smart	smart	ADJ
ap-6074	266	16	gear	gear	NOUN
ap-6074	266	17	measurement	measurement	NOUN
ap-6074	266	18	standard	standard	NOUN
ap-6074	266	19	developed	develop	VERB
ap-6074	266	20	by	by	ADP
ap-6074	266	21	the	the	DET
ap-6074	266	22	cmi	cmi	NOUN
ap-6074	266	23	in	in	ADP
ap-6074	266	24	cooperation	cooperation	NOUN
ap-6074	266	25	with	with	ADP
ap-6074	266	26	the	the	DET
ap-6074	266	27	ctu	ctu	NOUN
ap-6074	266	28	are	be	AUX
ap-6074	266	29	introduced	introduce	VERB
ap-6074	266	30	.	.	PUNCT
ap-6074	267	1	all	all	PRON
ap-6074	267	2	of	of	ADP
ap-6074	267	3	the	the	DET
ap-6074	267	4	above	above	ADJ
ap-6074	267	5	mentioned	mention	VERB
ap-6074	267	6	artefacts	artefact	NOUN
ap-6074	267	7	are	be	AUX
ap-6074	267	8	considered	consider	VERB
ap-6074	267	9	to	to	PART
ap-6074	267	10	be	be	AUX
ap-6074	267	11	the	the	DET
ap-6074	267	12	calibration	calibration	NOUN
ap-6074	267	13	standards	standard	NOUN
ap-6074	267	14	for	for	ADP
ap-6074	267	15	freeform	freeform	ADJ
ap-6074	267	16	metrology	metrology	NOUN
ap-6074	267	17	a	a	DET
ap-6074	267	18	new	new	ADJ
ap-6074	267	19	,	,	PUNCT
ap-6074	267	20	rapidly	rapidly	ADV
ap-6074	267	21	evolving	evolve	VERB
ap-6074	267	22	specialisation	specialisation	NOUN
ap-6074	267	23	focused	focus	VERB
ap-6074	267	24	on	on	ADP
ap-6074	267	25	the	the	DET
ap-6074	267	26	quality	quality	NOUN
ap-6074	267	27	inspection	inspection	NOUN
ap-6074	267	28	of	of	ADP
ap-6074	267	29	generally	generally	ADV
ap-6074	267	30	shaped	shape	VERB
ap-6074	267	31	parts	part	NOUN
ap-6074	267	32	.	.	PUNCT
ap-6074	268	1	the	the	DET
ap-6074	268	2	main	main	ADJ
ap-6074	268	3	objective	objective	NOUN
ap-6074	268	4	of	of	ADP
ap-6074	268	5	involving	involve	VERB
ap-6074	268	6	these	these	DET
ap-6074	268	7	artefacts	artefact	NOUN
ap-6074	268	8	in	in	ADP
ap-6074	268	9	freeform	freeform	ADJ
ap-6074	268	10	metrology	metrology	NOUN
ap-6074	268	11	is	be	AUX
ap-6074	268	12	to	to	PART
ap-6074	268	13	determine	determine	VERB
ap-6074	268	14	the	the	DET
ap-6074	268	15	best	good	ADJ
ap-6074	268	16	measuring	measure	VERB
ap-6074	268	17	capabilities	capability	NOUN
ap-6074	268	18	of	of	ADP
ap-6074	268	19	coordinate	coordinate	NOUN
ap-6074	268	20	measuring	measure	VERB
ap-6074	268	21	machines	machine	NOUN
ap-6074	268	22	working	work	VERB
ap-6074	268	23	on	on	ADP
ap-6074	268	24	different	different	ADJ
ap-6074	268	25	principles	principle	NOUN
ap-6074	268	26	.	.	PUNCT
ap-6074	269	1	usually	usually	ADV
ap-6074	269	2	,	,	PUNCT
ap-6074	269	3	the	the	DET
ap-6074	269	4	basic	basic	ADJ
ap-6074	269	5	measurand	measurand	NOUN
ap-6074	269	6	in	in	ADP
ap-6074	269	7	freeform	freeform	ADJ
ap-6074	269	8	metrology	metrology	NOUN
ap-6074	269	9	is	be	AUX
ap-6074	269	10	a	a	DET
ap-6074	269	11	form	form	NOUN
ap-6074	269	12	deviation	deviation	NOUN
ap-6074	269	13	,	,	PUNCT
ap-6074	269	14	i.e.	i.e.	X
ap-6074	269	15	the	the	DET
ap-6074	269	16	normal	normal	ADJ
ap-6074	269	17	distance	distance	NOUN
ap-6074	269	18	between	between	ADP
ap-6074	269	19	the	the	DET
ap-6074	269	20	actual	actual	ADJ
ap-6074	269	21	point	point	NOUN
ap-6074	269	22	located	locate	VERB
ap-6074	269	23	on	on	ADP
ap-6074	269	24	the	the	DET
ap-6074	269	25	measured	measured	ADJ
ap-6074	269	26	workpiece	workpiece	NOUN
ap-6074	269	27	and	and	CCONJ
ap-6074	269	28	nominal	nominal	ADJ
ap-6074	269	29	point	point	NOUN
ap-6074	269	30	located	locate	VERB
ap-6074	269	31	on	on	ADP
ap-6074	269	32	the	the	DET
ap-6074	269	33	theoretical	theoretical	ADJ
ap-6074	269	34	cad	cad	NOUN
ap-6074	269	35	model	model	NOUN
ap-6074	269	36	of	of	ADP
ap-6074	269	37	the	the	DET
ap-6074	269	38	measured	measured	ADJ
ap-6074	269	39	surface	surface	NOUN
ap-6074	269	40	.	.	PUNCT
ap-6074	270	1	the	the	DET
ap-6074	270	2	geometrical	geometrical	ADJ
ap-6074	270	3	properties	property	NOUN
ap-6074	270	4	of	of	ADP
ap-6074	270	5	all	all	DET
ap-6074	270	6	the	the	DET
ap-6074	270	7	above	above	ADV
ap-6074	270	8	mentioned	mention	VERB
ap-6074	270	9	artefacts	artefact	NOUN
ap-6074	270	10	allow	allow	VERB
ap-6074	270	11	to	to	PART
ap-6074	270	12	use	use	VERB
ap-6074	270	13	of	of	ADP
ap-6074	270	14	advanced	advanced	ADJ
ap-6074	270	15	measurement	measurement	NOUN
ap-6074	270	16	procedures	procedure	NOUN
ap-6074	270	17	,	,	PUNCT
ap-6074	270	18	such	such	ADJ
ap-6074	270	19	as	as	ADP
ap-6074	270	20	measurement	measurement	NOUN
ap-6074	270	21	of	of	ADP
ap-6074	270	22	straight	straight	ADJ
ap-6074	270	23	lines	line	NOUN
ap-6074	270	24	and	and	CCONJ
ap-6074	270	25	curves	curve	NOUN
ap-6074	270	26	located	locate	VERB
ap-6074	270	27	on	on	ADP
ap-6074	270	28	the	the	DET
ap-6074	270	29	freeform	freeform	ADJ
ap-6074	270	30	surface	surface	NOUN
ap-6074	270	31	.	.	PUNCT
ap-6074	271	1	consequently	consequently	ADV
ap-6074	271	2	,	,	PUNCT
ap-6074	271	3	it	it	PRON
ap-6074	271	4	is	be	AUX
ap-6074	271	5	possible	possible	ADJ
ap-6074	271	6	to	to	PART
ap-6074	271	7	measure	measure	VERB
ap-6074	271	8	surface	surface	NOUN
ap-6074	271	9	roughness	roughness	NOUN
ap-6074	271	10	and	and	CCONJ
ap-6074	271	11	waviness	waviness	NOUN
ap-6074	271	12	along	along	ADP
ap-6074	271	13	the	the	DET
ap-6074	271	14	surface	surface	NOUN
ap-6074	271	15	lines	line	NOUN
ap-6074	271	16	.	.	PUNCT
ap-6074	272	1	all	all	DET
ap-6074	272	2	the	the	DET
ap-6074	272	3	artefacts	artefact	NOUN
ap-6074	272	4	have	have	AUX
ap-6074	272	5	been	be	AUX
ap-6074	272	6	applied	apply	VERB
ap-6074	272	7	not	not	PART
ap-6074	272	8	only	only	ADV
ap-6074	272	9	in	in	ADP
ap-6074	272	10	a	a	DET
ap-6074	272	11	determination	determination	NOUN
ap-6074	272	12	of	of	ADP
ap-6074	272	13	measurement	measurement	NOUN
ap-6074	272	14	uncertainty	uncertainty	NOUN
ap-6074	272	15	of	of	ADP
ap-6074	272	16	tactile	tactile	ADJ
ap-6074	272	17	and	and	CCONJ
ap-6074	272	18	optical	optical	ADJ
ap-6074	272	19	measuring	measure	VERB
ap-6074	272	20	machines	machine	NOUN
ap-6074	272	21	and	and	CCONJ
ap-6074	272	22	in	in	ADP
ap-6074	272	23	an	an	DET
ap-6074	272	24	inter	inter	ADJ
ap-6074	272	25	-	-	ADJ
ap-6074	272	26	laboratory	laboratory	ADJ
ap-6074	272	27	comparison	comparison	NOUN
ap-6074	272	28	at	at	ADP
ap-6074	272	29	the	the	DET
ap-6074	272	30	national	national	ADJ
ap-6074	272	31	level	level	NOUN
ap-6074	272	32	by	by	ADP
ap-6074	272	33	the	the	DET
ap-6074	272	34	cmi	cmi	NOUN
ap-6074	272	35	laboratories	laboratory	NOUN
ap-6074	272	36	but	but	CCONJ
ap-6074	272	37	also	also	ADV
ap-6074	272	38	,	,	PUNCT
ap-6074	272	39	in	in	ADP
ap-6074	272	40	the	the	DET
ap-6074	272	41	case	case	NOUN
ap-6074	272	42	of	of	ADP
ap-6074	272	43	the	the	DET
ap-6074	272	44	cmi	cmi	PROPN
ap-6074	272	45	freeform	freeform	PROPN
ap-6074	272	46	standard	standard	ADJ
ap-6074	272	47	hyperbolic	hyperbolic	ADJ
ap-6074	272	48	paraboloid	paraboloid	NOUN
ap-6074	272	49	,	,	PUNCT
ap-6074	272	50	at	at	ADP
ap-6074	272	51	the	the	DET
ap-6074	272	52	international	international	ADJ
ap-6074	272	53	level	level	NOUN
ap-6074	272	54	.	.	PUNCT
ap-6074	273	1	references	reference	NOUN
ap-6074	273	2	[	[	X
ap-6074	273	3	1	1	NUM
ap-6074	273	4	]	]	X
ap-6074	273	5	b.	b.	PROPN
ap-6074	273	6	ačko	ačko	PROPN
ap-6074	273	7	,	,	PUNCT
ap-6074	273	8	m.	m.	NOUN
ap-6074	273	9	mccarthy	mccarthy	PROPN
ap-6074	273	10	,	,	PUNCT
ap-6074	273	11	f.	f.	PROPN
ap-6074	273	12	haertig	haertig	PROPN
ap-6074	273	13	.	.	PUNCT
ap-6074	274	1	standards	standard	NOUN
ap-6074	274	2	for	for	ADP
ap-6074	274	3	testing	test	VERB
ap-6074	274	4	freeform	freeform	NOUN
ap-6074	274	5	measurement	measurement	NOUN
ap-6074	274	6	capability	capability	NOUN
ap-6074	274	7	of	of	ADP
ap-6074	274	8	optical	optical	ADJ
ap-6074	274	9	and	and	CCONJ
ap-6074	274	10	tactile	tactile	ADJ
ap-6074	274	11	co	co	ADJ
ap-6074	274	12	-	-	ADJ
ap-6074	274	13	ordinate	ordinate	ADJ
ap-6074	274	14	measuring	measure	VERB
ap-6074	274	15	machines	machine	NOUN
ap-6074	274	16	.	.	PUNCT
ap-6074	275	1	meas	meas	PROPN
ap-6074	275	2	sci	sci	PROPN
ap-6074	275	3	technol	technol	PROPN
ap-6074	275	4	23(9):23094013	23(9):23094013	NUM
ap-6074	275	5	,	,	PUNCT
ap-6074	275	6	2012	2012	NUM
ap-6074	275	7	.	.	PUNCT
ap-6074	276	1	[	[	X
ap-6074	276	2	2	2	X
ap-6074	276	3	]	]	X
ap-6074	276	4	g.	g.	PROPN
ap-6074	276	5	roger	roger	PROPN
ap-6074	276	6	,	,	PUNCT
ap-6074	276	7	d.	d.	PROPN
ap-6074	276	8	flack	flack	PROPN
ap-6074	276	9	,	,	PUNCT
ap-6074	276	10	m.	m.	NOUN
ap-6074	276	11	mccarthy	mccarthy	PROPN
ap-6074	276	12	.	.	PUNCT
ap-6074	277	1	a	a	DET
ap-6074	277	2	review	review	NOUN
ap-6074	277	3	of	of	ADP
ap-6074	277	4	industrial	industrial	ADJ
ap-6074	277	5	capabilities	capability	NOUN
ap-6074	277	6	to	to	PART
ap-6074	277	7	measure	measure	VERB
ap-6074	277	8	freeform	freeform	ADJ
ap-6074	277	9	surfaces	surface	NOUN
ap-6074	277	10	.	.	PUNCT
ap-6074	278	1	npl	npl	PROPN
ap-6074	278	2	report	report	NOUN
ap-6074	278	3	,	,	PUNCT
ap-6074	278	4	depcem	depcem	NOUN
ap-6074	278	5	014	014	NUM
ap-6074	278	6	2007	2007	NUM
ap-6074	278	7	.	.	PUNCT
ap-6074	279	1	[	[	X
ap-6074	279	2	3	3	X
ap-6074	279	3	]	]	X
ap-6074	279	4	v.	v.	ADP
ap-6074	279	5	zelený	zelený	PROPN
ap-6074	279	6	,	,	PUNCT
ap-6074	279	7	i.	i.	PROPN
ap-6074	279	8	linkeová	linkeová	PROPN
ap-6074	279	9	,	,	PUNCT
ap-6074	279	10	p.	p.	NOUN
ap-6074	279	11	skalník	skalník	NOUN
ap-6074	279	12	.	.	PUNCT
ap-6074	280	1	calibration	calibration	NOUN
ap-6074	280	2	of	of	ADP
ap-6074	280	3	freeform	freeform	ADJ
ap-6074	280	4	standard	standard	NOUN
ap-6074	280	5	.	.	PUNCT
ap-6074	281	1	euspen	euspen	PROPN
ap-6074	281	2	’s	’s	PART
ap-6074	281	3	15th	15th	ADJ
ap-6074	281	4	international	international	ADJ
ap-6074	281	5	conference	conference	PROPN
ap-6074	281	6	&	&	CCONJ
ap-6074	281	7	exhibition	exhibition	PROPN
ap-6074	281	8	,	,	PUNCT
ap-6074	281	9	leuven	leuven	PROPN
ap-6074	281	10	,	,	PUNCT
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ap-6074	281	13	.	.	PUNCT
ap-6074	282	1	[	[	X
ap-6074	282	2	4	4	NUM
ap-6074	282	3	]	]	X
ap-6074	282	4	i.	i.	PROPN
ap-6074	282	5	linkeová	linkeová	PROPN
ap-6074	282	6	,	,	PUNCT
ap-6074	282	7	p.	p.	NOUN
ap-6074	282	8	skalník	skalník	NOUN
ap-6074	282	9	,	,	PUNCT
ap-6074	282	10	v.	v.	ADP
ap-6074	282	11	zelený	zelený	PROPN
ap-6074	282	12	.	.	PUNCT
ap-6074	283	1	calibrated	calibrate	VERB
ap-6074	283	2	cad	cad	NOUN
ap-6074	283	3	model	model	NOUN
ap-6074	283	4	of	of	ADP
ap-6074	283	5	freeform	freeform	ADJ
ap-6074	283	6	standard	standard	NOUN
ap-6074	283	7	.	.	PUNCT
ap-6074	284	1	xxi	xxi	PROPN
ap-6074	284	2	imeko	imeko	PROPN
ap-6074	284	3	world	world	PROPN
ap-6074	284	4	congress	congress	PROPN
ap-6074	284	5	measurement	measurement	PROPN
ap-6074	284	6	in	in	ADP
ap-6074	284	7	research	research	NOUN
ap-6074	284	8	and	and	CCONJ
ap-6074	284	9	industry	industry	NOUN
ap-6074	284	10	,	,	PUNCT
ap-6074	284	11	prague	prague	NOUN
ap-6074	284	12	2015	2015	NUM
ap-6074	284	13	.	.	PUNCT
ap-6074	285	1	[	[	X
ap-6074	285	2	5	5	X
ap-6074	285	3	]	]	PUNCT
ap-6074	285	4	l.	l.	PROPN
ap-6074	285	5	piegl	piegl	PROPN
ap-6074	285	6	,	,	PUNCT
ap-6074	285	7	w.	w.	PROPN
ap-6074	285	8	tiller	tiller	NOUN
ap-6074	285	9	.	.	PUNCT
ap-6074	286	1	the	the	DET
ap-6074	286	2	nurbs	nurbs	PROPN
ap-6074	286	3	book	book	PROPN
ap-6074	286	4	.	.	PUNCT
ap-6074	286	5	springer	springer	NOUN
ap-6074	286	6	-	-	PUNCT
ap-6074	286	7	verlag	verlag	PROPN
ap-6074	286	8	berlin	berlin	PROPN
ap-6074	286	9	heidelberg	heidelberg	PROPN
ap-6074	286	10	1997	1997	NUM
ap-6074	286	11	.	.	PUNCT
ap-6074	287	1	doi:10.1007/978	doi:10.1007/978	ADJ
ap-6074	287	2	-	-	PUNCT
ap-6074	287	3	3	3	NUM
ap-6074	287	4	-	-	PUNCT
ap-6074	287	5	642	642	NUM
ap-6074	287	6	-	-	PUNCT
ap-6074	287	7	59223	59223	NUM
ap-6074	287	8	-	-	PUNCT
ap-6074	287	9	2	2	NUM
ap-6074	287	10	.	.	PUNCT
ap-6074	288	1	[	[	X
ap-6074	288	2	6	6	NUM
ap-6074	288	3	]	]	PUNCT
ap-6074	288	4	v.	v.	ADP
ap-6074	288	5	zelený	zelený	PROPN
ap-6074	288	6	,	,	PUNCT
ap-6074	288	7	i.	i.	PROPN
ap-6074	288	8	linkeová	linkeová	PROPN
ap-6074	288	9	,	,	PUNCT
ap-6074	288	10	j.	j.	PROPN
ap-6074	288	11	sýkora	sýkora	PROPN
ap-6074	288	12	,	,	PUNCT
ap-6074	288	13	p.	p.	PROPN
ap-6074	288	14	skalník	skalník	PROPN
ap-6074	288	15	.	.	PUNCT
ap-6074	289	1	mathematical	mathematical	ADJ
ap-6074	289	2	approach	approach	NOUN
ap-6074	289	3	to	to	PART
ap-6074	289	4	evaluate	evaluate	VERB
ap-6074	289	5	involute	involute	ADJ
ap-6074	289	6	gear	gear	NOUN
ap-6074	289	7	profile	profile	NOUN
ap-6074	289	8	and	and	CCONJ
ap-6074	289	9	helix	helix	ADJ
ap-6074	289	10	deviations	deviation	NOUN
ap-6074	289	11	without	without	ADP
ap-6074	289	12	using	use	VERB
ap-6074	289	13	special	special	ADJ
ap-6074	289	14	gear	gear	NOUN
ap-6074	289	15	software	software	NOUN
ap-6074	289	16	.	.	PUNCT
ap-6074	290	1	mechanism	mechanism	NOUN
ap-6074	290	2	and	and	CCONJ
ap-6074	290	3	machine	machine	NOUN
ap-6074	290	4	theory	theory	NOUN
ap-6074	290	5	135:150	135:150	PROPN
ap-6074	290	6	–	–	PUNCT
ap-6074	290	7	164	164	NUM
ap-6074	290	8	,	,	PUNCT
ap-6074	290	9	2019	2019	NUM
ap-6074	290	10	.	.	PUNCT
ap-6074	291	1	doi:10.1016	doi:10.1016	PROPN
ap-6074	291	2	/	/	SYM
ap-6074	291	3	j.mechmachtheory.2019.01.030	j.mechmachtheory.2019.01.030	PROPN
ap-6074	291	4	.	.	PUNCT
ap-6074	292	1	[	[	X
ap-6074	292	2	7	7	X
ap-6074	292	3	]	]	X
ap-6074	292	4	h.	h.	NOUN
ap-6074	292	5	stachel	stachel	PROPN
ap-6074	292	6	.	.	PUNCT
ap-6074	293	1	on	on	ADP
ap-6074	293	2	spatial	spatial	ADJ
ap-6074	293	3	involute	involute	ADJ
ap-6074	293	4	gearing	gearing	NOUN
ap-6074	293	5	.	.	PUNCT
ap-6074	294	1	6th	6th	ADJ
ap-6074	294	2	international	international	ADJ
ap-6074	294	3	conference	conference	NOUN
ap-6074	294	4	on	on	ADP
ap-6074	294	5	applied	apply	VERB
ap-6074	294	6	informatics	informatic	NOUN
ap-6074	294	7	(	(	PUNCT
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ap-6074	294	9	)	)	PUNCT
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ap-6074	294	17	39	39	NUM
ap-6074	294	18	.	.	PUNCT
ap-6074	295	1	[	[	X
ap-6074	295	2	8	8	NUM
ap-6074	295	3	]	]	X
ap-6074	295	4	h.	h.	NOUN
ap-6074	295	5	stachel	stachel	PROPN
ap-6074	295	6	.	.	PUNCT
ap-6074	296	1	comments	comment	NOUN
ap-6074	296	2	on	on	ADP
ap-6074	296	3	helical	helical	ADJ
ap-6074	296	4	developables	developable	NOUN
ap-6074	296	5	.	.	PUNCT
ap-6074	297	1	proceedings	proceeding	NOUN
ap-6074	297	2	of	of	ADP
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ap-6074	297	5	international	international	ADJ
ap-6074	297	6	conference	conference	NOUN
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ap-6074	297	17	)	)	PUNCT
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ap-6074	300	2	2019	2019	NUM
ap-6074	300	3	-	-	SYM
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ap-6074	300	5	-	-	SYM
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ap-6074	303	8	,	,	PUNCT
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ap-6074	311	9	.	.	PUNCT
ap-6074	312	1	proceedings	proceeding	NOUN
ap-6074	312	2	of	of	ADP
ap-6074	312	3	the	the	DET
ap-6074	312	4	18th	18th	ADJ
ap-6074	312	5	conference	conference	NOUN
ap-6074	312	6	on	on	ADP
ap-6074	312	7	applied	apply	VERB
ap-6074	312	8	mathematics	mathematic	NOUN
ap-6074	312	9	(	(	PUNCT
ap-6074	312	10	aplimat	aplimat	ADJ
ap-6074	312	11	2019	2019	NUM
ap-6074	312	12	)	)	PUNCT
ap-6074	312	13	,	,	PUNCT
ap-6074	312	14	bratislava	bratislava	PROPN
ap-6074	312	15	,	,	PUNCT
ap-6074	312	16	slovakia	slovakia	PROPN
ap-6074	312	17	(	(	PUNCT
ap-6074	312	18	2019):500	2019):500	NUM
ap-6074	312	19	–	–	PUNCT
ap-6074	312	20	507	507	NUM
ap-6074	312	21	.	.	X
ap-6074	312	22	109	109	NUM
ap-6074	312	23	http://dx.doi.org/10.1007/978-3-642-59223-2	http://dx.doi.org/10.1007/978-3-642-59223-2	PROPN
ap-6074	312	24	http://dx.doi.org/10.1016/j.mechmachtheory.2019.01.030	http://dx.doi.org/10.1016/j.mechmachtheory.2019.01.030	PROPN
ap-6074	312	25	https://www.ptb.de/emrp/eng56-standards.html	https://www.ptb.de/emrp/eng56-standards.html	PROPN
ap-6074	312	26	https://www.ptb.de/emrp/eng56-standards.html	https://www.ptb.de/emrp/eng56-standards.html	PROPN
ap-6074	312	27	https://www.ptb.de/emrp/eng56-standards.html	https://www.ptb.de/emrp/eng56-standards.html	PROPN
ap-6074	312	28	https://www.ptb.de/emrp/eng56-standards.html	https://www.ptb.de/emrp/eng56-standards.html	PROPN
ap-6074	312	29	acta	acta	PROPN
ap-6074	312	30	polytechnica	polytechnica	PROPN
ap-6074	312	31	61(si):99–109	61(si):99–109	NUM
ap-6074	312	32	,	,	PUNCT
ap-6074	312	33	2021	2021	NUM
ap-6074	312	34	1	1	NUM
ap-6074	312	35	introduction	introduction	NOUN
ap-6074	312	36	2	2	NUM
ap-6074	312	37	surface	surface	NOUN
ap-6074	312	38	of	of	ADP
ap-6074	312	39	hyperbolic	hyperbolic	ADJ
ap-6074	312	40	paraboloid	paraboloid	ADJ
ap-6074	312	41	2.1	2.1	NUM
ap-6074	312	42	freeform	freeform	NOUN
ap-6074	312	43	standard	standard	ADJ
ap-6074	312	44	hyperbolic	hyperbolic	ADJ
ap-6074	312	45	paraboloid	paraboloid	ADJ
ap-6074	312	46	2.2	2.2	NUM
ap-6074	312	47	physical	physical	ADJ
ap-6074	312	48	freeform	freeform	NOUN
ap-6074	312	49	standard	standard	ADJ
ap-6074	312	50	hyperbolic	hyperbolic	ADJ
ap-6074	312	51	paraboloid	paraboloid	NOUN
ap-6074	312	52	3	3	NUM
ap-6074	312	53	solid	solid	ADJ
ap-6074	312	54	of	of	ADP
ap-6074	312	55	hyperbolic	hyperbolic	ADJ
ap-6074	312	56	paraboloid	paraboloid	ADJ
ap-6074	312	57	3.1	3.1	NUM
ap-6074	312	58	spatial	spatial	ADJ
ap-6074	312	59	hyperbolic	hyperbolic	ADJ
ap-6074	312	60	paraboloid	paraboloid	NOUN
ap-6074	312	61	standard	standard	NOUN
ap-6074	312	62	3.1.1	3.1.1	NUM
ap-6074	312	63	physical	physical	ADJ
ap-6074	312	64	spatial	spatial	ADJ
ap-6074	312	65	hyperbolic	hyperbolic	ADJ
ap-6074	312	66	paraboloid	paraboloid	ADJ
ap-6074	312	67	standard	standard	NOUN
ap-6074	312	68	4	4	NUM
ap-6074	312	69	surfaces	surface	NOUN
ap-6074	312	70	generated	generate	VERB
ap-6074	312	71	by	by	ADP
ap-6074	312	72	motion	motion	NOUN
ap-6074	312	73	of	of	ADP
ap-6074	312	74	a	a	DET
ap-6074	312	75	circle	circle	NOUN
ap-6074	312	76	involute	involute	ADJ
ap-6074	312	77	4.1	4.1	NUM
ap-6074	312	78	tangent	tangent	NOUN
ap-6074	312	79	surface	surface	NOUN
ap-6074	312	80	of	of	ADP
ap-6074	312	81	a	a	DET
ap-6074	312	82	cylindrical	cylindrical	ADJ
ap-6074	312	83	helix	helix	NOUN
ap-6074	312	84	4.2	4.2	NUM
ap-6074	312	85	involute	involute	NOUN
ap-6074	312	86	ruled	rule	VERB
ap-6074	312	87	surface	surface	NOUN
ap-6074	312	88	4.3	4.3	NUM
ap-6074	312	89	smart	smart	ADJ
ap-6074	312	90	gear	gear	NOUN
ap-6074	312	91	measurement	measurement	NOUN
ap-6074	312	92	standard	standard	NOUN
ap-6074	312	93	4.3.1	4.3.1	NUM
ap-6074	312	94	physical	physical	ADJ
ap-6074	312	95	smart	smart	ADJ
ap-6074	312	96	gear	gear	NOUN
ap-6074	312	97	standard	standard	ADJ
ap-6074	312	98	5	5	NUM
ap-6074	312	99	conclusion	conclusion	NOUN
ap-6074	312	100	references	reference	NOUN