Cycloid - Revision history

DT Online: Added Template

2016-06-02T19:00:31Z

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← Older revision		Revision as of 19:00, 2 June 2016
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			__TOC__


			=====Description=====

	An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design [https://en.wikipedia.org/wiki/Cycloid_gear gear teeth] and has sometimes been used by architects to design the shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].		An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design [https://en.wikipedia.org/wiki/Cycloid_gear gear teeth] and has sometimes been used by architects to design the shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].

	A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[[loci]]''')''.		A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[[loci]]''')''.


			=====Constructions=====

	{\| cellpadding="5"		{\| cellpadding="5"
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	The cycloid is a special case of [https://en.wikipedia.org/wiki/Trochoid '''Trochoid'''] in which the point traced is on the circumference of the rolling circle. Using a similar technique, '''''Superior''''' and '''''Inferior''''' Trochoids can also be generated by plotting points either outside ''(as the tip of a paddle wheel as a boat is propelled by it)'' or inside the rolling circle ''(as if marked on a rolling disc for example)''		The cycloid is a special case of [https://en.wikipedia.org/wiki/Trochoid '''Trochoid'''] in which the point traced is on the circumference of the rolling circle. Using a similar technique, '''''Superior''''' and '''''Inferior''''' Trochoids can also be generated by plotting points either outside ''(as the tip of a paddle wheel as a boat is propelled by it)'' or inside the rolling circle ''(as if marked on a rolling disc for example)''
	.		.
	Also, by similar trechniques, the '''base line''' can be replaced by a '''base circle''' and the rolling circle rolled around either the inside or the outside of it to generate [https://en.wikipedia.org/wiki/~~Hypocycloid~~ '''Hypocycloids'''] or [https://en.wikipedia.org/wiki/Epicycloid '''Epicycloids'''] - as used in [https://en.wikipedia.org/wiki/Epicyclic_gearing '''Epicyclic Gearing'''] for example ,		Also, by similar trechniques, the '''base line''' can be replaced by a '''base circle''' and the rolling circle rolled around either the inside or the outside of it to generate [https://en.wikipedia.org/wiki/Hypocy4cloid '''Hypocycloids'''] or [https://en.wikipedia.org/wiki/Epicycloid '''Epicycloids'''] - as used in [https://en.wikipedia.org/wiki/Epicyclic_gearing '''Epicyclic Gearing'''] for example ,
	</span>		</span>
	----		----


			{{Drawing Instruments Buyers Guide}}


	[[Category:Secondary]]		[[Category:Secondary]]
	[[Category:Geometry]]		[[Category:Geometry]]

DT Online: Corrected link

2015-02-22T10:34:59Z

Corrected link

← Older revision		Revision as of 10:34, 22 February 2015
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	An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design [https://en.wikipedia.org/wiki/Cycloid_gear gear teeth] and has sometimes been used by architects to design the shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].		An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design [https://en.wikipedia.org/wiki/Cycloid_gear gear teeth] and has sometimes been used by architects to design the shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].

	A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[ [loci]]''')''.		A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[[loci]]''')''.

	{\| cellpadding="5"		{\| cellpadding="5"
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	\| <span style="color:#B00000">		\| <span style="color:#B00000">
	* Draw a starting circle and divide into equal segments ''(say, 12)''		* Draw a starting circle and divide into equal segments ''(say, 12)''
	* Draw a horizontal line for the circle to roll along, of length equal to the circle circumference, and divide this into the same number of equal parts. ''(~~Constructing a~~ '''[[~~Scale~~]]''' ~~is a~~ convenient ~~way~~ of doing this)''.		* Draw a horizontal line for the circle to roll along, of length equal to the circle circumference, and divide this into the same number of equal parts. ''(Constructions used to create '''[[Scales]]''' are convenient ways of doing this)''.
	* Project lines parallel to the base line at heights representing the heights reached by the points on the circle as it rolls round.		* Project lines parallel to the base line at heights representing the heights reached by the points on the circle as it rolls round.
	* Start at 0 then describe a circle from the second centre position on to the first line above the baseline, which shows the height the point now reaches.		* Start at 0 then describe a circle from the second centre position on to the first line above the baseline, which shows the height the point now reaches.

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2015-02-21T15:54:55Z

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	* Repeat this procedure for each progressive centre position as shown.		* Repeat this procedure for each progressive centre position as shown.
	* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''.</span>		* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''.</span>
	\| [[ File:~~CycloidCurve~~.~~jpg~~\|350px\|right]]		\| [[ File:CycloidConstruction.png\|350px\|right]]
	\|}		\|}
	----		----

DT Online at 14:27, 19 February 2015

2015-02-19T14:27:05Z

← Older revision		Revision as of 14:27, 19 February 2015
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	An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has ~~sometmes~~ been used by architects to design ~~and~~ shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].		An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design [https://en.wikipedia.org/wiki/Cycloid_gear gear teeth] and has sometimes been used by architects to design the shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].

	A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[[loci]]''')''.		A line produced by a point following a set of rules in this way is known as the '''[[Loci\|locus of a point]]''' ''(plural is '''[ [loci]]''')''.

	{\| cellpadding="5"		{\| cellpadding="5"

DT Online: Created Cycloid

2015-02-19T14:05:04Z

Created Cycloid

New page

An [https://en.wikipedia.org/wiki/Cycloid '''Cycloid'''] is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has sometmes been used by architects to design and shape of a [http://en.wikipedia.org/wiki/Kimbell_Art_Museum curved roof]. The term ''‘cycloid’'' is used also to describe the shape of some [http://en.wikipedia.org/wiki/Fish_scale fish scales].

A line produced by a point following a set of rules in this way is known as the '''[[Loci|locus of a point]]''' ''(plural is '''[[loci]]''')''.

{| cellpadding="5"
|-
| '''Drawing a Cycloid'''
| <span style="color:#B00000">
* Draw a starting circle and divide into equal segments ''(say, 12)''
* Draw a horizontal line for the circle to roll along, of length equal to the circle circumference, and divide this into the same number of equal parts. ''(Constructing a '''[[Scale]]''' is a convenient way of doing this)''.
* Project lines parallel to the base line at heights representing the heights reached by the points on the circle as it rolls round.
* Start at 0 then describe a circle from the second centre position on to the first line above the baseline, which shows the height the point now reaches.
* Repeat this procedure for each progressive centre position as shown.
* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''.</span>
| [[ File:CycloidCurve.jpg|350px|right]]
|}
----
<span style="color: green">'''Note:'''
The cycloid is a special case of [https://en.wikipedia.org/wiki/Trochoid '''Trochoid'''] in which the point traced is on the circumference of the rolling circle. Using a similar technique, '''''Superior''''' and '''''Inferior''''' Trochoids can also be generated by plotting points either outside ''(as the tip of a paddle wheel as a boat is propelled by it)'' or inside the rolling circle ''(as if marked on a rolling disc for example)''
.
Also, by similar trechniques, the '''base line''' can be replaced by a '''base circle''' and the rolling circle rolled around either the inside or the outside of it to generate [https://en.wikipedia.org/wiki/Hypocycloid '''Hypocycloids'''] or [https://en.wikipedia.org/wiki/Epicycloid '''Epicycloids'''] - as used in [https://en.wikipedia.org/wiki/Epicyclic_gearing '''Epicyclic Gearing'''] for example ,
</span>
----

[[Category:Secondary]]
[[Category:Geometry]]