Cycloid: Difference between revisions
From DT Online
m (Corrected link) |
(Added Template) |
||
| Line 1: | Line 1: | ||
__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" | ||
| Line 19: | Line 27: | ||
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/ | 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]] | ||
Latest revision as of 19:00, 2 June 2016
Description
An 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 gear teeth and has sometimes been used by architects to design the shape of a curved roof. The term ‘cycloid’ is used also to describe the shape of some fish scales.
A line produced by a point following a set of rules in this way is known as the locus of a point (plural is loci).
Constructions
| Drawing a Cycloid |
|
 |
Note: The cycloid is a special case of 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 Hypocycloids or Epicycloids - as used in Epicyclic Gearing for example ,
