Cycloid: Difference between revisions
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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]]''')''. | ||
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* 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. ''( | * 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. | ||
Revision as of 10:34, 22 February 2015
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).
| Drawing a Cycloid |
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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 ,