Cyclocycloid
![]() | It has been suggested that this article be merged into Epitrochoid. (Discuss) Proposed since February 2024. |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/20/EpitrochoidIn3.gif/400px-EpitrochoidIn3.gif)
A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/HypotrochoidOutThreeFifths.gif/400px-HypotrochoidOutThreeFifths.gif)
The parametric equations for a cyclocycloid are
where is a parameter (not the polar angle). And r can be positive (represented by a ball rolling outside of a circle) or negative (represented by a ball rolling inside of a circle) depending on whether it is of an epicycloid or hypocycloid variety.
The classic Spirograph toy traces out these curves.