Cyclocycloid
An 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. The parametric equations for a cyclocycloid are where formula_3 is a parameter (not the polar angle). And r can be positive or negative depending on whether it is of an Epicycloid or Hypocycloid variety. The classic Spirograph toy traces out these curves.