page_title: Cyclocycloid
hierarchical_section_title: Cyclocycloid
caption_attribution_description: English: Animation of a Hypotrochoid. Made by myself with MuPAD. Română: Animație a unei curbe hipotrohoide. Făcută de mine însumi cu MuPAD.
context_page_description: 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 is a parameter. 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.
context_section_description: 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  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.
caption: The red curve is a cyclocycloid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5, r = -3, d = 5).