A hypotrochoid is a roulette traced by a point attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where the point is a distance h from the center of the interiour circle.

The parametric equations for a hypotrochoid are:

Special cases include the hypocycloid with h = b and the ellipse with a = 2b

The classic Spirograph toy traces out hypotrochoid curves.