The Hypotrochoid


The hypotrochoid is similar to the epitrochoid, except that the smaller circle rolls on the inside edge of the larger one. It has as special cases the ellipse (a = 2b) and the hypocycloid (h = b). In general, it has a/b loops.


Geometrically, the hypotrochoid is traced by a point P, attached at a distance h to the center of a small circle of radius b as it rolls along the inside edge of a larger circle of radius a.


Velocity and Acceleration:

The Tangent Vector:

Arc Length: