The Epitrochoid

Introduction:

The epitrochoid has as special cases the circle (a = 0), the limaçon (a = b), and the epicycloid (h = b). In general, it has a/b loops.

Definition:

Geometrically, the epitrochoid is traced by a point P attached at a distance h to the center of a circle of radius b rolling along another circle of radius a.

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: