The Epicycloid

Introduction:

The epicycloid is like a cycloid on the circumference of a circle. It has as special cases the cardioid (when b = a in the definition below) and the nephroid (when b = a/2). It is a special case of the epitrochoid.

Definition:

Geometrically, the epicycloid is traced by a point on the radius of a small circle (of radius b) rolling on the edge of a larger circle (of radius a), as shown below.

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: