The Hypocycloid

Introduction:

The hypocycloid is similar to an epicycloid, but in this case the smaller circle rolls along the inside edge of the larger one. Special cases of the hypocycloid are the deltoid (b = a/3) and the astroid (b = a/4).

Definition:

Geometrically, the hypocycloid is formed by a point on the edge of a small circle of radius b rolling along the inside edge of a larger, stationary circle with radius a.

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: