Epicycloid

Epicycloid is the name of a peculiar curve. When a circle moves upon a straight line, any point in its circumference describes a Cycloid (q.v.); but if the circle moves on the convex circumference of another circle, every point in the plane of the first circle describes an epicycloid; and if on the concave circumference, a hypocycloid. The circle that moves is the generating circle; the other, the base. The describing point is not necessarily in the circumference of the generating circle, but may be anywhere in a radius or its prolongation. It has many remarkable properties, and is even useful in the practical arts. The teeth of wheels in machinery must have an epicycloidal form, in order to secure uniformity of movement.