Roulette (Epitrochogon) of a Disk Rolling around a Regular Polygon

This Demonstration simulates a circle rolling without slipping on the outside of a stationary regular polygon of circumradius 1. A point is attached to the circle; its trace is called an epitrochogon.

For generalized cyclogons [1] and generalized trochoidal curves [2], these roulettes can be considered a limiting case of epitrochogons with an infinite number of vertices of the rolling polygon.

These epitrochogons consist of sequences of two distinct curve types, each generated by a different type of motion:

1. a cycloidal or rolling motion of the circle along the straight edges of the polygon.

2. a circular motion when turning around the vertices of the polygon.