- Steve Phelps
If a curve rolls, without slipping, along another fixed curve, any point of line which moves with the rolling curve describes a roulette. The locus of a point attached to the rolling curve is a point-roulette, and the envelope of a line attached to the rolling curve is a line-roulette.
Cycloid as a Special Case of a Point-Roulette
The cycloid is a point-roulette, as it is the locus of a point on the circumference of a circle that rolls on a fixed straight line.
A Cycloid as a Line-Roulette
A Epicycloid Envelope
Drag the green point along the circumference of the circle. There will be n–1 cusps.
A Hypocycloid Envelope
Drag the green point along the circumference of the circle. There will be n+1 cusps.