# Roulettes

- Author:
- 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.

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