If a curve rolls, without slipping, along another fixed curve, any point of line which moves with the rolling curve describes a [i]roulette[/i].[br][br]The locus of a point attached to the rolling curve is a [i]point-roulette[/i], and the envelope of a line attached to the rolling curve is a [i]line-roulette[/i].

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.

Drag the green point along the circumference of the circle. There will be n–1 cusps.

Drag the green point along the circumference of the circle. There will be n+1 cusps.