Cycloid Cycloid A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity, and is also the form of a curve for which the period of an object in descent on the curve does not depend on the object's starting position. The cycloid has been
Roulette (curve) in the fixed plane called a roulette. In the illustration, the fixed curve (blue) is a parabola, the rolling curve (green) is an equal parabola, and the generator is the vertex of the rolling parabola which describes the roulette (red). In this case the roulette is the cissoid of Diocles. In the case where the rolling curve is a line and the generator is a point on the line, the roulette is called an involute of the fixed curve. If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid. If,