High Quality Content by WIKIPEDIA articles! A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes. Roughly speaking, it is the curve described by a point (called the generator or pole) attached to a given curve as it rolls without slipping along a second given curve that is fixed. More precisely, given a curve attached to a plane which is moving so that the curve rolls without slipping along a given curve attached to a fixed plane occupying the same space, then a point attached to the moving plane describes a curve in the fixed plane called a roulette.

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