Epitrochoid

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The Epitrochoid with R=1, r=1/3 and d=1/6

An epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.

The parametric equations for an epitrochoid are:

[x = (R + r)\cos\theta - d\cos\left(\theta\right)]

[y = (R + r)\sin\theta - d\sin\left(\theta\right)]

Special cases include the limaçon with R = r and the epicycloid with d = r

The classic Spirograph toy traces out epitrochoid and hypotrochoid curves.

See also: hypotrochoid

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