Epitrochoid

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An epitrochoid (IPA [ɛpɪˈtrɒkɔɪd, -ˈtrəʊ-]) 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

<math>x = (R + r)\cos\theta - d\cos\left({R + r \over r}\theta\right),\,</math>

<math>y = (R + r)\sin\theta - d\sin\left({R + r \over r}\theta\right).\,</math>

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

The classic Spirograph toy traces out epitrochoid and hypotrochoid curves.

The stator of the Wankel engine is an epitrochoid.