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Epitrochoid




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 Equation s for an epitrochoid are:
:x = (R + r)\cos heta - d\cos\left({R + r \over r} heta ight)
:y = (R + r)\sin heta - d\sin\left({R + r \over r} heta ight)

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