Epitrochoid
An epitrochoid (/ɛpᵻˈtrɒkɔɪd/ or /ɛpᵻˈtroʊkɔɪd/) 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 at a distance d from the center of the exterior circle.
The parametric equations for an epitrochoid are
where is a parameter (not the polar angle).
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 orbits of planets in the once popular geocentric Ptolemaic system are epitrochoids.
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