The Collaborative International Dictionary
Epitrochoid \Ep`i*tro"choid\, n. [Pref. epi- + Gr. ? wheel + -oid.] (Geom.) A kind of curve. See Epicycloid, any Trochoid. [1913 Webster] ||
Wiktionary
n. A geometric curve traced by a fixed point on one circle which rotates around the perimeter of another circle. Examples include the shape of the Wankel engine
Wikipedia
An epitrochoid ( or ) 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
$$x (\theta) = (R + r)\cos\theta - d\cos\left({R + r \over r}\theta\right),\,$$
$$y (\theta) = (R + r)\sin\theta - d\sin\left({R + r \over r}\theta\right).\,$$
where θ 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.
The combustion chamber of the Wankel engine is an epitrochoid.
Usage examples of "epitrochoid".
Eliza had sat next to him and pronounced their names: the Limaçon of Pascal, the Kampyle of Eudoxus, the Conchoid of de Sluze, the Quadratrix of Hippias, the Epitrochoid, Tractrix, and the Cassinian Ovals.