Epicycloid vs. Epitrochoid

Epicycloidnoun

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.

Epicycloidnoun

A curve traced by a point in the circumference of a circle which rolls on the convex side of a fixed circle.

Epicycloidnoun

a line generated by a point on a circle rolling around another circle

Epicycloid

In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. It is a particular kind of roulette.

Epitrochoidnoun

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

Epitrochoidnoun

A kind of curve. See Epicycloid, any Trochoid.

Epitrochoid

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 ( θ ) = ( R + r ) cos ⁡ θ − d cos ⁡ ( R + r r θ ) , {\displaystyle x(\theta )=(R+r)\cos \theta -d\cos \left({R+r \over r}\theta \right),\,} y ( θ ) = ( R + r ) sin ⁡ θ − d sin ⁡ ( R + r r θ ) .