Definition:Epicycloid

Definition

Let a circle $C_1$ roll around the outside of another circle $C_2$.

The locus of a given point on the circumference of $C_1$ is known as an epicycloid.

The circles $C_1$ and $C_2$ can be referred to as the generators of the epicycloid.

The circle $C_2$ can be referred to as the deferent of the epicycloid.

The circle $C_1$ can be referred to as the epicycle of the epicycloid.

A cusp of the epicycloid is defined as a point where the epicycloid meets the static circle, the deferent.

An arc of the epicycloid is defined as one of the curves between two of the cusps of the epicycloid.

An epicycloid is also seen referred to as a common epicycloid, to distinguish it from the extended epicycloid and contracted epicycloid.

The latter two concepts are referred to on $\mathsf{Pr} \infty \mathsf{fWiki}$ as the prolate epitrochoid and curtate epitrochoid respectively.

He used it to represent the motion of the planets.

The epi- prefix in the term epicycloid comes from the Greek word meaning on or above.

The prefix can be seen in other common words, for example epicenter.