Definition:Trochoid

Definition
Consider a circle $C$ rolling without slipping along a straight line.

Consider a point $P$ on the line of a radius of $C$ at a distance $b$ from the center of $C$.

The curve traced out by $P$ is called a trochoid.

Cycloid
The special case where $a = b$ is usually treated separately:

Also see

 * Equation of Trochoid