In this page, we use the narrowest definition of the term cycloid, defined as the trace of a point on the circumsference of a circle rolling on a line without slipping. In the right figure, c is the rolling circle.
P is the tracing point.
A is the point of contact with line. The locus of E is the evolute of the cycloid. Tracing a Cycloid. The catacaustic of a cycloid with respect to parallel rays coming beneath its arc are two smaller cycloids. The evolute of a cycloid is another cycloid shifted under it.