The path of contact which it traces is identical with itself; and the flanks of the teeth c are internal and their faces ex ternal epicycloids for wheels, and both flanks and faces are **cycloids** For a pitch-circle of twice the P, - / radius of the rolling or describing /, -~- circle (as it is called) the internal B ~, epicycloid is a straight line, being, / E in fact, a diameter of the pitch- circle, so that the flanks of the teeth for such a pitch-circle are planes radiating from the axis.

The name cycloid is now restricted to the curve described when the tracing-point is on the circumference of the circle; if the point is either within or without the circle the curves are generally termed trochoids, but they are also known as the prolate and curtate **cycloids** respectively.

For epiand hypo-**cycloids** and epiand hypo-trochoids see Epicycloid.