Epicycloidal \Ep`i*cy*cloid"al\, a. Pertaining to the epicycloid, or having its properties.

Epicycloidal wheel, a device for producing straight-line motion from circular motion, on the principle that a pin fastened in the periphery of a gear wheel will describe a straight line when the wheel rolls around inside a fixed internal gear of twice its diameter.

Source: Webster's Revised Unabridged Dictionary (1913)