Source : Webster's Revised Unabridged Dictionary (1913)

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.