Source : Webster's Revised Unabridged Dictionary (1913)

Epicycloid \Ep`i*cy"cloid\, n. [Epicycle + -oid: cf. F.
   ['e]picyclo["i]de.] (Geom.)
   A curve traced by a point in the circumference of a circle
   which rolls on the convex side of a fixed circle.

   Note: Any point rigidly connected with the rolling circle,
         but not in its circumference, traces a curve called an
         epitrochoid. The curve traced by a point in the
         circumference of the rolling circle when it rolls on
         the concave side of a fixed circle is called a
         hypocycloid; the curve traced by a point rigidly
         connected with the rolling circle in this case, but not
         its circumference, is called a hypotrochoid. All the
         curves mentioned above belong to the class class called
         roulettes or trochoids. See {Trochoid}.

Source : WordNet®

epicycloid
     n : a line generated by a point on a circle rolling around
         another circle