ep·i·cy·cloid 
(ĕp′ĭ-sīkloid′)
(ĕp′ĭ-sīkloid′)n.
The curve described by a point on the circumference of a circle as the circle rolls on the outside of the circumference of a second, fixed circle.
ep′i·cy·cloidal (-kloidl) adj.
epicycloidThe parametric equations of an epicycloid are
x = (a + b) cos θ - b cos ( a + b/b
θ)
y = (a + b) sin θ - b sin ( a + b/b
θ).