Real Dictionary

epicycloid in American English
the curve traced by a point on the circumference of an epicycle that rolls around the outside of a fixed circle
noun: a curve generated by the motion of a point on the circumference of a circle that rolls externally, without slipping, on a fixed circle. Equation x = (a + b) cos θ − b cos [(a + b)θ/b] and y = (a + b) sin θ − b sin [(a + b)θ/b]

epicycloid in British English
noun: the curve described by a point on the circumference of a circle as this circle rolls around the outside of another fixed circle, the two circles being coplanar