[ ep-uh-sahy-kloid ]
/ ˌɛp əˈsaɪ klɔɪd /

noun Geometry.

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].
Compare epitrochoid.

Origin of epicycloid

First recorded in 1780–90; epicycle + -oid

Related forms

ep·i·cy·cloi·dal, adjective
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

Examples from the Web for epicycloid

British Dictionary definitions for epicycloid


/ (ˌɛpɪˈsaɪklɔɪd) /


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 coplanarCompare hypocycloid, cycloid (def. 4)

Derived Forms

epicycloidal, adjective
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Science definitions for epicycloid


[ ĕp′ĭ-sīkloid′ ]

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.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.