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The parametric equations of an epicycloid are
x = (a + b) cos θ - b cos ( a + b/b
y = (a + b) sin θ - b sin ( a + b/b


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·cloid′al (-kloid′l) adj.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


(Mathematics) 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. Compare hypocycloid, cycloid4
ˌepicyˈcloidal adj
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014


(ˌɛp əˈsaɪ klɔɪd)

a curve generated by the motion of a point on the circumference of a circle that rolls externally, without slipping, on a fixed circle.
ep`i•cy•cloi′dal, adj.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.epicycloid - a line generated by a point on a circle rolling around another circleepicycloid - a line generated by a point on a circle rolling around another circle
line roulette, roulette - a line generated by a point on one figure rolling around a second figure
cardioid - an epicycloid in which the rolling circle equals the fixed circle
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
The surface of sinuses was represented by the extrusion of curtate epicycloid. The analytical surface model of the valve leaflets is based on the hypocycloidal type surface of extrusion.
In this paper, the epicycloid crack problem is formulated into solving the hypersingular integral equation numerically for finding the stress intensity factors, maximum stress intensity and energy release rate for the crack subject to shear loading.
The unicycle frame comes with an epicycloid crank system and a magnetised main wheel to generate resistance.
Orrico inscribed eight large circles, each a revisualization of the geometric form known as an epicycloid. Orrico's choice of gestures for each of the eight circles pays homage to Hildreth Meiere's portrayal of the eight sciences on the ceiling of the National Academy of Sciences' Great Hall.
If the circle is rolling outside another circle we call the given curve the epicycloid. If it is rolling inside another one we call it the hypocycloid.
Digmesa used PEEK for the two epicycloid vanes located in the flowmeter's two epicycloid turbines, according to Victrex.