# epicycloid

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].

## Origin of epicycloid

^{1}

## Other words from epicycloid

- ep·i·cy·cloi·dal, adjective

- Compare epitrochoid.

## Words Nearby epicycloid

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## How to use epicycloid in a sentence

The

*epicycloid*shown is termed the “three-cusped*epicycloid*” or the “*epicycloid*of Cremona.”External

*epicycloid*, described by a circle rolling about a fixed circle inside of it.The curve may be regarded as an epitrochoid (see

*epicycloid*) in which the rolling and fixed circles have equal radii.It follows that a line from B to M will always be tangential to the

*epicycloid*.Cycloid External

*epicycloid*, described by a circle rolling about a fixed circle inside of it.

## 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 coplanar: Compare hypocycloid, cycloid (def. 4)

## Derived forms of epicycloid

- 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

## Scientific definitions for epicycloid

[ ĕp′ĭ-sī′kloid′ ]

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.

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