Try Our Apps

# epicycloid

[ep-uh-sahy-kloid] /ˌɛp əˈsaɪ klɔɪd/
noun, Geometry.
1.
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
1780-1790
First recorded in 1780-90; epicycle + -oid
Related forms
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2018.
Cite This Source
Examples from the Web for epicycloid
Historical Examples
• It follows that a line from B to M will always be tangential to the epicycloid.

• Suppose b a tracing point on b, then as b rolls on a it will describe the epicycloid a b.

• It is impossible to mill out even a convex cycloid or epicycloid, by the means and in the manner above described.

• But if a circle be made to roll along the circumference of another circle, it becomes an epicycloid (which see).

William Henry Smyth
• The epicycloid shown is termed the “three-cusped epicycloid” or the “epicycloid of Cremona.”

British Dictionary definitions for epicycloid

## epicycloid

/ˌɛpɪˈsaɪklɔɪd/
noun
1.
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 (sense 4)
Derived Forms
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Cite This Source
epicycloid in Science
 epicycloid   (ěp'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