epicycloid

American  

[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 ].

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epicycloid British  

/ 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

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epicycloid Scientific  

/ ĕp′ĭ-sī′kloid′ /

1. 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.

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Other Word Forms

• epicycloidal adjective

Etymology

Origin of epicycloid

First recorded in 1780–90; epicycle + -oid

Example Sentences

In epicycloidal teeth the curve forming the face of the tooth is designated an epicycloid, and that forming the flank an hypocycloid.

From Project Gutenberg

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

From Project Gutenberg

When c = a or = ∞ the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

From Project Gutenberg

They are Involute teeth. in fact epicycloids traced by a rolling circle of infinite radius, i.e. a straight line.

From Project Gutenberg

If the generating circle proceeds along the convexity of the periphery, it is called an upper or exterior epicycloid; if along the concavity, a lower or interior epicycloid.

From Project Gutenberg