EPICYCLOID Definition & Meaning

epicycloid

[ ep-uh-sahy-kloid ]

Phonetic (Standard)IPA

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 ].

epicycloid

/ ˌɛ��ɪˈ��ɪ��ɔɪ�� /

noun

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

epicycloid

/ ĕ��′ĭ-��ī′��Ǿ��′ /

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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Derived Forms

ˌ��辱��ˈ��Ǿ��岹��, adjective

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Other 51�Թ� Forms

��i·��·��Ǿ�d�� adjective

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51�Թ� History and Origins

Origin of epicycloid¹

First recorded in 1780–90; epicycle + -oid

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Example Sentences

Examples have not been reviewed.

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

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

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

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

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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.

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