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

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

From Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 5 "Cat" to "Celt" by Various

Thomson shows that if, in certain conditions, a conductor is placed in a magnetic field, the ions have to describe an epicycloid, and their journey is thus lengthened, while the electric resistance must increase.

From The New Physics and Its Evolution by Poincaré, Lucien

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 The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. by Belcher, Edward, Sir

The Study and Construction of Toothed Gear.—Involute, cycloid, and epicycloid.

From Scientific American, Volume 40, No. 13, March 29, 1879 A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures by Various

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

From Modern Machine-Shop Practice, Volumes I and II by Rose, Joshua