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Definition: EPITROCHOID

Part of Speech Definition
Noun 1. A kind of curve.[Websters].

Source: Webster's Revised Unabridged Dictionary (1913)

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Date "Epitrochoid" was first used in popular English literature: sometime before 1914. (references)

Etymology:Epitrochoid \Ep`i*tro"choid\, noun. [Prefix epi- Greek expression wheel -oid.]. (references)


Extended Definition: EPITROCHOID

Epitrochoid

The epitrochoid with R = 3, r = 1 and d = 1/2
The epitrochoid with R = 3, r = 1 and d = 1/2

An epitrochoid (IPA: /ɛpɨˈtrɒkɔɪd, -ˈtroʊ-/) is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.

The parametric equations for an epitrochoid are

x = (R + r)\cos\theta - d\cos\left({R + r \over r}\theta\right),\,
y = (R + r)\sin\theta - d\sin\left({R + r \over r}\theta\right).\,

Special cases include the limaçon with R = r and the epicycloid with d = r.

The classic Spirograph toy traces out epitrochoid and hypotrochoid curves.

The orbits of planets in the once popular geocentric Ptolemaic system are epitrochoids.

The stator of the Wankel engine is an epitrochoid.

See also

  • Spirograph (game)

External links

Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "Epitrochoid". Image Credit.
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