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From Wikipedia, the free encyclopedia

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

An epitrochoid (/ɛpɪˈtrɒkɔɪd/ or /ɛpɪˈtrkɔɪd/) 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 at a distance d from the center of the exterior circle.

The parametric equations for an epitrochoid are

The parameter is geometrically the polar angle of the center of the exterior circle. (However, is not the polar angle of the point on the epitrochoid.)

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 orbit of the moon, when centered around the sun, approximates an epitrochoid.

The combustion chamber of the Wankel engine is an epitrochoid.

YouTube Encyclopedic

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  • Epitrochoid in Animation Nodes I Blender 2.8 Tutorial
  • Deriving the Equations of an Epicycloid
  • Blender Animation Nodes Tutorial: Epitrochoid in 3D

Transcription

See also

References

  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 160–164. ISBN 0-486-60288-5.

External links

This page was last edited on 31 August 2021, at 16:45
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