- Epitrochoid
An epitrochoid (IPAEng|ɛpɨˈtrɒkɔɪd, -ˈtroʊ-) is a roulette traced by a point attached to a
circle ofradius "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 equation s for an epitrochoid are:x = (R + r)cos heta - dcosleft({R + r over r} heta ight),,:y = (R + r)sin heta - dsinleft({R + r over r} heta ight).,
Special cases include the
limaçon with "R = r" and theepicycloid with "d = r".The classic
Spirograph toy traces out epitrochoid andhypotrochoid curves.The orbits of planets in the once popular geocentric
Ptolemaic system are epitrochoids.The
stator of theWankel engine is an epitrochoid.ee also
*
Hypotrochoid
*Cycloid
*Epicycloid
*Hypocycloid
*Spirograph References
*
External links
* [http://www.mekanizmalar.com/epitrochoid.html Flash Animation of Epitrochoid]
* [http://mathworld.wolfram.com/Epitrochoid.html Epitrochoid at Mathworld]
* [http://xahlee.org/SpecialPlaneCurves_dir/Epitrochoid_dir/epitrochoid.html Visual Dictionary of Special Plane Curves] Xah Lee
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