Epitrochoid

Epitrochoid

An epitrochoid (IPAEng|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 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 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.

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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Look at other dictionaries:

  • Epitrochoid — Ep i*tro choid, n. [Pref. epi + Gr. ? wheel + oid.] (Geom.) A kind of curve. See {Epicycloid}, any {Trochoid}. [1913 Webster] || …   The Collaborative International Dictionary of English

  • epitrochoid — /ep i troh koyd/, Geom. a plane curve generated by the motion of a fixed point on the radius or extension of the radius of a circle that rolls externally, without slipping, on a fixed circle. The epitrochoid is a generalization of the epicycloid …   Universalium

  • epitrochoid — noun A geometric curve traced by a fixed point on one circle which rotates around the perimeter of another circle. Examples include the shape of the Wankel engine …   Wiktionary

  • epitrochoid — epi·trochoid …   English syllables

  • epitrochoid — A geometric path followed by a specific point located in a generating circle which is rolled around the periphery of a base circle …   Dictionary of automotive terms

  • epitrochoid — …   Useful english dictionary

  • Centered trochoid — In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both… …   Wikipedia

  • Cycloid — For other uses, see Cycloid (disambiguation). A cycloid generated by a rolling circle A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line. It is an example of a roulette, a curve… …   Wikipedia

  • Wankel engine — The Wankel engine is a type of internal combustion engine which uses a rotary design to convert pressure into a rotating motion instead of using reciprocating pistons. Its four stroke cycle is generally generated in a space between the inside of… …   Wikipedia

  • Hypocycloid — In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a… …   Wikipedia

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