(mathematics) A curve traced by a point rigidly attached to a circle at a point other than the center when the circle rolls without slipping on the outside of a fixed circle.
Epitrochoid
| Sci-Tech Dictionary: epitrochoid |
(¦ep·ə′trō′köid)
| 5min Related Video: Epitrochoid |
| Wikipedia: Epitrochoid |
An epitrochoid (pronounced /ɛpɨˈtrɒkɔɪd, ɛpɨˈtroʊkɔɪd/) 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
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 combustion chamber of the Wankel engine is an epitrochoid.
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
- Flash Animation of Epitrochoid
- Epitrochoid at Mathworld
- Visual Dictionary of Special Plane Curves on Xah Lee 李杀网
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 | epicycloid |
| Plane curve (mathematics) |
| Hypotrochoid |
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