Hypotrochoid

From Wikipedia, the free encyclopedia

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.

The red curve is a hypotrochoid traced as the smaller black circle rolls around inside the larger black circle (parameters are R = 1.0, r = 0.6, d = 1.2).
The red curve is a hypotrochoid traced as the smaller black circle rolls around inside the larger black circle (parameters are R = 1.0, r = 0.6, d = 1.2).

The parametric equations for a hypotrochoid 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 hypocycloid with d = r and the ellipse with R = 2r.

The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.

[edit] See also

[edit] External links

 This geometry-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../h/y/p/Hypotrochoid.html"