The Straight Line as a Roulette

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A roulette is the path that a point attached to a circle follows when the circle rolls around another circle. A straight line is a special roulette, when the rolling circle is half as large as the other circle. This phenomenon can be used to convert rotary motion to linear motion.

Contributed by: Sándor Kabai (December 2007)
Open content licensed under CC BY-NC-SA



A suggested experiment for Mathematica programmers: make the radius variable, which is now set to in the first line of the program. When you vary the radius, the cylinder (planet) follows a different path. A guide in the shape of the path has to be used to ensure proper operation. A straight guide is used in the basic case.

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