The Straight Line as a Roulette
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.
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.