1. The orbit is a circle with radius R (= constant). The center of rotation is in a distance d from the center of the orbit. (see attachment)
2. From the Cosine rule you know:
This ia a quadratic equation in r. Solve for r. I've got:
3. Use this equation together with a polar coordinate system.
4. For instance with R = 4, d = 2 you'll get a circle around (2, 0) radius 4 and the center of rotation (of the "arm") is the origin.