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Roulettes and Involutes

"A roulette is the curve generated by a point which is carried by a curve which rolls on a fixed curve. [...] The locus of a point carried by a circle rolling on a straight line is a trochoid. If the point is inside the circle the trochoid has inflexions; if it is outside the circle, but rigidly attached to it, the trochoid has loops. [...] In the particular case when the point is on the circumference of the rolling circle the roulette is a cycloid. When the circle rolls on the outside of another circle the corresponding curves are the epitrochoids and epicycloids; if it rolls on the inside, they are the hypotrochoids and hypocycloids."
H. Martyn Cundy and A. P. Rollett, Mathematical Models, p. 46.