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.