Question: Suppose you have two circles, one with radius r1 centered at the origin, and one with radius r2 centered at (r1 + r2 ; 0). Thus, the circles have the point P = (r1 ; 0) in common. Suppose the circle with radius r2 begins rolling counterclockwise along the outside of the other circle. As the circle rotates, the point that was originally at P will also rotate, tracing out a path in the plane. Find parametric equations for this path.

x(t) = (r1 + r2).cos (t) - r2.cos ( t.(r1+r2)/r2 )
y(t) = (r1 + r2).sin (t) - r2.sin ( t.(r1+r2)/r2 )

Pretty nice curves. See what happens when r1/r2 does lie in Q, and when it doesn't.

edit : a sign has been fixed.

This post was edited by feanur on Jun 7 2015 05:04pm

Hey, thanks! That's pretty rad