I have been in a couple of discussions before on rolling cycloids, that fit together exactly, I found a new cool variation: The innermost and outermost cycloid both stand still.
What's the trick that makes these work? I took the liberty of reposting this to Azimuth, where we have quite a gallery of rolling cycloids and hypocycloids:
+John Baez Thanks for putting it Azimuth, the place where the rolling hypocycloids I guess first appeared. I will try and write a post explaning the trick behind this.