[masraum]

< disregard >What am I doing wrong then?

C = 2πr or πd

C of big coin = 6π

C of little coin = 2π

One rotation takes the point on the edge of the small coin so it's 2π or 1/3 of the way around the large coin's circumference, the second takes you around to 2/3, and the third rotation takes you around so that the starting point on the outside of the small coin has traveled to the same point on the outside of the large coin. If the two outside points have again met2, the center should be in the same location as it started.
< /disregard, crap, it's all wrong >