[mannykannot]

Here's another way of putting it, without explicitly mentioning frames of reference:

Before starting, imagine drawing a radius on the moving coin from its center to its point of contact with the stationary coin. It is pointing down.

As the moving coin goes clockwise around the fixed coin, this radius will also rotate clockwise around the center of the moving coin.

The next time the end of the radius is in contact with the fixed coin is after the moving coin has gone 1/4 of the way around the fixed one - but now the radius is pointing to the left. It has passed the point where it is pointing down again (which is when the moving coin has made one full revolution) and gone a 1/4 turn beyond that.

Repeat until you are back at the top again.