Either you have explained this poorly or you are simply wrong. Try this instead:
Roll the small coin over three time on a flat 3*D line. Once it is at the end, take that flat line and bend it into a complete circle. Note as you do the bending the small coin goes through one more rotation.
Corallary: if you had bent the line around the small coin, you would be SUBTRACTING a rotation. This even applies if the radii are equal: the inner coin does not have to rotate at all to touch the other one all the way around. Think about it!