A circle with radius 1 rolls without slipping once around a circle with radius 3. How many revolutions does the smaller circle make?
Does it matter if the smaller circle rolls on the inside or outside of the larger circle?
The length of the larger curve is 6 times the length of the smaller. The revolution of the small circle over the larger one can be thought of as "cutting" the small curve and "stretching" it over the larger curve. (Think about circles made of strings.) So, we have 6 revolutions.
Following the same reasoning, it doesn't matter if the small circle is insede or outside the larger one.
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