The radius of the rolling circle is 1/n th that of the fixed circle.
dn is then the number of rotations GGB will consider before resetting the positions.
By default, n is an integer.
To include fractions, increase dn.
Check "allow irrational" to change the radius smoothly.
Trace applies to the diameter of the rolling circle.

Notes:
The purple and green curves are arbitrary intersections among the given objects (and are not fixed arms).
I think I found what I was looking for. The smooth (continuous) change of a deterministic, cyclic system is altogether a separate question from mathematical periodicity.