Wheels on wheels on wheels

Just found this post from Walking Randomly which presents a Mathematica demo of motion path of a point of wheels on wheels on wheels:

Generally, for a series of radii and corresponding spherical frequencies , a particle on the “outer-most” wheels follows the path

I compiled another one following the demo code above, and in this one animation is among the output, besides, by inputing lists, the depth of circles is arbitrary, following pictures contains a sample with four wheels.

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