It is well known that the shadow of the tip of a rotating rod traces out a sine wave:
It’s also well known that the Fourier components of a square wave are:
So consider a rotating arm, of length 1 and rotation rate 1. On the arm a hand of length 1/3 rotates at a rate of 3. On the hand a finger of length 1/5 rotates at a rate of 5… and so on.