As it seems that no one is going to get this one:
The first spindle, A, has a torque advantage while it is positioned at the top and at the bottom of the spin circle. But at each side, the torque advantage becomes negative, a disadvantage. By integrating the proper formula for the torque advantage, one can see that the total advantage summed around the entire circle is zero = no advantage.
The question was, “from where does the energy come?” Obviously it has something to do with the twisted spring, but interestingly, the spring always has the same number of twists, implying that it isn’t giving up the energy within the twists. No matter how many times the spindles rotate, there will always be the same number of twists in the spring.
The answer for this one is actually similar to that for a pendulum swing, except with a pendulum swing the arm never actually return to the same position it started. But the pendulum begins to swing because the initial position is one of higher potential energy. The pendulum must start at the top of the swing. Similarly, the spindles must start at the top of the rotation circle where spindle A has temporary advantage.
Because of the temporary advantage, Spindle A forces a rotation to begin and the length of the spring prevents the motion of spindle B from directly countering spindle A. For a brief moment, the B end of the coil spring is more tightly wound than the A end. And by the time that greater tightness catches up to the A end, spindle A is no longer at the top where it had advantage but rather at the first side (3 o’clock) being slowed down by its new disadvantage. So the extra boost from the B end of the spring as a momentary pulse helps spindle A to get around the negative arc. The initial advantage of A gets passed through the spring back for A to use during its disadvantage arc period. And at that point end B is back to the same amount of twist with which it began.
During the lower portion of the rotation, the same thing is occurring. Spindle A has an advantage which it uses to put extra twist back into the B end of the spring which propagates around to help A out during its next upcoming negative arc (at 9 o’clock). Do the math.
So does it continue forever? No. There is friction using up the initial potential energy and eventually the spindles stop turning during one of the negative arc periods (3 or 9 o’clock) even though there is still the same number of twists in the spring as in the beginning.
So the answer as to where the energy came from is that it is “momentum pulse energy” provided by the system beginning at a high potential energy state, just like a pendulum swing starting from the raised pendulum position. And the number of twists in the spring is analogous to the gravity field of the pendulum.