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Prior to the advent of stepper-motor clocks, electric clocks that still used balance wheels worked as follows. There was a spring that, when wound, kept the clock running for a short period of time...perhaps ten minutes or so (I cannot recall for sure). Once the spring was close to losing energy, contact was made that completed a circuit through a solenoid. The solenoid then wound the spring for the next cycle. This was repeated until the battery was dead. I don't think a direct application of this idea will work because it takes a considerable amount of energy to wind this thing. However, I discovered (while assembling) that the drive train does not need a lot of power to operate. Not sure how to take advantage of that...but it is a very interesting problem to ponder.