Most of the popular electronics books I've seen use a water or fluid metaphor to describe how components work (eg the fantastic Practical Electronics for Inventors).
Not at all intending to be critical with my question, just curious.
As a non-electrical engineer who dabbles in electronics, I'm excited for your work to help others learn and happy I can back it!
So I stepped back and thought about how to do it mechanically. But the hardest part of a mechanical circuit is the absolute simplest part in electronics: the junction. That is, where electricity flows in one wire and splits along two wires. How do you make chain or a belt split? Not only that, but it has to follow Kirchoff's law: the sum of currents leaving the junction must equal the current entering the junction. I finally realized that's what a differential gear arrangement does, and planetary gears are a sort of differential arrangement that would work perfectly for this. It was very, very hard to make the mechanical junction so that it had low resistance while under load, but I eventually got it. Once I had that, I knew it would all work.