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I'm wondering if it would be feasible to swap the string bow with gears and a crank, like this:
I feel like it could be done with clay (for the basic shape) and sticks (to give the gears some internal structure); or even by carving wood with a stone, although that would be extremely laborious. The advantage would be obvious, higher and more consistent speed without too much effort.
Gears would have to be really well made, otherwise it won't roll well and you would lose speed. I think a better chance would be to use two cylinders and the rope as the belt between them.
That would perhaps work even better, as long as the rope is strong enough to keep up with the stress.
If you're looking for reliable, primitive gears: look at an old watermill's wooden "crown wheel" and pinion.
That being said, you'd get the same effect with pulleys and belt. Hand carving wooden pulleys or turning them on a simple pole lathe with a sharp or abrasive rock would much easier than making gears.
It’d have to be clay and that sounds hard, but I believe he has the skill to pull it off.
Clay gears would likely not work well. They'd be very uneven and probably just grind each other off. Wooden gears would be more feasible (which look very different) but that also would require tools for higher precision. And if we go the gears route, he might as well would use a water wheel to power the whole thing instead of doing it my hand.