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(I am not a mechanical engineer) Are capstan drives a solution to some of these gearing problems?
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They don't back-drive well. The whole point of this hand design is to back-drive the contact forces into the motor, where there's force control. They're somewhat bulky, too.

Key concept: force-based motor control works quite well. Preserve that property through the gear train and force-based hand control works.

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> They don't back-drive well

What? An ideal capstan drive can be backdriven perfectly fine. You only run into problems once it stops being ideal (e.g. built out of heavy parts, high gear ratio, etc.)

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It's the high reduction ratio that's the problem. If you build a 200:1 capstan, it's not going to back drive well. And it won't be anywhere near ideal.
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Why is a pancake motor too large for fingers? Human motors aren't placed on the fingers either...
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This is what a pancake motor looks like.[1] Thin and flat. Wrong form factor for fitting into a wrist.

Strings ("tendons") have their own problems. Wear at bearing points, mostly. You need an opposed pair, too. So there's a motor, a winding drums, and something like a spring to maintain tension. Or two motors and two winding drums, which gives better control.

That's why snake robots have never caught on. They're good painting robots, because they can get into tight spots. But repetitive cycling wears the tendons at the same place on each cycle.

There was a good application - Tesla's snake charging robot.[2] All the complicated stuff is in the pedestal, and you can surround that with concrete to prevent damage if it's hit by a car. The snake part has no motors, just discs and strings, plus the connector and probably a cell phone camera at the end. It can be made easily replaceable, like a gas station hose.

But some people thought it was too creepy.

[1] https://www.maccon.com/pancake-motors.html

[2] https://www.youtube.com/watch?v=uMM0lRfX6YI

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