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>A humanoid robot takes roughly 5,000 steps per hour. Each step sends a shock of 2–3× body weight through the leg actuators—forces that would be fine occasionally, but become destructive when repeated thousands of times without pause.

As someone who comes from the world of running and knee problems, I feel this misses the issue. Normal walking should not produce these kinds of shocks unless your gait is really jumpy or otherwise screwed up. You only start to see these forces when running and that's where technique becomes important even for humans if you want to prevent damage to your joints over long distances. But at least for walking I suppose that a fully articulated humanoid with all the degrees of freedom of human gait should be mostly a control problem, not a mechanical engineering one.

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The force an impulse generates on a contact depends on the speed of deceleration. It's just F=m*a

Slow deceleration leads to low forces. If you have a contact event with a hard substance, like a rigid metal for accurate kinematics, the deceleration to zero upon a contact has to happen instantly. Meaning the deceleration is incredibly high, resulting in extremely high forces for a few milliseconds.

Human bodies are made out of a flexible and impact resistant material: water. When a contact event happens, your body deforms, which means that the deceleration happens over a longer time frame with less force. Not just that, your muscles also have a certain amount of flexibility in them and basically zero internal inertia. All the inertia is in the limb as a whole, whereas for a robot there is a spinning motor and gearbox that needs to slow down as well.

You could solve this as a control problem by adding series elastic actuators, which means you need to change your mechanical design.

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The human body goes further than that too, when you're out jogging - as your foot approaches the ground for a stride, you slow the velocity of your foot downwards towards the ground so there's less of a sudden deceleration.

Imagine when you throw a tennis ball high in the sky, and then you catch it on your racket without bouncing by matching it's velocity, your feet do the same thing with the ground on a smaller scale.

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Then you have several hinges absorbing/dissipating that energy if you're using good form: foot flexes with a pivot in the arch of your foot, calf/achilles stretches with a pivot in your ankle and quad with a pivot in your knee. It should look like an angled, backwards Z at strike with nothing just straightened and tanking the impact.

Nobody actually runs perfectly enough to take 100% of the impact out of your joints but good form routes as much as possible into the muscles/ligaments around the joints instead of straight through them. It's a lot of little bitty unconscious nerve endings and muscles so one could expect it will take a while to iron out for robots.

Thinking about it more, maybe the issue here is that there's no self-healing stretchy ligaments involved in robots to begin with, even before the control issue.

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