What an interesting post! I have a couple of minor quibbles (minor=less than an order of magnitude).
You’re scaling off of a human being, which gives an unnecessarily massive robot. Metal tubes have a strength to weight ratio many times better than bone. That lightens the limbs, which decreases the force required, which means smaller motors and power plant. This implies less load on the limbs, so they can be lightened further. I’m not sure what the total gain is from this when all is said and done.
I think the analysis of walking speed in terms of pendulum frequency is missing a factor of two. The planted leg is also a pendulum— an inverted pendulum with the weight at the top. This swings the hips forward at the same time as the lifted leg is swinging forward relative to the hips, doubling the total velocity.
Yes, in some cases it’s possible for a robot to have proportionately lighter limbs, but fiberglass or carbon fiber would be better than metal tubes, and greater material strength is offset by increased height. Maybe you’re underestimating bone; it’s less dense than steel and its specific strength isn’t always worse. It’s possible to get higher speeds with parallel robots like delta robots, or run long cables, but there are real tradeoffs between series and parallel kinematic chains that often justify putting drive systems out on limbs.
Or maybe you were thinking of decreasing overall mass evenly. It’s certainly possible for humans to be relatively skinny for a given height. Similarly, it’s possible to drive hydraulic cylinders very slowly, but the goal here is specifically a human-like robot, with similar gaits and payload capability. Note that air resistance is also an issue if mass is much lower relative to height.
My math for pendulum swinging was just calculating step cadence, not walking speed with 2 legs—which is doubled that way, yes. I was just making a point about the relation of pendulum frequency to walking dynamics.
What an interesting post! I have a couple of minor quibbles (minor=less than an order of magnitude).
You’re scaling off of a human being, which gives an unnecessarily massive robot. Metal tubes have a strength to weight ratio many times better than bone. That lightens the limbs, which decreases the force required, which means smaller motors and power plant. This implies less load on the limbs, so they can be lightened further. I’m not sure what the total gain is from this when all is said and done.
I think the analysis of walking speed in terms of pendulum frequency is missing a factor of two. The planted leg is also a pendulum— an inverted pendulum with the weight at the top. This swings the hips forward at the same time as the lifted leg is swinging forward relative to the hips, doubling the total velocity.
Thanks.
Yes, in some cases it’s possible for a robot to have proportionately lighter limbs, but fiberglass or carbon fiber would be better than metal tubes, and greater material strength is offset by increased height. Maybe you’re underestimating bone; it’s less dense than steel and its specific strength isn’t always worse. It’s possible to get higher speeds with parallel robots like delta robots, or run long cables, but there are real tradeoffs between series and parallel kinematic chains that often justify putting drive systems out on limbs.
Or maybe you were thinking of decreasing overall mass evenly. It’s certainly possible for humans to be relatively skinny for a given height. Similarly, it’s possible to drive hydraulic cylinders very slowly, but the goal here is specifically a human-like robot, with similar gaits and payload capability. Note that air resistance is also an issue if mass is much lower relative to height.
My math for pendulum swinging was just calculating step cadence, not walking speed with 2 legs—which is doubled that way, yes. I was just making a point about the relation of pendulum frequency to walking dynamics.