Electric motor scaling laws and inertia in robot actuators
https://robot-daycare.com/posts/actuation_series_1/https://youtube.com/watch?v=MwIBTbumd1Q
Eight months ago he built a quadrupedal robot that could step sideways using three of them per leg. I’m not going to link that, you’ll have to find it from his YouTube page because you should look around.
Too much gear reduction, and you can't back-drive or sense forces from the motor end. Too little gear reduction, and your motors are too bulky or too weak. Reflected inertia goes up as the square of the gear ratio, as the article points out, because the gear ratio gets you both coming and going. So high gear ratios really hurt.
Robots, like drones, need custom motors sized for the specific requirements of the joint. For a long time, the robotics industry was too tiny to get such custom motors engineered, and had to use motors designed for other purposes. This will become a non-problem as volume increases. Especially since 3-phase servomotor controllers, which drones need, are now small and cheap. They used to be the size of a paperback book or larger.
(I've been out of this for years. I've used hydraulic robots and R/C servo powered robots. The newer machinery sucks a lot less.)
The other side of the scaling laws say that motor torque scales as a square of air gap radius (roughly rotor radius), and output torque scales as linearly with gearing ratio.
When you balance these out, the reflected inertia depends on the inverse of power dissipated for a fixed output torque.
In an ideal world, your total reflected inertia is independent of the gearbox and largely depends on the motor fill factor and how hot you can run it.
Cooling in general is not a bad idea to allow you dissipate heat as you push motors to their saturation limits.