The power density of electric motors is pretty amazing. Take for instance quadcopters, a couple of brushless motors can lift their own weight, batteries, and still have plenty of thrust left over to accelerate[0]. Yes those power densities are probably for continuous power.
The problem is not power density, but torque density. Brushless motors spin really, really fast with low torque, which is the exact opposite of what we need for robots.
Electric motors have maximum torque at zero speed. Maximum power is at half of no-load speed.[1] You can design motors for higher torques at lower speeds; it's a standard design parameter.
The maximum torque an electric motor can produce is proportional to the magnetic field in the windings which is proportional to number of turns and current. Increasing the number of turns means more mass, increasing the current means more heat. More heat is particularly insidious, because as temperature goes up resistance increases, which makes more heat, which increases temperature, and so forth and so on.
SCHAFT found a solution to the more current problem with their ultracapacitor driven water cooled motors. Except one cannot drive said motors continuously and alone they still don't have that much torque, so if one wants more torque more windings must be added.
You can design motors for higher torques at lower speeds but the torque density suffers. Luckily we have compact high reduction gearing to transform high speed low torque to low speed high torque.
You've made some good points in this thread about actuation. Can you point me to more info on SCHAFT's actuation strategy? I've been trying to turn up info, but haven't found anything great.
The problem is not power density, but torque density. Brushless motors spin really, really fast with low torque, which is the exact opposite of what we need for robots.
[0]https://www.youtube.com/watch?v=8p5uDf9i_Yc