Industrial manipulators do not collapse under their own weight when powered off due to the friction in their joints. Although these mechanism are effective for stiff position control of pick-and-place, they are inappropriate for legged robots that must rapidly regulate compliant interactions with the environment. However, no metric exists to quantify the robot's performance degradation due to mechanical losses in the actuators and transmissions. This paper provides a fundamental formulation that uses the mechanical efficiency of transmissions to quantify the effect of power losses in the mechanical transmissions on the dynamics of a whole robotic system. We quantitatively demonstrate the intuitive fact that the apparent inertia of the robots increase in the presence of joint friction. We also show that robots that employ high gear ratio and low efficiency transmissions can statically sustain more substantial external loads. We expect that the framework presented here will provide the fundamental tools for designing the next generation of legged robots that can effectively interact with the world.

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To be useful tools in real scenarios, humanoid robots must realize tasks dynamically. This means that they must be capable of applying substantial forces and also mitigating impacts that may occur during the motion. Towards creating capable humanoids, this letter presents the leg of the robot Tello and demonstrates how it embodies two new fundamental design concepts for dynamic legged robots. The limbs follow the principles of: (i) Cooperative Actuation (CA), by combining motors in differential configurations to increase the force capability of the limb. We demonstrate that the CA configuration requires half the motor torque to perform a jump in comparison to conventional serial design configurations. And (ii) proximal actuation, by placing heavy motors near the body to reduce the inertia of the limb. To quantify the effect of motor placement on the robot's dynamics, we introduce a novel metric entitled Centroidal Inertia Isotropy (CII). We show that the design of state-of-the-art dynamic legged robots empirically reduces the range of CII to improve agility and facilitate model-based control. We hope this metric will enable a quantifiable way to design these machines in the future.

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