Reflected Inertia

The effective inertia felt at a joint's output after the motor rotor's inertia is amplified by the reducer.

Reflected inertia is the rotational inertia of the motor rotor (and any reducer parts on its input side) converted to an equivalent value at the joint's output, roughly equal to the rotor's inertia multiplied by the square of the gear ratio. The larger the gear ratio, the “heavier” the joint feels from the outside: an impact has to accelerate the rotor along with everything else, making the impact force larger, and it also becomes harder for an external force to push the joint back — backdrivability gets worse, and force-control bandwidth drops. This is one of the main reasons legged robots like the MIT Cheetah chose low-gear-ratio “proprioceptive actuators”: a leg needs to be able to yield on impact when it lands. Joint design often has to trade off torque density, which wants a large gear ratio, against low reflected inertia.

ExampleThe same motor with a 6:1 reducer has a reflected inertia about 36 times the rotor's own inertia; swap in a 100:1 harmonic drive instead, and it becomes about 10,000 times.

Also called

Reflected Rotor Inertia, Equivalent Inertia

Related

Proprioceptive Actuator · Backdrivability · Gear Ratio · Moment of Inertia · Quasi-Direct Drive · Strain Wave Gear (Harmonic Drive)

Sources

Proprioceptive Actuator Design in the MIT Cheetah (Wensing et al., IEEE T-RO 2017)