GoKawiilThis is the beginning of a series of posts about robot actuation. The intent here is not to prescribe some specific architecture or solution, but to talk about the fundamentals, with as little bias as I can manage. Hopefully you learn something.
Here’s an ostensibly straightforward question for anyone who’s spent time thinking about robot actuators. Take a look at the three cartoon actuators below. One has a large, direct-drive motor, one has a medium-sized motor with a single-stage gear reduction, and the third has a small motor with a a two-stage reduction. The gear ratios are chosen so that the actuators can all produce the same output torque, and all have the same resistive dissipation in the motor for a given output torque. Assume the gears are massless and 100% efficient.
Which of these actuators has the lowest reflected inertia? Defined as the rotor inertia times gear ratio squared.
We’ll come back to this.
First order motor scaling
How do torque, $\tau$, mass, $m$, power dissipation, $p$, and rotor inertia, $j$, scale with motor size? For this analysis, we’ll assume the radial thickness of the stator & rotor is a constant.
First, what happens if only the length, $l$, changes, keeping the current density in the windings constant (equivalent to keeping the magnetic shear pressure constant)? This is pretty intuitive – double the length of the motor, and torque should double, rotor inertia should double, and power dissipation should double (ignoring end-turns): $$\tau, m, p, j \propto l$$
What if only the radius, $r$, changes, again keeping current density in the windings constant?
$$m, p\propto r$$ $$\tau \propto r^{2}$$ $$j\propto r^{3}$$
A simple figure of merit
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