Actuator Sizing & Transmission Guide: Strain Wave vs Planetary vs Direct Drive

Selecting the Right Transmission for Humanoid Joints

Designing an articulated robot joint requires balancing peak output torque ($T_{peak}$), continuous root-mean-square torque ($T_{RMS}$), backdrivability, and reflected rotor inertia.

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1. Transmission Architecture Comparison

| Transmission Type | Typical Ratio ($N$) | Backdrivability | Backlash | Best Suited Joints | | :--- | :--- | :--- | :--- | :--- | | Quasi-Direct Drive (QDD) | $1:1$ to $1:10$ | Extremely High | Minimal ($< 1\text{ arcmin}$) | Dynamic leg hopping, foot strike absorption | | Planetary Reducers | $1:6$ to $1:30$ | High | Moderate ($1–3\text{ arcmin}$) | Knee joints, hip roll/yaw, mobile manipulation | | Strain Wave (Harmonic) | $1:50$ to $1:160$ | Low / Non-backdrivable | Zero ($< 0.1\text{ arcmin}$) | Shoulders, elbows, precision wrist positioning | | Cycloidal Drives | $1:20$ to $1:100$ | Moderate | Low ($< 1\text{ arcmin}$) | High-impact heavy payload hips and waists |

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2. Rotor Inertia Matching

When an actuator is geared with reduction ratio $N$, the reflected inertia of the rotor seen at the joint link is amplified by the square of the ratio:

$$J_{reflected} = N^2 \cdot J_{rotor}$$

For highly dynamic motions (such as 100m sprinting or combat recovery), an excessively high gear ratio ($N > 100$) multiplies reflected inertia to the point where impact forces from foot strikes cannot backdrive the motor, transferring shock loads directly into mechanical gear teeth and causing gear shearing.

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3. Sizing Rules of Thumb:

* Hip Pitch / Knee Joints: Target $N \le 20$ with high-torque frameless motors ([Kollmorgen TBM2G](/parts/part-act-kollmorgen-tbm2g) or equivalent) to maintain compliance and shock absorption. * Arm / Neck Articulation: Target $N = 50\text{--}100$ with Strain Wave gearing for compact form factor and zero backlash during precision tool use.