Backdrivable Actuator Sizing Tool & Guide

A backdrivable actuator lets output-side torque move the motor through the transmission in a specified electrical state. This page covers the complete motor, transmission, driver, and sensing package. For measured torque screening and basic reducer terminology, see the backdrivability guide.

Rotor inertia is referred through an ideal rigid ratio. The resistance expression is a heuristic: efficiency is undefined at standstill, and gearbox drag must exclude losses already included in η_rev. Forward efficiency is entered independently. The output-torque expression applies to an assumed moving operating point; it does not model a joint thermal rating or stall losses. All fields are required, with example defaults and stated input ranges.

Record measured breakaway torque and running drag at multiple speeds, temperatures, loads, and drive states. Do not equate the input starting torque in a reducer catalog with output backdriving torque. [HARMONIC-CATALOG]

The model describes stored rotor energy and average rotor inertial torque under a linear stop. It omits links, payload, gearing, elasticity, and external work. It cannot estimate peak tooth stress, contact force, or energy dissipated in an impact. [WENSING2017]

Use these qualitative engineering comparisons to shortlist candidates. Ratios below are examples, not class boundaries. No architecture alone guarantees impact tolerance, human contact safety, low drag, or a particular force bandwidth. [KATZ2018][HUTTER2016]

For a radial-flux motor with uniform tangential air-gap shear stress σ and active length L, T = 2πσr²L. This is a scaling relation under fixed loading assumptions, not proof of a fixed torque-density advantage. A larger radius can increase rotor inertia as well as torque. Compare the complete motor-reducer pair at the required duty. [SEOK2015]

Snapshot checked 2026-10-27. These are manufacturer claims for specific revisions, not independent tests or an apples-to-apples ranking. A reducer component set excludes the motor and driver present in an integrated module. Peak torque is not continuous torque and requires a duration and operating condition.

The cited AK80-9 V3.0 page currently lists rotor inertia as 1118.3238 g·cm². Earlier material and other revisions use different values; request the supplied revision and reference plane before deriving reflected inertia. The GO-M8010-6 page does not provide a comparable breakaway or rotor-inertia test. Leave those inputs unknown until the supplier confirms them.

The displayed noise contribution omits friction, current-loop bias, cogging, gravity, inertial torque, and filtering. A joint torque in N·m becomes contact force in N only through known contact geometry and a suitable Jacobian. Calibrate an external torque observer across angle, speed, load, and temperature before using its output for control. [WENSING2017][MAXON]

For observer design and control tradeoffs, continue with force control in robotics and impedance control.

Synchronize and unwrap both encoder angles, remove zero offsets, and identify stiffness with known bidirectional loads. Encoder quantization, offsets, backlash, nonlinear stiffness, and hysteresis can dominate a small deflection signal. Use an error budget and reference torque calibration; two encoders do not automatically make a torque sensor. The Harmonic Drive product data, for example, lists multiple stiffness regimes. [HARMONIC]

Use a separately measured K_e with a documented voltage and speed convention. Here it means DC-equivalent rectified open-circuit voltage per motor mechanical rad/s. K_t and K_e are numerically interchangeable only with compatible definitions. EMF = K_eN|ω_joint| is a nominal comparison, not a bus-voltage prediction.

An active inverter can regenerate below the nominal bus voltage. In an unpowered but connected drive, rectifier paths depend on the bridge and electrical state. Establish the actual energy path, voltage/current ratings, and supply charge acceptance; a TVS for short transients is not a substitute for a rated repetitive braking sink.

The current limit sets a lower resistance bound; power absorption sets an upper bound. Evaluate current at the highest allowed bus voltage, and include pulse and average thermal limits. The general selection logic is documented by Schneider Electric; its industrial drive voltage examples are not robot-driver recommendations. [BRAKING]

This compact expression requires matched torque, current, and resistance conventions, including phase factors for three-phase motors. K_m has units N·m/√W. It is not torque per watt. Account for speed-dependent iron loss, inverter loss, ambient temperature, mounting conduction, and torque-speed-time duty. The calculator uses your entered motor rating; it does not simulate cooling or prescribe a universal derating percentage. [SEOK2015][MAXON]

Before requesting a quote, specify torque-speed duty, load inertia, drag limits, thermal mounting, electrical states, bearing loads, envelope, and regeneration behavior. Set acceptance limits from your application and the supplier manual. The following plan is an engineering proposal, not a published industry threshold.

Discuss joint requirements

1. Restrain gravity loads and use a guarded fixture with a calibrated output torque transducer and encoder.
2. Document the exact electrical state: mechanically disconnected motor, open phases, connected unpowered driver, or active torque control. Follow the driver manual; do not improvise phase shorting.
3. Ramp output torque slowly in both directions. Record onset of motion, running drag versus speed, lubricant and winding temperature, preload, and mounting conditions.
4. Repeat under the intended load and thermal envelope. Report uncertainty and compare against the agreed application limit.

The catalog backdriving values use stated reference conditions and cannot be assumed to hold for every assembled joint. [HARMONIC-CATALOG]

The three calculations below are illustrative scenarios, not customer results or measured product performance. Their assumptions and arithmetic can be reproduced independently.

Published low-ratio design evidence: Katz’s 2018 MIT thesis documents modular actuator hardware and controls for a small quadruped, with additional teleoperation and biped applications. It supports using an integrated motor, transmission, and control design process; it does not validate the tool presets as commercial product specifications. [KATZ2018]

Evidence against a universal SEA bandwidth ceiling: Hutter et al. report torque-control bandwidth above 70 Hz for the 2016 ANYmal compliant joint modules. That result belongs to the tested assembly and controller, not every series elastic actuator. [HUTTER2016]

These are application review prompts. Backdrivability is not a substitute for a system risk assessment, load restraint, or validated contact behavior. [ISOTS15066]

Responsible publisher: Humanoid Joint. First recorded: 2026-10-27 (source history; public publication date unverified). Reviewed 2026-10-27. Next evidence review due 2027-04-27. This is an engineering screening guide with source-backed facts, explicitly illustrative calculations, and proposed procurement checks. Unknown product values remain unknown. It does not certify hardware, predict injury, or validate a control system. Recheck manufacturer revisions and current standards before design approval.