Physical AI engineering tool

Robot Joint Actuator Torque & Gear Ratio Calculator

Check whether a motor plus reducer (or roller/ball screw) can hold the payload at a humanoid or robot-arm joint. The calculator turns continuous and peak motor torque, gear ratio and efficiency into joint torque, and compares it with the torque required by the payload, reach and link weight.

1. Actuator setup

Use the rated (continuous) and short-term maximum (peak) torque from the motor datasheet. The defaults are example assumptions.

Assumes the circular spline has two more teeth than the flexspline, so ratio = teeth ÷ 2 (e.g. 200 → 100:1).

Choosing planetary sets the default from a loss of about 3% per stage. The 70% default for other reducers is an assumption; replace it with the datasheet efficiency.

2. Load

These are whole-robot figures published by the makers. For a two-arm lift, enter the share one arm carries.

Distance perpendicular to gravity. A fully extended horizontal arm is the worst case.

Mass of the links, motors and hand outboard of the joint, and the horizontal distance from the joint to their centre of mass. Leave 0 if unknown and keep a larger margin.

Multiplier to cover acceleration, impacts and friction. The 1.5 default is an assumption.

3. Results

Joint output torque (continuous) -- N·m
Required joint torque (static × safety factor) -- N·m
Gear ratio --
Joint output torque (peak) -- N·m
Joint output speed --
Payload torque m·g·r -- N·m
Link weight torque -- N·m

4. Verdict

* Note: a static-pose estimate for early design. Acceleration torque, joint friction and thermal derating of continuous torque are not included; check motor and reducer datasheets and test data before selecting parts.

How joint torque and gear ratio are calculated

Sizing a joint actuator means comparing two numbers: the torque the motor and reducer (or screw) can deliver at the joint, and the torque the payload and arm pose demand. This calculator puts both in N·m and compares them on a continuous and a peak basis.

1. Formulas

A rotary joint multiplies motor torque by gear ratio and efficiency. A linear actuator turns motor torque into thrust through the lead, and the moment arm turns that thrust into joint torque.

T_out (N·m) = T_motor × i × η i (harmonic) = N_flexspline ÷ (N_circular − N_flexspline) = N_flexspline ÷ 2 i (planetary, ring fixed) = (1 + N_ring ÷ N_sun)^stages, η ≈ 0.97^stages F (N) = 2π × η × T_motor ÷ L (m), T_joint = F × moment_arm τ_required = (m_payload × g × r + m_link × g × r_cg) × safety_factor n_out (rpm) = n_motor ÷ i, v (mm/s) = n_motor × L (mm) ÷ 60

The strain wave ratio follows the Harmonic Drive technology page (the circular spline has two more teeth than the flexspline) and the tooth-difference formula in Strain wave gearing. The planetary ratio and the roughly 3% loss per stage come from Epicyclic gearing; the screw thrust rearranges the efficiency definition in Leadscrew (η = F·L ÷ 2πT). g = 9.80665 m/s².

2. Three reducer types compared

How a reducer gets its ratio sets its efficiency, backlash and backdrivability. The values below are ranges published by makers and reference sources; anything unpublished, such as efficiency, has to come from the datasheet.

Item Strain wave Cycloidal (RV) Planetary
Ratio 30:1 to 320:1 in the same space (source) Fixed ratios per product — check the catalog Typically about 10:1 per stage in the same space; stack stages for more (source)
Backlash Zero backlash per the maker (Harmonic Drive) RV-N series below 1 arcmin (Nabtesco) Depends on design and grade
Efficiency Not stated on the public page — check the datasheet Not stated on the public page — check the datasheet Typically about 3% loss per stage (source)

3. Rotary or linear?

Rotary actuators suit joints that need a wide range of rotation, such as shoulder, wrist and waist yaw; linear actuators are often considered for high-force bending joints such as elbows, knees and ankles. A linear actuator gets large thrust from the same motor, but its joint torque scales with the moment arm, so output torque changes with joint angle. Roller screws beat ball screws on load rating and stiffness but cost more.

4. Continuous vs peak torque

Holding a load in a fixed pose is a continuous-torque case; jumping, landing and fast acceleration are peak-torque cases. A "peak only" verdict means the motor may overheat if the pose is held for long. For reference, Unitree G1 publishes a maximum knee torque of 90 N·m (120 N·m on the EDU), measured on its largest joint motor.

5. FAQ

Q1. Is a higher gear ratio always better?

Output torque rises with the ratio, but output speed drops by the same factor and forces pushed back from the output reach the motor less easily, which hurts backdrivability. Leg joints that must absorb landing impacts are often built from a high-torque motor and a low ratio.

Q2. Where do the default efficiencies come from?

Planetary uses 0.97 to the power of the stage count, following the roughly 3% loss per stage in the Epicyclic gearing article. The 70% for strain wave and cycloidal reducers and the 80% for screws are example assumptions; replace them with the datasheet values of the actual parts.

Q3. Can I use the payload examples as they are?

They are whole-robot figures from the makers. Unitree notes that the G1 arm load varies greatly with arm extension, and the Digit 5 specs are preliminary estimates. For a two-arm lift, enter the share one arm carries.

Q4. How do I pick the moment arm for a linear actuator?

It is the perpendicular distance from the joint axis to the line of the screw force. It changes as the joint bends, so measure it across the working range in CAD and enter the shortest value for a conservative result.

Q5. Why are acceleration and friction left out?

The calculator only covers the torque gravity creates in a static pose. Inertial torque from fast motion and friction inside the reducer must be covered by the safety factor or checked separately with dynamics simulation and testing.

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Primary sources

Data and formulas last verified: 2026-10-23 · Operator: Huni ([email protected])