Gear Ratio in Humanoid Joints: How One Number Trades Torque, Speed and Reflected Inertia

Joints & actuators · Explainer

Gear ratio in humanoid joints: one number that trades torque, speed and reflected inertia

Every rotary humanoid joint puts a reduction between a fast, weak motor and a slow, strong limb. The ratio of that reduction multiplies torque, divides speed and multiplies the motor’s inertia by its square. Published humanoid joints range from 6:1 to 160:1, and where a designer lands on that scale decides how the joint feels when it hits something.

6:1
Single-stage planetary in the MIT Mini Cheetah actuator, the template for low-ratio legged joints
22.5:1
Two-stage planetary in the Unitree G1 knee actuator, according to a teardown
160:1
Highest standard ratio in Harmonic Drive’s CSF strain-wave component sets
N²
How motor rotor inertia scales when seen from the joint output

Sources: Katz 2018 (MIT thesis); China-Amass G1 knee teardown; Harmonic Drive CSF product data; Human-Level Actuation for Humanoids, 2025.

Three things a gearbox multiplies

Electric motors are good at spinning fast and bad at producing large torque. A humanoid knee needs the opposite: well over 100 N·m at a few hundred degrees per second. The reducer bridges the gap. With a ratio of N:1, the joint sees roughly N times the motor torque (less gearbox losses) at one-Nth of the motor speed. That part is intuitive, and it is why the first instinct is to pick a high ratio and a small motor.

The third effect is less visible on a spec sheet. The motor’s own rotor inertia, as felt at the joint, grows with the square of the ratio. A 9:1 joint carries 81 times the rotor inertia at its output. A 100:1 joint carries 10,000 times. The authors of Human-Level Actuation for Humanoids (2025) put the trade-off plainly: raising N raises static torque but also increases reflected inertia, and higher ratios add friction that lowers torque-mode bandwidth, mid-speed efficiency and the range of stable impedance control.

Figure 1 · What a reduction of N:1 does between motor and joint

Motor torque τm (low) speed ωm (high) rotor inertia Jm Reducer N : 1 efficiency η Joint output τ = N · η · τm ω = ωm / N J reflected = N² · Jm TORQUE × NSPEED ÷ NINERTIA AT JOINT × N²FRICTION ↑ WITH N More holding andlifting torque Lower top joint speedfor the same motor Harder impacts, slowerreaction to contact Harder to back-drive,lower torque bandwidth Idealised relationships; real gearboxes add losses that vary with load, speed and temperature.

Illustration: humanoid.guide, after Human-Level Actuation for Humanoids (arXiv 2511.06796). Schematic, not a specific product.

Why reflected inertia matters more in a humanoid than in a factory arm

An industrial arm moves through free space and rarely hits anything on purpose. A walking humanoid hits the ground with every step, and an assistant humanoid is expected to bump into people and furniture without hurting either. In those moments the joint cannot react through software fast enough to hide the rotor. The spinning motor behaves like a flywheel bolted to the limb through the gearbox, and its effective mass at the foot or hand scales with N².

That is the argument behind quasi-direct-drive design. Ben Katz’s MIT Mini Cheetah actuator pairs a large-diameter motor with a single 6:1 planetary stage, giving 17 N·m peak and 6.9 N·m continuous torque in a joint that can be pushed around by hand and absorb landings. Berkeley Humanoid uses 9:1 QDD actuators in four sizes from 9.7 to 81.1 N·m peak. At those ratios the rotor contributes 36 and 81 times its inertia, compared with thousands of times for a strain-wave joint.

Figure 2 · Animated · A 3:1 stage: the pinion turns three times for each output turn

MOTOR PINIONJOINT OUTPUT 1 turn / 2 s1 turn / 6 s 3× torque, ⅓ speed, 9× reflected inertia Pinion radius r Output radius 3r

Illustration: humanoid.guide. A 3:1 ratio is used so the motion stays visible; gears are drawn as touching pitch circles without teeth. CSS animation; stops when reduced motion is requested.

Published ratios, from quasi-direct drive to strain wave

Most humanoid makers do not publish their joint ratios, so hard numbers come from research platforms, off-the-shelf actuator modules and teardowns. Grouped together they show three clusters. Quasi-direct-drive modules sit between 6:1 and about 10:1. Leg joints that need more torque from a compact motor move into two-stage planetary territory, with the Unitree G1 knee at 22.5:1. Strain-wave (harmonic) reducers, common in arms and in many Chinese humanoids, start at 30:1 and run to 160:1.

Table 1 · Gear ratios published for humanoid and legged-robot joint actuators

Actuator / jointReducerRatioPeak torqueNotes
MIT Mini Cheetah actuatorSingle-stage planetary6:117 N·m6.9 N·m continuous; QDD reference design
RobStride 02Planetary QDD module7.75:117 N·m6 N·m rated; 405 g; 24–60 V
RobStride 04Planetary QDD module9:1120 N·m40 N·m rated; 167 rpm rated, 200 rpm no-load; 1.42 kg
Berkeley HumanoidQDD, four sizes9:19.7–81.1 N·mResearch platform for learned locomotion
Unitree G1 kneeTwo-stage planetary22.5:1120 N·mAbout 1 kg; dual encoders; teardown figures
BHR8-J1 knee (fixed-ratio equivalent)Variable-ratio linkage≥30:1318 N·mFixed ratio would push motor above 4,500 rpm; variable design stays under 3,000 rpm
Harmonic Drive CSF setsStrain wave30–160:1Size-dependentMax input speed 1,800–8,500 rpm by size (grease)
Berkeley Humanoid Lite3D-printed cycloidalNot stated in paper—$136–188 per actuator; cycloidal chosen to tolerate printer resolution

Sources: Katz 2018; RobStride 02 and 04 product listings; Liao et al. 2024; China-Amass G1 knee teardown; BHR8 variable-ratio knee paper (arXiv 2506.12314); Harmonic Drive CSF product data; Chi et al. 2025 (Berkeley Humanoid Lite). — means not published in these sources.

Chart 1 · Gear ratio by actuator, log scale, with the N² reflected-inertia factor

1:110:1100:11000:1 GEAR RATIO N (LOG SCALE) MIT Mini Cheetah RobStride 02 RobStride 04 Berkeley Humanoid Unitree G1 knee BHR8 knee, fixed equivalent Strain wave, CSF set Strain wave, CSF set Strain wave, max CSF ratio 6:1 · N² 36 7.75:1 · N² 60 9:1 · N² 81 9:1 · N² 81 22.5:1 · N² 506 ≥30:1 · N² ≥900 50:1 · N² 2,500 100:1 · N² 10,000 160:1 · N² 25,600

Sources: Katz 2018; RobStride product listings; Liao et al. 2024; China-Amass G1 teardown; arXiv 2506.12314; Harmonic Drive CSF ratios (30, 50, 80, 100, 120, 160). N² is the factor by which rotor inertia is multiplied at the joint; it is arithmetic, not a measured value.

A worked example: same motor, two ratios

The RobStride 04 gives 120 N·m peak through a 9:1 reducer and runs at 200 rpm with no load. Working backwards and ignoring losses, the motor behind it delivers roughly 13 N·m and spins at about 1,800 rpm. Put the same motor behind a 22.5:1 reducer, the G1 knee ratio, and the ideal joint would reach about 300 N·m but top out near 80 rpm. Its reflected rotor inertia would rise by a factor of 6.25, the square of 2.5.

Neither version is wrong. The higher ratio suits a knee that has to carry body weight through deep squats and stairs. The lower ratio suits a joint that has to swing fast, absorb impacts and be controlled through motor current without a separate torque sensor. The Human-Level Actuation paper uses a related example: a knee or hip lifting case calling for about 150 N·m continuous and 300 N·m burst, and an N = 200 design that reaches high low-speed torque but loses it at speed to reflected inertia and friction.

Gear ratio is not a quality score. A higher ratio gives a smaller, cheaper motor more torque, but the joint gets slower, stiffer to push and harder on whatever it hits. The right ratio follows from the joint’s job: its peak torque, top speed, duty cycle and how often it touches the world.

Ways around a fixed ratio

Because no single ratio fits a whole motion, some designs change the effective ratio with joint angle. Beihang’s BHR8-J1 humanoid uses a crank-and-pushrod knee whose reduction varies as the knee extends, giving high torque at the bottom of a jump and high speed at the top. The authors calculate that a fixed-ratio knee matching its torque would need a ratio of at least 30 and motor speeds above 4,500 rpm, while their variable design stays under 3,000 rpm. The robot, 45 kg with 14 degrees of freedom, has made 0.5 m vertical and 1.1 m forward jumps.

Linkages, ball screws and roller screws all do something similar: the screw lead sets a linear ratio, and the lever arm to the joint turns it into a torque that changes with angle. Other levers are outside the gearbox. A larger-diameter motor raises torque without raising N. Liquid or forced-air cooling raises continuous torque. A torque sensor at the output lets a high-ratio joint fake some of the compliance a low-ratio joint has naturally.

What to check on a joint spec sheet

  • Ratio and reducer type together. 9:1 planetary and 100:1 strain wave are different kinds of joint, not two points on one scale. The reducer type tells you about backlash and stiffness; the ratio tells you about speed, impact and back-drivability.
  • Rated speed at rated torque. Peak torque without a speed is half a spec. The RobStride 04 lists 167 rpm at rated load and 200 rpm with none.
  • Rotor inertia or output inertia. If a supplier publishes rotor inertia, multiply by N² to compare joints at the output. Few do; ask.
  • Back-drive torque. The torque needed to turn the output by hand captures friction and ratio in one number and tells you how well current-based torque control will work.

Go deeper: The Humanoid Actuation Report

249 pages on motors, reducers, screws, bearings, encoders and drives, the vendors behind every major platform, and the cost curves that decide adoption to 2036.

The Humanoid Actuation Report All joints & actuators articles All humanoid.guide reports

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FAQ

What gear ratio do humanoid robot joints use?

Published values run from about 6:1 in quasi-direct-drive actuators such as the MIT Mini Cheetah module, through 9:1 in RobStride 04 and Berkeley Humanoid joints and 22.5:1 in the Unitree G1 knee, to 30:1–160:1 for strain-wave reducers. Most commercial humanoid makers do not publish their ratios.

What is reflected inertia?

The motor rotor’s inertia as felt at the joint output. It equals the rotor inertia multiplied by the square of the gear ratio, so a 100:1 joint feels 10,000 times the rotor inertia. High reflected inertia makes impacts harder and the joint slower to respond to contact.

Is a higher gear ratio better?

Not in general. It gives more torque from a smaller motor, but lowers top speed, increases friction and reflected inertia, and makes the joint harder to back-drive. Joints that touch the world often, such as legs, tend to use lower ratios; joints that hold loads, such as some arm joints, can use higher ones.

Can a joint change its gear ratio?

Not inside a normal gearbox, but linkages and screw mechanisms change the effective ratio with joint angle. The BHR8-J1 humanoid knee uses this to get high torque at the start of a jump and high speed at the end.

Sources