Quick answer: what torque density does a humanoid joint need?
There is no universal Nm/kg requirement for a humanoid hip, knee or ankle. Start with robot mass distribution, joint geometry and the intended motion cycle. Determine required output torque and speed, then compare rated and peak torque divided by complete actuator mass. Check thermal capability, peak duration, bearing loads and interfaces before shortlisting a model.
Updated September 18, 2026. This page provides a load-case worksheet, not a certified actuator design or a category-wide performance benchmark.
1. Calculate two ratios with one mass boundary
Rated density = rated output torque / complete actuator mass. Peak density = peak output torque / the same mass. Keep units in Nm and kg. Record the rated speed, voltage, cooling conditions and allowed peak duration alongside the numbers.
Use the motor, reducer, housing, bearings, encoder and integrated drive mass. If a brake, external drive or mounting structure is excluded, label that exclusion. A bare frameless motor and a complete joint module do not have the same mass boundary.
For an illustrative, hypothetical 2 kg joint module rated at 40 Nm with a 100 Nm peak limit, rated density is 20 Nm/kg and peak density is 50 Nm/kg. These figures describe one assumed example; they are not a ZHR specification or a recommended humanoid target.
2. Write a load case for each joint
| Joint | Inputs to collect | Checks beyond Nm/kg |
|---|---|---|
| Hip | Axis orientation, body and limb mass, gait trajectory and contact forces | Torque-speed envelope, support-phase heating, bearing moments and peak events |
| Knee | Link geometry, stance and swing loads, squat depth and cycle duration | Sustained loading, reversals, speed and gearbox load limits |
| Ankle | Foot geometry, contact force, balance motions and landing conditions | Packaging, output bearing loads, controllability and fault response |
| Shoulder / elbow | Payload, lever arm, tool mass, reach and acceleration | Static holding temperature, positioning requirements and distal mass |
| Wrist | Tool moment, required speed, cable route and available diameter | Output bearing, precision, hollow-bore needs and installed mass |
For a simple static load, torque about an axis equals force times perpendicular lever arm. A full humanoid motion case also includes inertial and contact effects; use the resulting joint torque and speed traces rather than applying one static multiplier to every joint.
3. Match the duty cycle and thermal boundary
A brief peak event and a long hold can require different actuator sizes. Supply the duration and repetition of each motion segment. Ask for torque-speed capability at the proposed voltage and cooling condition, plus peak duration and temperature limits. Include the expected mounting heat path and ambient range.
For sampled segments, RMS torque = √(Σ(torque² × duration) / total duration). It is a screening input for thermal evaluation, not proof that a module can run the cycle. Speed-dependent losses, the reducer and heat transfer still need evaluation. A supplier's peak number cannot substitute for this check.
4. Choose an architecture by evidence
| Design priority | Compare | Decision gate |
|---|---|---|
| Positioning and package size | Harmonic and other compact reduction configurations | Documented lost motion, stiffness, envelope and actual torque-speed capability |
| Backdriving and contact interaction | Low-ratio planetary / QDD and other suitable configurations | Measured backdrive effort, reflected inertia, control behavior and load limits |
| Custom packaging | Custom motor integration versus a complete module | Equivalent installed mass, validation scope and engineering resources |
| Network integration | Exact actuator hardware and firmware | Supported protocol and measured command/feedback timing |
A reducer family does not guarantee zero lost motion, impact survival or regenerative behavior. Treat these as requirements to verify for the selected model. Review the rated-versus-peak comparison method and protocol compatibility guide before issuing a specification.
5. Build a documented ZHR shortlist
Start with the public specifications for each family. Ask for the exact ratio, dimensions, mass definition, torque-speed curve and interface manual for the model under consideration. Public information does not establish suitability for an entire humanoid application.
Frequently asked questions
What torque density does a humanoid hip need?
There is no universal Nm/kg threshold. Derive torque and speed from the robot mass distribution, geometry and motion cycle, then compare complete actuator mass under matching rated and peak conditions.
Should I compare bare-motor mass or complete joint-module mass?
Use the same installed assembly boundary for every candidate. Include the motor, reducer, housing, bearings, encoder and drive where applicable, and state all exclusions.
Can I choose a humanoid actuator from peak torque alone?
No. Check continuous torque, torque-speed capability, peak duration, cooling, bearing loads and controller compatibility against the complete motion cycle.
Request a humanoid joint load-case review
Send the joint role, robot and payload mass, link geometry, torque-speed trace or motion sequence, continuous and peak torque, peak duration, cooling, diameter and mass limits, voltage, protocol and prototype quantity. Identify which inputs are estimates so the first review can focus on missing evidence.
Submit your joint requirementsRelated Articles
Torque Density Formula & Definitions
Rated and peak torque-density definitions and comparison methods.
Selection GuideMotor Selection for Humanoid Robots
In-depth mathematical sizing for bipedal joint motors.
Design GuideHigh Torque Density Joint Motor Guide
Selection considerations for humanoid, cobot and exoskeleton joints.
Engineering RFQ path
Map the humanoid joint load case to a module review
Send the joint role, rated and peak torque, speed, duty cycle, thermal boundary, envelope, protocol, and sample quantity. We can then compare ZHR-P and ZHR-H against the actual requirement instead of a generic Nm/kg target.