Cogging Torque and Torque Ripple in Humanoid Joints: Why a Joint Motor Is Never Perfectly Smooth
Cogging torque and torque ripple: why a humanoid joint motor is never perfectly smooth
Turn an unpowered joint motor by hand and you feel it click from notch to notch. That is cogging torque. Power it up and other bumps join in. Each one is small, often a few percent of rated torque, but each one lands on the feature humanoid builders rely on most: reading joint torque from motor current.
Sources: CubeMars RO100 listing; Zhu et al. 2024 (arXiv 2410.16591); Piccoli & Yim, RSS 2014; Wu et al. 2023 (arXiv 2310.15875).
Three different bumps with similar names
Motor engineers use three terms that buyers often mix up. Cogging torque is the pull between the rotor’s permanent magnets and the steel teeth of the stator. It exists with the power off, depends only on rotor position, and averages to zero over a turn. As the magnets pass the slot openings, the magnetic resistance of the air gap changes, and the rotor is pulled toward preferred positions. Kollmorgen describes the result as uneven torque, jerky running at low speed, and a rotor that stops only at certain positions. Motors without iron in the armature, such as the coreless motors used in humanoid hands, have no cogging at all.
Torque ripple is the wider term: any periodic variation in output torque while the motor is energised. Besides cogging, it comes from a back-EMF that is not a perfect sine, from the current waveform the drive produces, and from errors in its current sensors. The motion-control industry association’s paper on these terms draws the line simply: cogging is an open-circuit effect, present with no power applied, while ripple appears only when the motor is energised. Detent torque is mostly a stepper-motor term for the same unpowered holding effect.
In a humanoid joint, a fourth source sits after the motor: the reducer. A strain-wave gear has a kinematic error whose main component repeats twice per wave-generator revolution. A cycloidal disk that is slightly out of balance shakes once per turn. These errors reach the limb as torque or position ripple, at frequencies tied to motor speed.
Figure 1 · What cogging and ripple look like against rotor angle (schematic)
Illustration: humanoid.guide. Shapes and amplitudes are schematic, not measured; the 6° period follows from LCM(12 slots, 10 poles) = 60 cycles per revolution.
Why slot and pole counts matter
Cogging repeats every time the magnet pattern lines up with the tooth pattern in the same way. The number of such alignments per mechanical revolution is the least common multiple (LCM) of the slot count and the pole count. A high LCM means many small, partly cancelling pulls instead of a few strong ones, so it generally gives lower cogging. That is why most joint motors use fractional-slot designs, where slots per pole per phase is not a whole number. Zhu and co-authors showed in 2003 that a four-pole, six-slot machine had about half the cogging of a comparable 12-slot design, because only half the pole edges met slot openings at the same time.
Motor makers then tune the remaining cogging with the magnet arc (the same paper found a minimum near 0.68 of the pole pitch), skewed magnets or skewed stator stacks, and shaped slot openings. Each fix costs a little average torque or adds manufacturing steps. Frameless joint motors are typically high-pole-count designs: Kollmorgen’s TBM2G robot series uses 7 or 10 pole pairs depending on size, and CubeMars lists 14 pole pairs for its RO50 Lite and 21 for the RO100.
Table 1 · Cogging cycles per revolution for common slot/pole combinations
| Slots / poles | Slots per pole per phase | Cogging cycles per motor turn (LCM) | Cogging period | Cycles per output turn at 9:1 |
|---|---|---|---|---|
| 12 / 8 | 0.5 | 24 | 15° | 216 |
| 12 / 10 | 0.4 | 60 | 6° | 540 |
| 12 / 14 | 0.29 | 84 | 4.3° | 756 |
| 18 / 16 | 0.375 | 144 | 2.5° | 1,296 |
| 36 / 42 | 0.29 | 252 | 1.4° | 2,268 |
Calculation: humanoid.guide, from the LCM rule described by MCMA/A3 and Zhu et al. (2003). A higher LCM usually means lower cogging amplitude, but magnet shape, skew and tolerances decide the final figure. 9:1 is the Berkeley Humanoid and RobStride 04 ratio.
Figure 2 · Animated · Magnets sliding past stator teeth, the source of cogging
Illustration: humanoid.guide. Schematic of a radial-flux motor cut and laid flat; not to scale. CSS animation, stops when reduced motion is requested.
How big is it in real joint hardware?
Few actuator suppliers publish cogging, and those that do rarely say how they measured it. CubeMars is an exception for some frameless motors: the RO50 Lite lists 10 N·mm of cogging against 0.3 N·m rated and 0.9 N·m peak torque, and the larger RO100 KV55 lists 55 N·mm against 4 N·m rated and 12 N·m peak. Kollmorgen gives cogging for several housed servo families at ±1.5 to ±2 percent, without stating the base, and its TBM2G frameless robot motors are sold as a “low cogging design” with no figure.
At the joint output, the reducer adds its own ripple. UCLA researchers measured an average torque ripple of ±1.5 N·m on a 10:1 cycloidal quasi-direct-drive actuator rated at 37.5 N·m, and traced it to cycloid disk imbalance. For strain-wave gears, EPFL researchers fitted the kinematic error of a harmonic drive and found its dominant component at twice per wave-generator turn, with smaller components at higher even orders, and cited roughly a 20 percent change in error size over a 56 °C temperature span.
Chart 1 · Published cogging and ripple as a share of rated and peak torque
Sources: CubeMars RO50 Lite and RO100 KV55 listings (10 and 55 N·mm cogging); Zhu, Tanaka, Rafeedi & Hong, arXiv 2410.16591 (±1.5 N·m ripple, 37.5 N·m rated, 89.9 N·m measured peak). Percentages calculated by humanoid.guide. Motor cogging and actuator output ripple are different quantities and are shown together only for scale.
Why a humanoid cares about a few percent
An industrial servo running point-to-point barely notices cogging, which mainly shows up at the start and end of a move. A humanoid joint is used differently. Most legged and many humanoid joints estimate their output torque from motor current instead of a torque sensor, and they spend much of their time at low speed or holding still, where cogging is not smoothed out by rotor inertia. Every unmodelled bump becomes an error in the torque the joint thinks it is applying, and in the contact forces the controller infers from it.
Gear ratio multiplies the effect. Behind a 9:1 reducer, a 12-slot, 10-pole motor puts 540 cogging cycles into each output turn, and the cogging torque reaches the limb multiplied by the ratio, like any other motor torque. At walking speeds the frequency is high enough to be filtered by the structure, but during slow manipulation and standing balance it sits inside the control bandwidth. Torque ripple is also one source of the acoustic hum covered in our noise explainer, and one of the actuator effects that sim-to-real work has to cover, either with a learned actuator model or by training through randomised disturbances.
Fixing it in hardware and in software
Hardware fixes come first: fractional-slot combinations with a high LCM, optimised magnet arcs, skew and careful manufacturing tolerances. The software fix is a cogging map. The drive spins the motor slowly in both directions, records the current needed at each encoder position, and stores the position-dependent part as a lookup table. A US patent with a 2013 priority date describes exactly this for a robot actuator: the difference between the two directions cancels load and friction and leaves the cogging profile, which then becomes a feedforward term. Piccoli and Yim at the University of Pennsylvania used position-based characterisation on 11 low-cost brushless motors and removed an average of 69 percent of torque ripple without adding a force sensor.
The method is now a standard drive feature. The open-source ODrive controller runs an anticogging calibration that takes six minutes by default and adds the result as feedforward, with the warning that a poor position estimate can reduce stability margins. Kollmorgen’s S300 and S700 amplifiers include a cogging compensation function. Reducer ripple is harder to map because it changes with load and temperature, so research has turned to observers and learned models: the UCLA team’s recurrent network predicted the ripple amplitude of its cycloidal actuator to within 0.23 N·m on average and its frequency at 17.6 Hz against a measured 17.2 Hz.
Table 2 · Where torque variation in a humanoid joint comes from
| Source | Present when | Repeats | Main fixes |
|---|---|---|---|
| Cogging (magnets vs stator teeth) | Always, even unpowered | LCM(slots, poles) per motor turn | Slot/pole choice, magnet arc, skew; cogging map in drive |
| Back-EMF and current harmonics | Motor energised | Multiples of electrical frequency | Winding design, sinusoidal field-oriented control, harmonic compensation |
| Current-sensor offset and gain error | Motor energised | Once and twice per electrical cycle | Drive calibration |
| Strain-wave kinematic error | Gear turning | Mainly 2× per wave-generator turn | Feedforward maps, observers, dual encoders |
| Cycloid disk imbalance | Gear turning | Tied to input speed | Balancing, twin disks, learned estimators |
| Coreless motor (hands) | — | No cogging | Trade-off: lower torque per size |
Sources: Kollmorgen; MCMA/A3; Wu, Schuchert & Karimi (EPFL), arXiv 2310.15875; Zhu et al., arXiv 2410.16591. Electrical-harmonic and sensor-error rows summarise standard motor-control practice.
What to ask an actuator supplier
- Cogging torque, with its base. Ask for a peak-to-peak figure in N·m and whether it is measured on the motor or at the joint output. A bare percentage without a reference torque cannot be compared.
- Slot and pole count. They tell you the cogging period and, through the gear ratio, the frequency the controller will see.
- Output torque ripple at low speed. Ripple measured at the output on a dynamometer includes the reducer, which is the number the robot actually feels.
- Compensation in the drive. Whether the drive stores a per-unit cogging map, how it is calibrated in production, and whether it survives a motor or encoder swap in the field.
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 reportsKeep reading · Joints & actuators
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FAQ
What is cogging torque in a robot joint motor?
The position-dependent torque caused by the rotor magnets being pulled toward the steel teeth of the stator. It is present even with the power off, averages to zero over a revolution, and is felt as notchiness when the motor is turned by hand.
Is torque ripple the same as cogging torque?
No. Cogging is one cause of torque ripple. Torque ripple is any periodic variation in output torque while the motor runs, and also comes from back-EMF and current harmonics, current-sensor errors and, in a joint, the reducer.
How large is cogging in humanoid joint motors?
Published figures are rare. CubeMars lists 10 N·mm for its RO50 Lite (about 3.3% of rated torque) and 55 N·mm for its RO100 KV55 (about 1.4% of rated). Most humanoid makers do not publish cogging for their joints.
Can software remove cogging?
Largely. Drives can measure a cogging map against rotor position and cancel it with a feedforward current. Piccoli and Yim removed an average of 69% of torque ripple this way across 11 motors; ODrive and Kollmorgen drives offer similar functions.
Sources
- Kollmorgen, Cogging (definition, ironless armatures have no cogging, ±1.5–2% figures for housed families, S300/S700 compensation)
- MCMA / A3, Understanding the distinctions among torque ripple, cogging torque and detent, 2013 (definitions, fractional-slot designs, mitigation options)
- Z. Q. Zhu et al., Reduction of cogging torque in interior-magnet brushless machines, IEEE Trans. Magnetics, 2003 (6- vs 12-slot comparison, LCM, 0.68 pole-arc optimum)
- M. Piccoli and M. Yim, Cogging torque ripple minimization via position based characterization, RSS 2014 (69% average ripple removal over 11 motors)
- US patent 9,205,556, Cogging torque measurement for a robot actuator (bidirectional current measurement, lookup table, feedforward)
- ODrive, Anticogging guide (six-minute calibration, feedforward, stability caveat)
- CubeMars RO50 Lite frameless motor listing (14 pole pairs, 10 N·mm cogging, 0.3/0.9 N·m)
- CubeMars RO100 KV55 frameless motor listing (21 pole pairs, 55 N·mm cogging, 4/12 N·m)
- Kollmorgen TBM2G frameless motor selection guide (low cogging design, 7 and 10 pole pairs)
- Zhu, Tanaka, Rafeedi and Hong (UCLA), Cycloidal quasi-direct drive actuator designs with learning-based torque estimation, 2024 (±1.5 N·m ripple, 10:1, 37.5 N·m rated, GRU estimator)
- Wu, Schuchert and Karimi (EPFL), Data-driven modeling and analysis of transmission error in harmonic drive systems, 2023 (2× wave-generator component, temperature effect)
