Parallel Springs in Humanoid Joints: Parallel Elastic Actuators and Gravity Compensation

Joints & actuators · Explainer

Parallel springs in humanoid joints: letting a spring carry the load

A humanoid that stands still is still burning power. Every joint fighting gravity pushes current through its motor windings, and copper loss grows with the square of torque. A spring mounted alongside the motor, instead of in line with it, can take over part of that torque for free. Lab hardware has cut joint energy by 15% to 79% this way. Production humanoids mostly haven’t adopted it yet.

79%
Energy saved per stance phase by a clutched parallel spring on a half-scale humanoid knee test bed
93%
Cut in dissipated power at Sandia STEPPR’s hip roll joint with a one-way parallel spring, bench test
35%
Predicted drop in STEPPR’s whole-robot cost of transport with springs at four joints
30%
Lower peak knee torque on ANYmal with a parallel-elastic knee, with no loss of tracking

Sources: Haeufle et al. 2012; Mazumdar et al. 2015 (ICRA); Bjelonic et al. 2023 (IEEE RA-L).

Series or parallel: where the spring sits

Springs in actuators come in two layouts, and they do different jobs. In a series elastic actuator, the spring sits between gearbox and limb. All the joint torque flows through it and also through the motor. The spring buys shock tolerance and a torque measurement, but the motor still produces every newton-metre the joint delivers.

A parallel elastic actuator (PEA) moves the spring to the side. One end attaches to the frame, the other to the moving link, so the spring and the motor push on the joint side by side. Joint torque becomes the sum of the two. If the spring supplies 15 N·m of a 20 N·m load, the motor only has to make 5. Delft’s Plooij, Wisse and Vallery state the consequence directly in their 2016 IEEE Transactions on Robotics paper: parallel springs can save more energy than series springs because they take over part of the task from the motor, while in a series design the force still passes through the motor.

Figure 1 · Series versus parallel spring placement in a joint

SERIES ELASTICPARALLEL ELASTIC Motor Gear Link spring τ joint = τ motor (via gear) All torque passes through the motor and through the spring. Motor Gear Link frame parallel spring τ joint = τ motor + τ spring The spring loads the link directly, so the motor supplies only the remainder. Schematic only. Real designs fold the spring into the joint housing as a torsion, coil or leaf spring, often with a clutch.

Illustration: humanoid.guide, after Plooij, Wisse & Vallery (IEEE T-RO, 2016).

Why a holding joint wastes power

An electric joint has no way to hold torque without current. A shoulder keeping an arm out at 90°, or a knee bent under body weight, draws steady current that does zero mechanical work and turns into heat in the windings. That copper loss scales with torque squared, which is why the motor constant Km and the continuous torque rating matter so much for joints that spend their day resisting gravity.

Halve the motor’s share and you cut that heat to a quarter. Take 90% of it away and only 1% remains. This square-law payoff is why even an imperfect spring is worth considering. It also explains why the result depends so heavily on the task: a spring tuned for one posture helps there and can hurt elsewhere.

Take a simple case. An arm link whose gravity torque peaks at 20 N·m when horizontal, about what a 4 kg arm with its centre of mass 0.5 m from the shoulder produces. Its gravity torque follows a sine curve from hanging down (0°) to horizontal (90°). A plain linear torsion spring fitted by least squares across that range comes out at about 15.5 N·m/rad. It never matches the sine exactly, but the residual the motor has to cover stays below 2 N·m up to 60° and peaks at 4.3 N·m at the horizontal end. Averaged over the range, holding copper loss falls to about 1.4% of the no-spring value.

Chart 1 · Holding torque for a 20 N·m arm link, with and without a linear parallel spring

2520151050−5 0°15°30°45°60°75°90° ARM ANGLE FROM HANGING DOWN TORQUE (N·M) Gravity torque, 20·sin θLinear spring, 15.5 N·m/radMotor share = gravity − spring 20−4.3

Calculation: humanoid.guide. Static holding only; spring stiffness fitted by least squares over 0–90°; residual copper loss averaged uniformly over angle. Real arms add dynamic torque, payloads and posture distributions that change the optimum.

Mechanism designers can do better than a linear spring. A so-called zero-free-length spring, arranged between the frame and the link, produces a torque that follows the same sine law as gravity and can balance a link exactly at every angle. Industrial robots have used this logic for decades. KUKA’s heavy-payload arms carry a hydropneumatic balancer on axis 2, the joint that the company’s own patent says may see the greatest torque. Willow Garage’s PR2 hid two spring cans in its arm turret so the upper arm and forearm “float”, even with the power off.

Figure 2 · Animated · A gravity-balanced link: no static torque at any angle

m 4m JOINT PIVOT (HUNG FROM FRAME) Arm mass m at 4 units, counterweight 4m at 1 unit: m·4 = 4m·1, so gravity torque about the pivot is zero at every angle. A zero-free-length spring between frame and link gives the same sine-law torque without the extra mass.

Illustration: humanoid.guide, after Whitney & Hodgins (Disney Research), who balanced an anthropomorphic arm with low-mounted counterweights. Lever swings ±35° about its pivot; CSS animation stops when reduced motion is requested.

Disney Research’s John Whitney and Jessica Hodgins built an anthropomorphic arm along these lines, with a cable differential at the shoulder matching the cos θ1 · cos θ2 shape of the gravity load and counterweights mounted low in the torso. Their argument for a humanoid is about motor size: once gravity is cancelled, motors can be sized for the momentary torque of a motion instead of the continuous torque of holding a pose, which they estimate can halve motor mass or better. The catch is mass. Counterweights for a compact design can weigh six or more times the arm they balance, which is why the same paper points to springs instead.

What the hardware has shown

Legs are harder than arms. A knee carries body weight in stance but swings freely through the air half the time, and a fixed parallel spring would fight that swing. The answer in most legged designs is to engage the spring only when it helps, with a clutch, a one-way contact or a linkage that only loads in stance.

Haeufle, Taylor, Schmitt and Geyer did this in 2012 for the knee of a half-sized humanoid leg (about 0.5 m long, 20 kg). An electric clutch locked a 5,549 N/m extension spring in parallel with a Maxon RE-40 motor during stance. On the test bed, stance energy fell from 33.5 J to 7.07 J, a 79% cut, and peak knee torque dropped from 30 N·m to 10 N·m. The prototype was also 20% lighter than the series elastic actuator it replaced. Sandia’s STEPPR biped took a similar line at the ankle and hip in 2015, with stance-only and one-way springs; its hip roll spring cut dissipated power by 93% on the bench at full load and speed.

Table 1 · Parallel springs tested in legged and humanoid joints

Robot / rigJointSpringResultBasis
Half-scale humanoid leg (Haeufle et al., 2012)Knee5,549 N/m extension spring, electric clutch−79% energyHardware test bed; peak torque 30 → 10 N·m
Sandia STEPPR (Mazumdar et al., 2015)Hip roll500 N·m/rad, one-way−93% powerBench, dissipated power, crouched gait
Sandia STEPPRWhole robotAnkle, hip and knee springs−35% CoTSimulation, 3.34 → 2.16
Delft BIC-PEA (Plooij et al., 2016)1-DoF rotaryTorsion spring, differential, two locks−53% energyHardware, four-position task, 25.0 → 11.8 J
ANYmal (Bjelonic et al., 2023)KneeParallel-elastic knee, learned design−30% peak torqueHardware; 33% better torque-square efficiency, 11% longer run time
Notre Dame ankle (Yang et al., 2024)Prosthetic ankle2.9 N·m/rad printed spiral spring−32% energyDynamometer, weighted over four tasks
MUPS monoped (2025)KneeUnidirectional compression spring−15% energyHardware, in-place hopping; 38.8% CoT cut in simulation
CHARLI-L (Han & Hong, 2011)Knee (four-bar leg)980 N/m tension springs21 → 15 N·mDesign calculation, walking peak knee torque

Sources: Haeufle et al., BioRob 2012; Mazumdar et al., ICRA 2015; Plooij, Wisse & Vallery, IEEE T-RO 2016; Bjelonic et al., IEEE RA-L 2023; Yang et al., arXiv 2409.08889; arXiv 2503.05666; Han & Hong, ASME IDETC 2011. Metrics differ between studies and are not directly comparable.

Chart 2 · Measured reductions from parallel springs in hardware and bench tests

0%25%50%75%100% REDUCTION VERSUS SAME JOINT WITHOUT SPRING STEPPR hip roll · dissipated power Humanoid knee, clutched · energy Delft BIC-PEA · task energy ANYmal knee · torque-square Notre Dame ankle · energy ANYmal knee · peak torque MUPS hopper knee · energy 93% 79% 53% 33% 32% 30% 15%

Sources: Mazumdar et al. 2015; Haeufle et al. 2012; Plooij et al. 2016; Bjelonic et al. 2023; Yang et al. 2024 (32.3%); MUPS, arXiv 2503.05666 (14.8%). Bar length = value × 4.2 px per percentage point. Each bar uses its own study’s metric and test; treat as a range, not a ranking.

The catch: a spring tuned for one task taxes another

A spring doesn’t know what the robot is doing. Notre Dame’s Yang, Dickens, Schmiedeler and Bolívar-Nieto showed how sharp that trade can be. A spring optimised only for walking on their prosthetic ankle cut walking energy by 44.9%, but sit-to-stand energy rose by 343%. Their multi-task spring gave up some of the walking gain (37.2%) to save 32.3% across walking, stairs and sit-to-stand combined, and even then sit-to-stand cost 75% more. For a general-purpose humanoid that walks, squats, carries boxes and kneels, that is the central design problem.

There are other costs. Springs add mass and volume at the joint, and the clutches that make them switchable add more parts, more control states and power of their own; Plooij’s 53% figure, for example, excludes the energy the locking mechanisms use. A preloaded spring stores energy that can move a limb when the motor is unpowered, which needs thought in a brake and safety design. And learned locomotion policies have to be trained with the spring in the model, which is the approach ETH’s ANYmal team took by optimising spring parameters and controller together.

Parallel springs pay off most where a joint holds a predictable load for a long time: an arm shoulder against gravity, a knee in stance, an ankle in push-off. They pay off least, or cost energy, when the same joint has to do many different jobs with one fixed spring.

Where this leaves production humanoids

Most commercial humanoids in 2026 run stiff electric joints with no parallel spring, and none of the major makers documents one publicly. Their bet is on better motors, higher Km and smarter control instead of extra mechanism. That leaves standing and holding power on the table. The energy efficiency question is getting louder as robots move to full shifts, though, and the research record gives a clear starting point.

  • Arms are the easy case. Gravity load is a known function of pose, and spring or counterweight balancing has been in industrial arms and the PR2 for years.
  • Knees and ankles need switching: clutches, one-way springs or stance-only engagement, as in the Haeufle knee, STEPPR and MUPS.
  • Ask suppliers for holding current at a reference pose and for the joint’s duty cycle. If a joint spends most of its time near one posture, a spring is worth modelling.

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

Keep reading · Joints & actuators

Related articles

03Actuator types & performanceSeries elastic actuatorsWhy Apollo keeps a measured spring in the joint, from NASA’s Valkyrie to Apptronik, and what it costs.Read the explainer → 04Actuator types & performanceVariable stiffness actuatorsJoints that retune their own spring with a second motor, what DLR’s designs achieve, and why production robots skip them.Read the explainer → 09Actuator types & performanceEnergy efficiency in humanoid jointsWhere the battery goes: copper loss rising with torque squared, gearbox friction, regeneration and cost of transport.Read the explainer → 08Actuator types & performancePeak vs continuous torqueThe thermal wall: why joints hold peak torque only briefly, the heat path out of the stator, and cooling options.Read the explainer →

FAQ

What is a parallel elastic actuator?

A joint actuator with a spring mounted alongside the motor, between the frame and the moving link, rather than in line with the gearbox. Joint torque is the sum of motor torque and spring torque, so the spring can carry part of the load and the motor makes only the rest.

How is it different from a series elastic actuator?

In a series elastic actuator all joint torque passes through the spring and through the motor. It adds compliance and torque sensing but doesn’t reduce the torque the motor must produce. A parallel spring does reduce it, which is where the energy savings come from.

How much energy can a parallel spring save?

Published hardware results range from about 15% (a hopping monoped knee) to 79% (a clutched knee on a half-scale humanoid leg test bed), with a 93% cut in dissipated power at STEPPR’s hip roll joint on the bench. Results depend heavily on the task the spring was tuned for.

Do commercial humanoids use gravity compensation springs?

Not that their makers document publicly. Spring and counterweight balancing is common in industrial robot arms, KUKA’s axis-2 balancers for example, and Willow Garage’s PR2 used spring counterbalanced arms, but production humanoids in 2026 mostly rely on stiff electric joints and control.

Sources