From one spring to a tunable spring

Most humanoid joints are built to be stiff: a motor, a high-ratio reducer and a crossed-roller bearing, with compliance added in software through torque control. Two hardware alternatives put the softness into the mechanism instead. A quasi-direct-drive joint keeps the gear ratio low, so it can be back-driven by an impact. A series elastic actuator (SEA) inserts a spring between gearbox and link, which filters shocks and lets the joint measure torque from how far the spring deflects.

The SEA has one limitation: its spring stiffness is picked once, at design time. A soft spring protects well and stores energy but makes precise positioning sluggish. A stiff spring tracks accurately but protects less. A variable stiffness actuator removes that compromise by adding a mechanism, and almost always a second motor, that changes the effective spring rate on the fly. Researchers group VSAs and their damping cousins under the name variable impedance actuators.

Why bother? Three reasons come up again and again in the literature. Safety and robustness, because a soft joint decouples the heavy motor and gearbox from the link during a collision. Explosive motion, because a spring that’s wound up and released can move the link faster than the motor alone. And efficiency in cyclic motion, because a spring tuned to the motion’s natural frequency can return energy each cycle instead of the motor burning it as heat.

How a VSA changes its stiffness

There are many mechanisms, but the classic one is easy to picture. One motor sets where the joint wants to be: its equilibrium position. A second motor pre-loads the spring that connects the motor side to the link. The more pre-load, the more torque the joint pushes back with for each degree it’s deflected, which is higher stiffness. The Vrije Universiteit Brussel’s MACCEPA design works exactly this way: one servo sets the angle of a lever arm, the other pulls a cable to pre-tension the spring, and the output torque is a linear function of that pre-tension and the deflection from equilibrium.

The 2016 review of VSA design in IEEE/ASME Transactions on Mechatronics, written by about twenty authors from the main European VSA labs, sorts the alternatives by how the two motors share the work:

• Antagonistic: two equal motors, each pulling through a non-linear spring. Moving them together changes position; pulling them against each other raises stiffness. qbrobotics’ qbmove and the Pisa VSA-Cube work this way.
• Serial or main-plus-adjuster: one big motor positions the joint and a small one only changes stiffness. DLR’s VS-Joint and floating spring joint (FSJ) follow this layout, which puts most of the motor mass where the torque is needed.
• Lever-ratio or structure-controlled: the spring stays the same, but the lever arm it acts through changes length. IIT’s AwAS family uses this route, which needs little energy to change stiffness.

What real VSAs can do

Published numbers are scattered across papers and catalogues measured in different ways, but a handful of actuators are well documented. Stiffness is given in newton-metres of torque per radian of deflection.

The headline result is about speed, not softness. In DLR’s kicking experiments, a stiff joint reached 3.06 m/s; the VS-Joint, winding its spring up first and releasing it, reached 6.35 m/s, with impact torque of 85 N·m. That doubling is the clearest demonstration of what a stored-energy joint adds that a motor and gearbox can’t.

The humanoid built on VSAs: DLR’s David

The German Aerospace Center (DLR) is the one group that has carried variable stiffness through an entire humanoid upper body. Its Hand Arm System, later called David, uses three VSA types. The four upper-arm joints are floating spring joints: one big motor positions the joint and a small motor changes stiffness through a single spring. The wrist’s two DoF and forearm rotation use a bidirectional antagonistic design. The 20-DoF hand uses antagonistic motor pairs with progressive springs in the tendons. DLR lists no torque sensors in the arm, and claims human-like strength and range of motion.

That takes a lot of hardware. The forearm alone holds 42 motor modules with integrated inverters at 180 W peak each, and the shoulder and upper arm another eight motors of up to 1 kW peak. The wheeled successor, neoDavid, has 52 degrees of freedom, 95 brushless DC motors, 184 position sensors and three force sensors, controlled at 3 kHz. DLR shows it hammering, drilling with a hammer drill and throwing, and says it built the first experimentally validated motion-tracking controller with link-side damping for a VSA robot.

The robustness claim was famously tested with a baseball bat. IEEE Spectrum reported that DLR researchers struck the arm and shoulder, after which the arm went back to gently touching a ball exactly as before. The fingers, driven through Dyneema tendons, were designed to survive impacts that would destroy a stiff hand.

Why production humanoids skip it

As far as public spec sheets show, none of the humanoids heading for volume production uses variable stiffness joints. They use stiff reducers with torque control, quasi-direct-drive, or a fixed series spring. The reasons are the ones the research community itself lists.

• Mass and size. A second motor and a spring mechanism add weight at every joint. In a leg, that weight sits far from the hip and costs energy on every step.
• Cost. Pisa’s VSA-Cube paper called cost “one of the fundamental barriers” to VSA adoption, noting earlier prototypes cost around €10,000 in materials alone.
• Design trade-offs. The 2016 review frames VSA engineering as a set of design contradictions between power, energy storage, stiffness range, efficiency and precision. No single mechanism maximises all of them.
• Control. A soft joint oscillates. Controllers have to damp the link-side vibration without throwing away the compliance, which is why DLR’s damping controller counts as a research milestone.
• Software caught up. Modern torque-controlled joints can emulate a wide range of stiffness in software at kilohertz rates. They can’t store energy or survive a bat strike the same way, but for most factory tasks that’s good enough.

Where variable stiffness could still win

The efficiency argument hasn’t gone away. A 2025 simulation study of a one-legged hopping robot found that choosing leg stiffness per speed instead of fixing it cut energy use by up to 20%, and by 6.8% on average across the speed range. That is a modelling result, not hardware, but it shows why legged-robot labs keep returning to tunable compliance. VUB’s VERONICA biped used MACCEPA joints to change its legs’ natural frequency, letting a passive-style walker walk at more than one speed.

The likeliest openings in humanoids are narrow ones: hands that must survive being knocked, arms that throw or hammer, and robots working in close contact with people where a mechanical fuse is worth more than a software limit. Watch for switchable designs, which lock between a few stiffness settings instead of adjusting continuously, as a cheaper middle ground.

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