How a twisted string pulls

A twisted string actuator has three parts: a motor, two or more strings fixed to its shaft, and a load tied to the far end. When the motor turns, the strings wind around each other into a helix. Each string keeps its length, but part of that length now goes round the bundle instead of along it, so the distance between motor and load shrinks. The motor’s rotation has become a linear pull, with no gear teeth, screw thread or nut in between.

The geometry is simple enough to write in one line. Unroll one string from the helix and it forms a right-angled triangle. The hypotenuse is the string length L. One side runs round the bundle and equals the motor angle θ times the bundle radius r. The other side is the twisted length X that remains along the actuator. So X = √(L² − θ²r²), and the contraction is p = L − X. This ideal model, set out by Würtz and colleagues in 2010 and developed by Palli and co-authors in IEEE/ASME Transactions on Mechatronics in 2013, is still the starting point for most TSA papers.

A transmission whose ratio changes as it turns

A gearbox has one ratio. A twisted string does not. Differentiate the contraction formula and the linear travel per radian of motor rotation is θr² / X. At the start, with θ close to zero, the strings barely move: the reduction is enormous. As the twist builds up, each extra turn pulls in more string, and the effective reduction falls.

Chart 1 shows this for an example actuator with a 100 mm string and an effective bundle radius of 0.5 mm. Five motor turns pull the load in by 1.2 mm. Turns 15 to 20 pull it in by 10.4 mm. Chart 2 shows the other side of the trade: with no losses, 0.01 N·m of motor torque, roughly what a small motor delivers without a gearbox, produces 125.7 N of pull after five turns but only 24.8 N after twenty. Designers usually pre-twist the strings to skip the slow first section and stop before the strings bunch up, which is why papers quote a usable range of about 30–40% of string length.

For a robot finger that varying ratio is not entirely a drawback. A finger closes fast through free air while the strings are lightly twisted, then meets the object with high force at a lower speed. The catch is that the controller needs a good model of the curve, and real strings make that model less tidy than the formula suggests.

Where twisted strings have been built

Most TSA work has been aimed at hands and wearable devices, where a small motor has to produce a large pull in a slim package. The EU-funded DEXMART project used twisted strings to drive the fingers of an anthropomorphic hand built at the University of Bologna. Its project materials described a prototype lifting 5 kg by 30 mm in under a second, with the motors placed in the forearm rather than the joints. Later groups pushed in two directions: more contraction and smaller packages.

The numbers show both the appeal and the scale. The University of Nevada, Reno gripper used eleven 9.5 g motors and reached a 6.8 N fingertip force with fingers that close at more than 200°/s. The 2025 Biomimetics hand weighs 335 g without motors and reaches 7.4 N. Those are modest forces, but they come from very small motors and simple parts. The Manchester and Bangor joint shows another use: three TSAs pulling against each other to steer a two-axis joint that weighs 61.6 g.

The weak points: wear, one-way pull and drift

Strings rub against each other every time they twist, and that limits life. Tavakoli and colleagues ran a two-string TSA to failure at different loads and twist levels. At 2 kgf and 20 turns the string lasted 1,512 cycles. At 5 kgf and 55 turns it lasted 13. More load and more twist both shorten life sharply. The Manchester team reports no string failures within its load limits and a model-based estimate of about 52,000 cycles at 5 kg, but says that figure has not been verified by test. A humanoid hand that grasps a few thousand times per shift would need far more than either.

• Pull only. A string cannot push, so every joint needs a return spring or a second, antagonistic TSA. Several of the designs in Table 1 use opposing pairs or triads.
• Nonlinear and history-dependent. String stretch, creep, friction in guide tubes and hysteresis all move the real curve away from the ideal one. The 2025 Biomimetics team trained a neural network on 9,000 data points because the classic model was off by more than 25% for some strings and loads.
• Length. The twisting zone needs free length along the actuator axis. That suits a forearm, but it is hard to fit inside a compact rotary joint.
• Load-dependent ratio. Under load the strings stretch and the bundle compresses, so the ratio changes with force as well as twist. The arXiv SMA-rod design turns this into a feature, with the ratio about doubling as the load rises.

Where twisted strings could fit in a humanoid

We found no commercial humanoid that publicly lists twisted string actuators. Today’s humanoid hands use one of two other routes: tendons wound on spools by motors in the forearm, as in Tesla Optimus, 1X NEO and the Shadow Hand, or pen-sized micro linear actuators that push finger linkages, as in Inspire and Unitree hands. A TSA competes with both. Compared with a spool, it needs no high-ratio gearbox to make a small motor pull hard. Compared with a micro lead-screw actuator, it has fewer precision parts and is naturally compliant, because the strings stretch under load.

The barriers are the ones above: string life measured in thousands of cycles rather than millions, a ratio that shifts with load and wear, and the need for a calibrated model in the controller. Those are engineering problems rather than physics limits; recent builds mostly use high-strength UHMWPE (Dyneema) fibre. For now, the TSA is best seen as a research option for light, cheap hands and wearable assist devices rather than for the main joints of a walking robot.

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