Ball Screws in Humanoid Robots: How Rolling Balls Set Efficiency, Back-Drive and Life
Ball screws in humanoid robots: the rolling thread that turns motor spin into push
A ball screw replaces the sliding thread of an ordinary lead screw with a row of steel balls. That one change lifts efficiency from well under half to around 90%, makes the screw back-drivable, and gives it a bearing-style life rating. It is why ball screws sit in humanoid fingers and in the legs of PAL Robotics’ Kangaroo, and why the heaviest humanoid joints move on to roller screws.
Sources: Thomson Linear; THK ball screw technical data; Kangaroo lower-body paper, arXiv 2312.04161; Rockford Ball Screw calculations.
From a sliding thread to rolling balls
Every linear actuator in a humanoid has to turn the fast rotation of an electric motor into a slow, strong push. The simplest way is a screw: turn the shaft and a nut threaded onto it travels along the axis. In an ordinary lead screw, with a trapezoidal or Acme thread, the nut’s flanks slide over the shaft’s flanks. That sliding friction eats most of the input: Thomson Linear puts lead-screw efficiency at 30–80%, and at the small lead angles a compact actuator needs, it sits near the bottom of that range.
A ball screw cuts a rounded, helical groove into both the shaft and the nut and fills the gap with hardened steel balls. When the shaft turns, the balls roll instead of the surfaces sliding. At the end of the nut each ball is lifted out of the groove by a return tube or an internal deflector and carried back to the start, so the balls circulate continuously. THK, one of the largest makers, says this cuts the driving torque to about one third of a conventional sliding screw. Thomson and Tolomatic both quote about 90% efficiency.
Figure 1 · Anatomy of a ball screw, nut cut away
Illustration: humanoid.guide. Schematic, not to scale; one ball circuit with an external return tube. Many miniature screws use internal deflectors instead of a tube. The bottom row of balls is offset by half a lead because the raceway is a single helix.
Lead: the gear ratio of a screw
The lead is how far the nut moves for one turn of the shaft. It does the job a gear ratio does in a rotary joint. The thrust a screw produces is F = 2π × η × T ÷ l, where T is the motor torque, η the efficiency and l the lead. A 1 N·m motor on a 5 mm lead at 90% efficiency pushes about 1,130 N. Put a small hand motor delivering 0.02 N·m onto a 1 mm-lead miniature screw and the nut pushes about 113 N, enough to drive a finger linkage. A shorter lead gives more force and finer resolution, but the nut moves more slowly at a given motor speed.
Miniature screws are named by shaft diameter and lead. A “0401” has a 4 mm shaft and a 1 mm lead, which works out to a lead angle of about 4.6°. THK’s MDK miniature range runs from 4 to 14 mm shafts with 1 to 5 mm leads, and KGG lists 040.5, 0401, 0402 and 0501 sizes for dexterous-hand actuators.
Figure 2 · Animated · One screw turn moves the nut one lead
Illustration: humanoid.guide. CSS animation: the screw makes 12 turns in 6 s and the nut travels 12 leads, then both reverse; the apparent drift of the groove equals the nut’s travel, as on a real single-start screw. Stops when reduced motion is requested.
Why efficiency matters twice
The efficiency gap is largest exactly where humanoid actuators live. Small lead angles give compact, forceful actuators, and at small lead angles sliding friction dominates. With a friction coefficient of 0.15, a sliding thread at 4.6° converts only about a third of the motor’s work into thrust; the rest becomes heat in the nut. A ball screw at the same angle stays above 90%. Chart 1 shows the calculation.
Efficiency also runs backwards. A sliding screw with a small lead angle is self-locking: pushing on the nut cannot turn the shaft, so a load stays put with the motor off. A ball screw is not. Roton puts its back-driving efficiency at about 80%, so a load on the nut will turn the motor. With a 5 mm lead, a 1,130 N load pushes back on the motor with roughly 0.7 N·m. That is useful when a controller wants to sense contact through motor current or let a leg comply on landing, and a cost when the robot has to hold a pose: it needs holding current, a brake or a spring. Thomson notes that ball screws generally need a brake where back-driving is not acceptable.
Chart 1 · Why balls win: efficiency versus lead angle, rolling and sliding threads
Chart: humanoid.guide calculation, square-thread model: forward η = tan λ ÷ tan(λ + ρ), back-driving η = tan(λ − ρ) ÷ tan λ, with tan ρ = μ. μ = 0.004 reproduces THK’s worked example (96% at a 5.5° lead angle); μ = 0.15 is Roton’s bronze-nut case, for which Roton’s Acme chart gives 45% forward at 8° and 65% / 52% at 20°. Real ball screws lose a few points more to seals and recirculation: catalogues quote about 90% forward and 80% back-driving.
Ball, roller or sliding thread?
Ball screws are one of three screw families in humanoid actuators. The planetary roller screw replaces the balls with threaded rollers, which gives many more contact points in the same envelope. Tolomatic says that buys up to ten times the life of a comparable ball screw, at a somewhat lower efficiency of about 80–85% and a higher price. That is why roller screws carry the heaviest linear loads: Tesla’s Optimus uses inverted planetary roller screws in its hips, knees and ankles, and NASA’s Valkyrie used roller screws in its linear series elastic actuators. The cheapest option, the sliding trapezoidal screw, survives where duty is light and self-locking is welcome.
Table 1 · Ball, roller and sliding lead screws compared
| Property | Ball screw | Planetary roller screw | Sliding (trapezoidal / Acme) screw |
|---|---|---|---|
| Load path | Steel balls rolling in a helical groove, recirculating | Threaded rollers with many more contact points | Thread flanks sliding on a bronze or polymer nut |
| Forward efficiency | ~90% | ~80–85% | 30–80% |
| Back-driving | Yes (~80% reverse); needs a brake or holding current | Yes | Can be self-locking at small lead angles |
| Life | L10 rating, inverse cube of load | Up to 10× a comparable ball screw | Set by wear of the nut |
| Typical humanoid use | Finger and wrist actuators; Kangaroo’s legs | Optimus hips, knees, ankles; Valkyrie’s linear SEAs | Low-cost, low-duty axes |
| Indicative China unit price | ~¥400 | ~¥1,500 | ~¥100 |
Sources: Tolomatic (efficiency, 10× life); Thomson Linear (30–80% vs 90%); Roton (80% back-driving); Rockford Ball Screw (cube law); Paine et al. 2015 (Valkyrie roller screws); 36Kr (Optimus); TechBuzz China lead-screw tracker for unit prices, which are secondary estimates for miniature ball screws versus roller screws, not quotes.
Life: the cube law
Because a ball screw is a rolling bearing wound into a helix, it is rated like one. The basic dynamic load rating Ca is the axial load at which 90% of a group of identical screws reach one million revolutions (some makers rate in travel instead). Life then scales with the inverse cube of load: halve the load and the rated life rises eight times, double it and life falls to an eighth.
For a 1 mm-lead miniature screw, one million revolutions is one kilometre of nut travel. In an illustrative finger that moves 20 mm per open-and-close cycle, that is 50,000 grasps at the full rated load, or 400,000 at half of it. This is why actuator designers size screws for the load they expect most of the time, not the peak. Speed has limits too: THK rates its MDK miniature screws at a DN value of 70,000 (ball-centre diameter in mm × rpm). For a screw around 4 mm, that allows roughly 17,500 rpm, or about 0.3 m/s of nut speed with a 1 mm lead.
Where ball screws sit in humanoids
The clearest published case is PAL Robotics’ Kangaroo. Its legs are driven by 12 linear actuators, six per leg, all mounted near the pelvis. According to the team’s 2023 paper, the actuators are “based on ball-screws” with absolute encoders on the motor side. The knee actuator applies up to 5,000 N, and the manufacturer gives the screw efficiency as 0.95. Putting the actuators near the pelvis and driving the joints through linkages keeps mass out of the lower legs, which helps both impact robustness and leg swing.
The largest market by unit count is the hand. Finger modules from Chinese suppliers combine a micro motor, a small gearbox and a miniature screw; Zhaowei’s hand drive modules integrate all three. One industry tracker, TechBuzz China, counts about 34 miniature ball screws in a typical full-size humanoid, mostly in fingers, wrists and elbows, at around ¥400 each, against about 14 planetary roller screws at around ¥1,500. Treat those numbers as estimates: they come from brokerage-style analysis, not maker disclosures, and the same report gives different counts for Optimus. It names NSK and THK as leaders at the precision end, and Beite Technology and Best Precision as Chinese miniature-screw challengers. KGG also markets ball screws for humanoid hands.
Many makers do not say what screw they use. Apptronik’s Apollo, for example, uses in-house linear actuators in joints such as the elbow and knee, but its published material does not name the screw type.
Table 2 · Where screws show up in published humanoid designs
| Robot or part | Screw type | Where | Published figures |
|---|---|---|---|
| PAL Robotics Kangaroo | Ball screw | 12 linear actuators near the pelvis: hip yaw, hip pitch/roll pair, knee, ankle pair per leg | 5,000 N max force; η = 0.95 (manufacturer); knee stroke 0.15 m |
| NASA Valkyrie (R5) | Roller screw | Linear SEAs: ankle pair, wrist pitch/yaw pair, torso-to-pelvis pair | Die springs as the elastic element; load cells at the output |
| Tesla Optimus | Inverted planetary roller screw | Hips, knees, ankles | About 14 per robot, per a 36Kr supply-chain analysis |
| Apptronik Apollo | Not disclosed | Linear actuators in leg and arm joints, e.g. elbow and knee | Sixth-generation in-house actuator |
| Dexterous-hand modules | Miniature ball screw | Finger drive modules: micro motor + gearbox + screw | KGG lists 040.5, 0401, 0402 and 0501 sizes for hands |
Sources: Kangaroo lower-body paper, arXiv 2312.04161; NASA R5 fact sheet and Paine et al., Journal of Field Robotics 2015; 36Kr; The Robot Report; KGG. Size codes follow the common shaft-diameter + lead convention (0401 = 4 mm shaft, 1 mm lead).
What to ask about a ball-screw actuator
- Diameter, lead and lead angle. These set thrust per newton-metre, resolution and top speed. Check the thrust formula against the stated motor torque.
- Dynamic load rating Ca and the load spectrum. Ask what fraction of Ca the screw sees in normal use; the cube law makes this the main life lever.
- Back-driving behaviour. Is the axis meant to be back-drivable? If not, what holds it with power off: a brake, a self-locking stage, or a spring?
- Accuracy grade and axial play. Lead accuracy and preload decide positioning precision and how much free play shows up at the finger or joint.
- Sealing and lubrication. Balls need clean grease; ask how the nut is sealed and what the relubrication interval is.
- Speed limit. Ask for the DN value and critical speed of the shaft at the installed length.
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 the difference between a ball screw and a lead screw?
A lead screw’s nut slides on the thread; a ball screw’s nut rides on recirculating steel balls. Rolling instead of sliding raises efficiency from 30–80% to about 90% and gives a bearing-style life rating, at a higher cost and without self-locking.
Is a ball screw back-drivable?
Yes. With a back-driving efficiency of around 80%, a load on the nut will turn the motor. Humanoid axes that must hold a pose with power off need a brake, a self-locking stage or a spring.
Why do humanoid legs often use roller screws instead of ball screws?
Planetary roller screws have many more contact points than a ball screw of the same size, so they carry higher loads and can last up to ten times longer. Optimus uses them in its hips, knees and ankles. PAL Robotics’ Kangaroo shows that ball screws can still drive a full biped’s legs.
How long does a ball screw last?
Its rated life is the number of revolutions 90% of screws reach at the dynamic load rating, usually one million. Life scales with the inverse cube of load, so running at half the rating gives about eight times the rated life.
Where are ball screws used in humanoid robots?
Mostly in small and medium linear axes: finger and wrist actuators in dexterous hands, and some leg actuators, as in PAL Robotics’ Kangaroo. Industry estimates put the count at a few dozen miniature ball screws per full-size humanoid, but makers rarely confirm it.
Sources
- Roig et al., Modeling and Numerical Analysis of Kangaroo Lower Body, arXiv 2312.04161 (12 ball-screw linear actuators near the pelvis, 5,000 N maximum force, η = 0.95, strokes)
- Paine et al., Actuator Control for the NASA-JSC Valkyrie Humanoid Robot, Journal of Field Robotics 2015 (linear SEAs with roller screw drivetrains and die springs)
- NASA, R5 (Valkyrie) fact sheet (linear actuator pairs at ankle, wrist and torso)
- Tolomatic, Ball screw or roller screw: which linear actuator is best? (~90% vs 80–85% efficiency, up to 10× roller-screw life)
- Thomson Linear, Ball screws vs lead screws (30–80% vs 90% efficiency, brakes for back-driving)
- Roton, Efficiency and backdriving (90% forward and 80% back-driving for ball screws; Acme efficiency at 8° and 20°)
- THK, Features and types of ball screws (driving torque one third of a sliding screw; 96% worked example)
- THK, Miniature ball screw model MDK (4–14 mm shafts, 1–5 mm leads, DN 70,000)
- Rockford Ball Screw, Ball screw calculations (90% efficiency, L10 life and the inverse-cube law, critical speed)
- KGG, Humanoid robot power core: ball screws (ball screws and miniature screw sizes for dexterous hands)
- TechBuzz China, Lead screws and linear actuators (estimated screw counts and unit prices per humanoid, suppliers)
- 36Kr, Elon Musk’s plan to build one million robots (~14 inverted planetary roller screws in Optimus hips, knees and ankles; Zhaowei hand modules)
- The Robot Report, Apptronik releases humanoid robot with bespoke linear actuators (Apollo linear actuators in elbow and knee)