Cycloidal drive

A cycloidal drive (also called a cycloidal speed reducer, cyclo drive, cycloidal gearbox, or, in industrial robotics, an RV reducer) is a compact mechanical speed reducer that converts high-speed, low-torque input into low-speed, high-torque output with low backlash and very high shock tolerance. Internally, an eccentric input shaft pushes one or more lobed cycloidal disks against a ring of stationary roller pins, and a set of output rollers passing through enlarged holes in the disks picks up only the disk's slow rotation, ignoring the wobble. The result is a single-stage transmission that reaches reduction ratios above 100:1 (up to 119:1 in one stage, and up to 7,569:1 in two stages) with high torque density and the ability to absorb momentary overloads of up to 500 percent of rated torque.^[6][7]

The principle was patented by German engineer Lorenz Braren, who filed his foundational patent in Germany on December 5, 1925 and received U.S. Patent 1,694,031, "Gear Transmission," on December 4, 1928.^[1] In that patent Braren set out to "provide a transmission with a fixed speed ratio of a very simple, compact and durable form."^[1] He commercialized the design in the 1930s under the trade name Cyclo, and 2025 marked the technology's 100th anniversary.^[2] After a 1937 license to the Japanese gear maker that became part of Sumitomo Heavy Industries, the technology spread through Japanese industry, then into industrial robot joints in the 1980s through Teijin Seiki's RV reducer.^[3][4]

Today the cycloidal drive sits inside the heavy joints of nearly every major six-axis articulated arm, including machines from FANUC, ABB, KUKA, and Yaskawa.^[4] It also appears, alongside strain wave gearing, in the lower-body joints of legged and humanoid robots such as those from Boston Dynamics and Unitree, where high shock tolerance matters more than the last gram of weight.^[12] The market for precision cycloidal reducers has been led for three decades by Nabtesco, the Japanese supplier formed when Teijin Seiki merged with Nabco in 2003. Nabtesco, which describes itself as "the world market leader in the field of robotic gears," holds about 60 percent of the precision reducer market for industrial robots, one of the more concentrated bottlenecks in the robotics supply chain.^[2][4] The rise of Chinese makers since the late 2010s has been driven largely by an explicit national effort to break that hold.

Quick facts

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When was the cycloidal drive invented?

Braren and the Cyclo principle

Lorenz Konrad Braren, born in 1886 on the North Frisian island of Foehr, was chief designer at the Friedrich Deckel machine-tool factory in Munich when he sketched the layout, drawing on the precision of Deckel's "COMPUR" camera shutter.^[2] He filed his foundational patent in Germany on December 5, 1925, and it was granted in 1927.^[1][2] The same invention issued as U.S. Patent 1,694,031, "Gear Transmission," on December 4, 1928 (filed November 30, 1926, and assigned to Friedrich Deckel), in which Braren described discs "forming a continuous cycloidal curve" engaged by stationary rolling members to transmit motion between fast and slow shafts.^[1] In 1931 Braren founded Cyclo GmbH in Munich and began serial production of gearboxes for conveyors, mills, and other constant-duty industrial drives, where the cycloidal reducer's compact form and shock tolerance gave it an edge over worm gears and multi-stage spur reducers.

Braren's geometry was not new mathematics. Cycloidal curves had been studied since the seventeenth century, and cycloidal tooth profiles already appeared in clockwork. What was new was the gearbox layout: an eccentric on the input shaft, two cycloidal disks running 180 degrees out of phase to balance the wobble, a ring of fixed pins, and an output carrier with rollers pinned through enlarged holes in the disks. As Nabtesco puts it, Braren's insight was to use "pins and rollers instead of the usual toothed gears."^[2] That arrangement allows a single-stage cycloidal drive to hit reductions in the tens or hundreds with rolling, not sliding, contact at every interface.

Sumitomo and the postwar spread

In 1937 Cyclo GmbH signed a license agreement with the Japanese gear maker that later became part of Sumitomo Heavy Industries. The first Japanese-built Cyclo reducer rolled off the line at the Niihama Works in 1939, and Sumitomo made the Cyclo a flagship product line.^[3] Today Sumitomo Drive Technologies still markets the Cyclo brand (and its bevel-geared Cyclo BBB and BBB1 derivatives) almost a century after the original patent.^[3] The Cyclo dominated heavy industrial gearing through the postwar decades, but it was the next leap, repackaging the principle for precision robotics, that made cycloidal drives a fixture of modern automation.

Teijin Seiki, the RV reducer, and the robot boom

Teijin Seiki, a Japanese aerospace and machinery firm, started building cycloidal reducers in the late 1970s for the swing motors on hydraulic excavators, an application that demands shock tolerance and a compact form factor. In the early 1980s the major Japanese robot makers asked Teijin Seiki to harden the design for use in the base and shoulder joints of their new generation of articulated arms. Teijin Seiki set out the theory of RV ("rotate vector," referencing the eccentric geometry) transmission in 1980 and, after securing patents, reached volume production of the RV reducer in 1986.^[4]

The RV reducer combines a planetary first stage with a cycloidal second stage in one housing. That hybrid layout multiplies ratios while keeping the rugged shock behavior of the cycloidal geometry. Within a few years it became the default solution for the high-load joints (J1, J2, J3) of six-axis industrial arms, while harmonic drives took the lighter wrist joints (J4, J5, J6). On September 29, 2003, Teijin Seiki merged with the brake and aerospace company Nabco to form Nabtesco Corporation, and the RV reducer line became Nabtesco's anchor product.^[4] By the 2010s the cycloidal drive had quietly become a component without which modern manufacturing would not look the way it does: arms welding car bodies, palletizing boxes, and loading semiconductor wafers all turn on cycloidal reducers, most from a single supplier in Japan.

How does a cycloidal drive work?

A single-stage cycloidal reducer has five functional parts: a high-speed input shaft, an eccentric cam keyed to that shaft, one or two cycloidal disks with a lobed (epicycloid or hypocycloid) outer profile, a stationary ring populated with cylindrical pin rollers, and a slow-speed output carrier carrying rollers that pass through enlarged holes drilled through the disks.^[18]

In operation, the input shaft spins the eccentric, which forces each cycloidal disk to wobble in a small circular orbit. The lobed edge of the disk presses against the ring of pins, but because the disk has one fewer lobe than the ring has pins, full revolutions of the input shaft only nudge the disk forward by one tooth. The disk therefore rotates slowly in the opposite direction of the input.

The output rollers pick up that slow rotation. They sit in oversized holes in the disk, and the eccentric wobble is absorbed by the gap between roller and hole, so only the disk's true rotation about the central axis transmits to the output shaft. The radial wobble cancels out at the output.^[6] Most real units use two cycloidal disks set 180 degrees out of phase. The phase offset cancels static imbalance and reduces vibration; high-speed designs use three or more disks for the same reason.

What is the reduction ratio of a cycloidal drive?

The basic single-stage reduction follows from the lobe count. If the ring has P pins and the cycloidal disk has L lobes, with L = P - 1, the single-stage reduction ratio equals L. Wikipedia and manufacturer references give the equivalent output-to-input form:

r = (P - L) / L

so a disk with 10 lobes engaging 11 ring pins gives a 10:1 reduction in a single stage.^[6] Commercial single-stage cycloidal drives have been built up to 119:1. Compound (two-stage) units, which combine two cycloidal stages or a planetary first stage with a cycloidal second stage, reach into the thousands; published designs go up to 7,569:1.^[6]

The two-stage RV layout

The RV reducer used in industrial robots is a two-stage cycloidal drive. The first stage is a planetary spur reduction (typically with three planet gears) that takes the input down by a modest factor. The second stage is the cycloidal stage proper, with two RV disks set 180 degrees apart, driven by eccentric cams on the carrier shafts of the first stage. This compound layout is what gives RV reducers their characteristic combination of compact diameter, high ratio (typically 30:1 to 200:1), and the very high shock tolerance robotics needs.^[7]

Variants

Several structural variants of the basic Braren layout are produced today: single-stage cycloidal (one or two disks driven by a single eccentric, used in industrial Cyclo gearmotors and most hobby builds); two-stage compound cycloidal, including the RV layout (planetary primary, cycloidal secondary) and pure stacked two-stage Braren designs that reach ratios into the thousands; twin-disk and multi-disk designs, where two or three offset disks reduce vibration from the eccentric motion (standard in Nabtesco RV and Sumitomo Fine Cyclo); the cycloidal-bearing combo of Spinea TwinSpin, which integrates a high-precision cross roller bearing into the housing;^[8] the segmented-tooth Wittenstein Galaxie, which swaps Braren's smooth-lobed disk for separate tooth segments moving on a logarithmic-spiral profile;^[9] and mini or 3D-printable cycloidals used in hobby robotics.

What performance can a cycloidal drive achieve?

The numbers below come from manufacturer datasheets and peer-reviewed comparisons. Real-world figures vary with size, ratio, lubrication, and load.

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Datasheet efficiency figures are best-case. An independent in-use study is a useful reality check: a 2018 Rice University MAHI Lab paper by Farrell and colleagues ran a cycloidal drive built for a lunar or Martian rover through 129,000 output cycles (about 7.6 million input cycles) and found that a substantial burn-in period was needed before it settled, after which it reached a peak efficiency of about 81 percent.^[11] Single-stage efficiency approaching 93 percent and two-stage efficiency approaching 86 percent are the numbers commonly quoted for well-loaded, well-lubricated units.^[6]

Backlash needs a caveat. Marketing copy that describes cycloidal drives as "zero backlash" is a useful approximation but not literally true. Actual angular play under load is small (around an arcminute or less in precision grades) and very stable over the lifetime of the unit because every contact is rolling rather than sliding. That stability matters as much as the absolute number for a robot running the same path a million times. Spinea, for example, quotes repeatable positioning accuracy of under 10 arcseconds and standard lost motion at or below 1 arcminute for its TwinSpin units.^[8]

Shock tolerance is the property that genuinely sets cycloidal drives apart from their main rival. Load is shared simultaneously across roughly half the ring pins, so an overload spike does not concentrate on one or two teeth. Nabtesco rates its RV reducers for a momentary maximum torque of 500 percent of rated torque (and an allowable acceleration or deceleration torque of 250 percent), which is what makes cycloidal reducers the natural choice for the base joint of a heavy six-axis arm or the knee of a 100-kilogram humanoid.^[7]

How does a cycloidal drive differ from a harmonic drive?

The two technologies that compete for the same niche, compact high-ratio reducers for robot joints, are cycloidal drives and strain wave gearing (commonly called harmonic drives after the original Harmonic Drive SE / Harmonic Drive LLC trade name). They are different enough in geometry that each has applications where the other simply will not fit.

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This is why most six-axis industrial arms use both. The bottom three joints carry the weight of the arm and absorb the shock of unloaded moves and crashes, so they run on RV-style cycloidal reducers. The wrist joints need light, compact, low-inertia transmissions and rarely see crash loads, so they run on harmonic drives.^[4]

A 2012 IEEE paper by Sensinger and Lipsey compared the two for high-ratio single-stage robotic transmissions. They designed six cycloid models to match corresponding harmonic drives and reported that the cycloid designs came out thinner, more efficient, and lower in reflected inertia at comparable torque, while harmonic drives stayed lighter at comparable size.^[5] The comparison gets more nuanced once planetary gears enter the picture: planetary stages are cheaper, give moderate ratios per stage (3:1 to 10:1), and dominate in cobots and lightweight humanoids that use quasi-direct drive actuator architectures. A cycloidal stage replaces two or three planetary stages in roughly the same axial length, at the cost of more demanding manufacturing and a small but nonzero amount of backlash.

How is a cycloidal drive manufactured, and why is it hard?

The cycloidal reducer is a notoriously hard precision part to make. The disk profile must be ground to micrometer-level accuracy or the drive will run with audible ripple and unacceptable backlash. Bearings, eccentrics, and pin rings all demand precision steel and careful heat treatment. For decades the practical knowledge of how to grind a good cycloidal disk was concentrated in a handful of Japanese plants, which is much of why Nabtesco's market share stayed near 60 percent.^[2][4]

Key manufacturing concepts include profile shifting (the mathematically pure cycloidal profile is rarely used; manufacturers shift the profile slightly to control the contact pattern and give the disk small clearance to the pin ring), improved tooth-difference designs (C.-F. Hsieh and other researchers have published variants that change the dynamics and stress distribution, showing for instance that pin-wheel designs can produce more vibration and stress fluctuation than nonpin designs), and pin-tooth wear analysis that ties contact stress, profile shift, and lubricant film to predicted lifetime.^[10] Production lines typically measure each ground disk and matched pin ring, then sort them into bins so paired components meet a target backlash without further fitting.

The Chinese push into precision reducers since around 2015 has been an explicit industrial-policy move, treating the cycloidal reducer as a strategic component on par with semiconductors. Chinese entrants include Shuanghuan, Ningbo Zhongda Leader, Suzhou Greenable, Hongfeng, and Yi Sheng. Chinese suppliers have driven local reducer prices well below Japanese import levels: Suzhou Green Harmonic, for example, prices its harmonic reducers at roughly 40 to 60 percent of comparable Japanese products, and RV-class prices have fallen on a similar path, though Chinese makers still trail on the very high-precision and ultra-low-backlash grades.^[13]

Who makes cycloidal drives?

The precision cycloidal reducer industry is concentrated, with one Japanese supplier holding the dominant position and a long tail of regional and Chinese entrants. This table covers the main producers and their flagship product lines.

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The market structure is unusually lopsided. As of the early 2020s, Nabtesco supplied roughly 60 percent of the world's precision reducers for industrial robots and held a near-monopoly on the medium-to-heavy-load RV joint reducers used in articulated arms.^[4] For its 2025 centennial, Nabtesco described itself as "the world's largest and most renowned manufacturer of precision cycloidal gears" and the "world market leader in the field of robotic gears" with "60% market share in industrial robotics sector."^[2] Nabtesco and Harmonic Drive together account for roughly three-quarters of the global precision reducer market, with Harmonic Drive around 15 percent; the remaining slice splits between Sumitomo, Spinea, Onvio, Wittenstein, and a growing list of Chinese suppliers.

Where are cycloidal drives used outside robotics?

Outside robotics, the cycloidal drive is a workhorse of heavy-duty industrial gearing. Common applications include CNC machine tool indexers and rotary tables, wind turbine yaw and pitch drives (where shock tolerance handles gust loads), conveyor and bulk-material drives, mining and quarry drives, steel-mill roll-table drives, and marine winches.

Where are cycloidal drives used in robotics?

Six-axis industrial arms

The canonical use of a cycloidal drive in 2026 is a Nabtesco RV reducer in the base or shoulder joint of an industrial robot. All Big Four robot makers (FANUC, ABB, KUKA, Yaskawa) source RV reducers from Nabtesco for the high-load joints of their arms, and Nabtesco's supply position has at times been strong enough to lock out competitors.^[4] Industry estimates put the share of cycloidal reducers in mid-to-large industrial robots at around 60 percent of all reduction gearing by unit, with harmonic drives taking most of the rest at the wrist.

The pattern is consistent across the major arms: J1 (base) uses an RV reducer at ratio roughly 100:1 to 200:1; J2 (shoulder) and J3 (elbow) use slightly smaller RV reducers; J4, J5, and J6 (wrist) use harmonic drives.^[7] Universal Robots' UR3 to UR16 cobots are an exception, sticking with planetary and harmonic stages to keep the safety-rated joint mass low.

Humanoid robots

Cycloidal and cycloidal-style reducers appear in the lower-body joints of some humanoid robots, where shock tolerance from walking and falling matters more than absolute weight. In practice, though, the current flagship humanoids lean more heavily on harmonic drives and roller screws than on cycloidals, and most makers build custom hybrid actuators that do not fit cleanly into one category.

• Boston Dynamics Atlas. In April 2024 Boston Dynamics retired the hydraulic Atlas and unveiled an all-electric version with, in CEO Robert Playter's words, "custom, high-powered and very flexible actuators at most joints."^[14] Published teardowns and patent filings suggest a mix of cycloidal-class and planetary reducers, plus planetary roller screws on some linear joints, optimized for shock loads in the legs.^[14]
• Tesla Optimus. Tesla's actuator architecture uses 14 rotary actuators (frameless torque motor plus reducer plus sensors) and 14 linear actuators (frameless motor plus planetary roller screw). The rotary reducers are documented as harmonic drives, sourced in part from China's Suzhou Green Harmonic, making Optimus a counter-example: a flagship humanoid that leans on harmonic drives where industrial arms use cycloidals.^[13]
• Figure 02. Figure AI's second-generation humanoid also leans harmonic: its rotary joints use harmonic drives and its linear joints use planetary roller screws, chosen for force density and stiffness. Public information on per-joint reducer choice remains limited.^[15]
• Unitree H1 and G1. Unitree builds its joint modules in-house. The G1 uses proprietary low-inertia permanent-magnet synchronous motors with compact gearboxes. The H1's M107 leg actuator delivers a peak knee torque of 360 Nm at a torque density of 189 Nm/kg, using high-ratio domestic reducers and crossed-roller output bearings.^[16]
• Research humanoids and quadrupeds. Recent papers describe quasi-direct-drive cycloidal actuators for legged robots at modest single-stage ratios (roughly 6:1 to 15:1), trading torque density for backdrivability and lower reflected inertia. A 2024 UCLA RoMeLa design (Zhu, Tanaka, Rafeedi, and Hong) reported a 10:1 cycloidal QDD actuator delivering 37.5 Nm continuous and 89.9 Nm peak torque at 64.21 Nm/kg, with about 7 arcminutes of backlash, arguing that "cycloidal gears have gained popularity as an alternative to planetary gears in legged robots due to their capacity to withstand large dynamic loads and frequent impacts."^[12]

The broad pattern: cycloidal-class reducers are favored where joints see both high torque and shock loads (hip, knee) in industrial and research machines; harmonic drives are favored where joints see high precision and tight packaging (wrist, elbow), and they currently dominate the rotary joints of flagship commercial humanoids. Most platforms use more than one reducer type.

Other robotics uses

Cycloidal drives also appear in robotic positioners and turntables, heavy-duty pick-and-place machines, robot welding cells (where collision shock is a real concern), mobile-robot drive trains, surgical and medical robotics (where Spinea's TwinSpin units pair low backlash with an integrated bearing), and quadruped knee and hip actuators in custom low-ratio cycloidal forms designed for backdrivability rather than maximum torque.^[8]

Open-source and hobby cycloidal designs

A cycloidal disk is one of the few precision gearbox parts that can be 3D-printed in plastic and still work, because the lobed contact spreads load over many points. The open-hardware robotics community has produced several reference designs. The most prominent is James Bruton's openDog V3 quadruped, which replaced its earlier belt drives with 3D-printed cycloidal gearboxes at a 25:1 reduction; Bruton reported testing one of the printed PLA units by having it push him on a skateboard for several miles with no visible wear.^[17] Other printable cycloidal designs come from makers such as Aaed Musa, How To Mechatronics, and ROBOTBUILD, aimed at desktop arms and small humanoids. (By contrast, the widely copied OpenTorque quasi-direct-drive actuator uses an 8:1 planetary gearset, not a cycloidal one.) These builds will not match a Nabtesco RV in stiffness or lifetime, but they have made the cycloidal layout the default learning vehicle for high-ratio mechanical reduction in the hobby community.

Modern variations

Beyond the variants section above, recent designs include cycloidal-pin gearing (rolling pins instead of fixed ones, which reduces sliding friction), the Wittenstein Galaxie (separate tooth segments on a logarithmic-spiral profile, marketed as free from backlash over the drive's service life and offered in torque ratings up to 7,500 Nm),^[9] magnetically preloaded cycloidals (research designs using magnetic preload to remove residual backlash for telescopes and surgical robots), and differential cycloidals (two stages in series at slightly different ratios, reaching ultra-high overall ratios for solar tracking and similar slow-motion applications).

What are the limitations of a cycloidal drive?

Cycloidal drives have known weaknesses. A single-disk drive has an unbalanced rotating eccentric that produces noticeable torque ripple; twin-disk and triple-disk designs cancel most but not all of it. The pin ring is the long-term wear surface even with rolling contact, so lubrication and load duty heavily influence service life. Below about 30:1, harmonic drives generally show lower backlash and hysteresis at comparable size.^[5] A high-end Nabtesco RV reducer for an industrial robot joint typically lists between 1,000 and 10,000 USD depending on size and grade, which is why the humanoid robotics industry treats reducer cost as a primary line item. At high ratios cycloidal drives are difficult to backdrive, limiting their appeal in compliant or impedance-controlled actuators. A cycloidal reducer that matches a harmonic drive on torque is typically heavier, because disks and pin rings are solid steel rather than thin-walled. Cheap cycloidals often show measurable ripple and high backlash because of imperfect grinding.

How is humanoid robot demand changing the market?

The humanoid robot wave that started in 2023 changed the demand profile. A single Tesla Optimus carries 28 actuators (14 rotary plus 14 linear), and other humanoids from Figure and Unitree use comparable counts, each actuator built around a precision reducer or roller screw.^[13][15] Projected unit volumes for mass humanoid production run well beyond the entire current industrial-robot reducer market, which has triggered fresh investment in cycloidal-style and harmonic-style joint modules from Japanese incumbents and Chinese challengers alike. Suzhou Green Harmonic, for example, has said its new Suzhou plant, due on line in 2026, will have annual capacity of 500,000 harmonic reducers.^[13] Whether the existing supply concentration holds, or whether humanoid demand finally pries the market open, is one of the more consequential open questions in robotics hardware.

See also

• Harmonic drive
• Planetary gear
• Industrial robot
• Humanoid robot
• Quasi-direct drive
• Direct drive
• Backlash (engineering)
• Gear
• Nabtesco
• Sumitomo Drive Technologies
• Robotics
• Actuator
• FANUC, ABB, KUKA, Yaskawa
• Boston Dynamics, Atlas
• Tesla Optimus, Figure 02
• Unitree, Unitree H1, Unitree G1

References

1. Braren, L. K. U.S. Patent 1,694,031, "Gear Transmission," filed November 30, 1926, granted December 4, 1928 (German priority December 5, 1925; assigned to Friedrich Deckel). https://patents.google.com/patent/US1694031A/en ↩
2. Nabtesco. "History: 100 years of cycloidal gears" (2025). https://www.nabtesco.de/en/company/news/history-100-years-of-cycloidal-gears ↩
3. Sumitomo Drive Technologies (Sumitomo Heavy Industries). "Our History" and "Cyclo Drives Continue to Evolve." https://us.sumitomodrive.com/en-us/our-history and https://www.shi.co.jp/english/particular/create/cyclo.html ↩
4. Nabtesco Precision Equipment Company. "Company" and "History" (RV reducer; Nabtesco formed September 29, 2003; approximately 60 percent global market share). https://precision.nabtesco.com/en/company/ ↩
5. Sensinger, J. W., Lipsey, J. H. (2012). "Cycloid vs. harmonic drives for use in high ratio, single stage robotic transmissions." IEEE International Conference on Robotics and Automation (ICRA), pp. 4130-4135. https://www.semanticscholar.org/paper/d5acd886c2f5a0f12f6af19df9f6baed1cb53664 ↩
6. Wikipedia contributors. "Cycloidal drive" (reduction ratio formula and range up to 119:1 single stage and 7,569:1 double stage; efficiency approaching 93 percent single and 86 percent double). https://en.wikipedia.org/wiki/Cycloidal_drive ↩
7. Nabtesco. "RV Series" precision reducer catalog (ratios; momentary maximum torque 500 percent of rated torque; allowable acceleration/deceleration torque 250 percent). https://www.nabtescomotioncontrol.com/pdfs/RVseries.pdf ↩
8. Spinea. "TwinSpin high-precision cycloidal zero-backlash reducers" (positioning accuracy under 10 arcseconds, standard lost motion at or below 1 arcmin, integrated output bearing, H series to 12,000 Nm). https://www.spinea.com/en ↩
9. Wittenstein. "Galaxie Drive System" (segmented-tooth kinematics on a logarithmic-spiral profile; freedom from backlash over service life; torque to 7,500 Nm; torsional rigidity to 2,500 Nm/arcmin). https://www.wittenstein-us.com/galaxie-gearboxes-drive-systems/ ↩
10. Hsieh, C.-F. (2015). "Traditional versus improved designs for cycloidal speed reducers with a small tooth difference: The effect on dynamics." Mechanism and Machine Theory. https://doi.org/10.1016/j.mechmachtheory.2014.11.003 ↩
11. Farrell, L. C., Holley, J., Bluethmann, W., O'Malley, M. K. (2018). "Cycloidal Geartrain In-Use Efficiency Study." ASME International Design Engineering Technical Conferences (IDETC), Rice University MAHI Lab (peak efficiency about 81 percent after burn-in over 129,000 output cycles). https://mahilab.rice.edu/sites/default/files/publications/Farrell2018IDETC.pdf ↩
12. Zhu, A., Tanaka, Y., Rafeedi, F., Hong, D. (2024). "Cycloidal Quasi-Direct Drive Actuator Designs with Learning-based Torque Estimation for Legged Robotics." UCLA RoMeLa. arXiv:2410.16591. https://arxiv.org/abs/2410.16591 ↩
13. Tesla AI Day technical presentations (2022, 2023) and Optimus hardware teardowns and supply-chain reporting describing 14 rotary harmonic-drive actuators and 14 planetary-roller-screw linear actuators, with harmonic reducers supplied in part by Suzhou Green Harmonic (STAR Market 688017). https://eu.36kr.com/en/p/3780414717129481 ↩
14. Boston Dynamics (2024). "An Electric New Era for Atlas," company blog, and IEEE Spectrum, "Hello, Electric Atlas." https://bostondynamics.com/blog/electric-new-era-for-atlas/ and https://spectrum.ieee.org/atlas-humanoid-robot ↩
15. Figure AI. Figure 02 humanoid robot (harmonic-drive rotary actuators and planetary-roller-screw linear actuators). https://www.figure.ai/ ↩
16. Unitree Robotics. H1 and G1 humanoid robot specifications (H1 M107 actuator: peak knee torque 360 Nm, 189 Nm/kg). https://www.unitree.com/h1/ ↩
17. James Bruton / 3D Printing Industry and Hackaday. openDog V3 open-source quadruped with 3D-printed 25:1 cycloidal drives. https://3dprintingindustry.com/news/james-bruton-begins-work-on-v3-of-his-open-source-3d-printed-robotic-dog-196644/ ↩
18. Tec-science. "How does a cycloidal drive work?" educational reference. https://www.tec-science.com/mechanical-power-transmission/planetary-gear/how-does-a-cycloidal-gear-drive-work/ ↩