A Cycloidal Drive is a high-ratio speed reducer that uses an eccentric cam to wobble a lobed disc against a ring of stationary pins, producing one slow output rotation for many input revolutions. Sumitomo's Cyclo gearboxes — used on conveyors at Amazon fulfilment centres and on the joints of FANUC industrial robots — are the most familiar example. The geometry shifts load across roughly two-thirds of the pins simultaneously, which is why these reducers absorb shock loads up to 500% of rated torque without tooth breakage and deliver ratios from 10:1 to 200:1 in a single stage.
Cycloidal Drive Interactive Calculator
Vary the ring pin count and cycloidal disc lobes to see the reduction ratio, reverse output motion, and load-sharing estimate.
Equation Used
The cycloidal disc has L lobes rolling inside P fixed ring pins. The reduction ratio is set by the lobe difference: R = L / (P - L). With the common one-lobe difference, a 5-lobe disc in 6 pins gives a 5:1 reducer, and the output turns in the opposite direction.
- Ring pin count is greater than disc lobe count.
- The output carrier removes orbital wobble and keeps only the slow retrograde rotation.
- Ideal kinematic ratio is shown; bearing losses and compliance are not included.
- Load sharing is estimated as 65% of ring pins in contact.
How the Cycloidal Drive Works
The drive starts with an input shaft carrying an eccentric cam — typically offset by 1 to 3 mm from the shaft centreline. That eccentric rides inside a needle bearing pressed into the bore of a cycloidal disc, which is a lobed plate cut with one fewer lobe than the surrounding ring of fixed pins. As the input shaft spins, the cam pushes the disc in a wobbling orbit, and the disc's lobes roll against the ring pins. Because there's a one-lobe difference, the disc retrogrades by exactly one pin-spacing per input revolution. That retrograde motion gets picked off through a second set of holes in the disc that ride on output rollers, and that's your slow output.
Why this geometry? Two reasons. First, contact is rolling, not sliding — efficiency runs 85-93% in a single stage, well above a worm gear at the same ratio. Second, at any moment 60-70% of the lobes are sharing load, so peak Hertzian stress on any one contact is far lower than a tooth-on-tooth gear mesh. That's the shock load tolerance Sumitomo Cyclo gearboxes are famous for.
Tolerances are unforgiving. The eccentricity must match the lobe profile to within ±0.005 mm — push that to 0.02 mm and you'll feel a low-frequency vibration through the housing as the disc starts to skip preload on alternating pins. Ring-pin diameter must be held to ±0.002 mm; oversized pins bind, undersized pins introduce backlash and you lose the zero-backlash spec the customer paid for. Common failures: needle bearing collapse on the eccentric (almost always a lubrication issue, not a load issue), pin galling from contaminated grease, and disc cracking from sustained reverse shock loads above 500% rated.
Key Components
- Input Shaft with Eccentric Cam: The cam offsets the disc bore by 1-3 mm from the input centreline, converting input rotation into the orbital wobble that drives the disc against the ring pins. Eccentricity tolerance is ±0.005 mm — looser than that and you'll see vibration at input frequency.
- Cycloidal Disc (Lobed Disc): A hardened steel plate machined with an epitrochoidal lobe profile, always cut with one fewer lobe than the ring pins (a 19-lobe disc against 20 pins gives a 19:1 ratio). Disc face hardness runs 58-62 HRC to resist Hertzian contact stress at the pin interface.
- Ring Pins (Outer Race): Hardened ground pins, typically 6-12 mm diameter, held in the housing on a precision bolt circle. Pin diameter tolerance is ±0.002 mm — this is the single most critical dimension for backlash performance.
- Output Rollers and Carrier: A second set of pins or rollers passes through oversized holes in the cycloidal disc and transfers only the disc's slow retrograde rotation to the output shaft, filtering out the orbital wobble. The hole-to-roller clearance is typically 2× the eccentricity.
- Eccentric Bearing: A heavy-duty needle bearing between the cam and the disc bore. This is the most failure-prone part of the assembly — it sees full input RPM combined with the orbital reaction force, which is why grease specification (NLGI 2 lithium-complex with EP additives) matters more here than anywhere else in the drive.
Real-World Applications of the Cycloidal Drive
Cycloidal Drives win wherever you need huge ratio reduction in a compact package and the load profile includes shock or reversing torque. They show up in industrial robotics, conveyor drives, machine-tool indexers, and lifting equipment. They're the standard choice when a planetary gearbox would survive the steady-state load but get its teeth chipped by a startup or jam event.
- Industrial Robotics: FANUC R-2000iC robot wrist and elbow joints use cycloidal reducers (Nabtesco RV-series) for the 100:1+ ratio and zero-backlash positioning needed for spot welding.
- Material Handling: Sumitomo Cyclo BBB4 gearboxes drive belt conveyors at Amazon fulfilment centres, surviving the daily shock loads from sudden parcel surges and emergency stops.
- Mixing and Process: Lightnin and SPX vertical mixer drives in pharmaceutical reactors at Pfizer plants — cycloidal reducers handle the unpredictable batch-to-batch viscosity changes without tooth damage.
- Wind Turbine Yaw and Pitch: Bonfiglioli 700T cycloidal reducers in Vestas V90 turbines drive the yaw rings, where wind gust reversals would destroy a conventional helical gearbox.
- Machine Tool Rotary Tables: Nikken CNC rotary indexers use cycloidal reducers between the servomotor and the tilt axis to hold ±10 arc-second positioning accuracy under interrupted milling cuts.
- Theatre and Stage Automation: TAIT Towers automated stage lifts on Cirque du Soleil productions run cycloidal drives for their 500% shock rating during emergency stops with performers on platform.
The Formula Behind the Cycloidal Drive
The single number that defines a cycloidal drive is its reduction ratio, set by the lobe count on the disc and the pin count on the housing. At the low end of the practical range — around 10:1 — you barely beat what a single-stage planetary can do, and the cycloidal's cost premium is hard to justify. The sweet spot sits between 30:1 and 80:1 in one stage, where no other compact reducer competes. Push past 120:1 and the lobe profile gets so shallow that manufacturing tolerances start eating your zero-backlash performance.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| i | Reduction ratio (input revs per output rev) | dimensionless | dimensionless |
| Np | Number of ring pins in the housing | count | count |
| NL | Number of lobes on the cycloidal disc (always Np − 1 in a standard fixed-ring layout) | count | count |
| nout | Output shaft speed | RPM | RPM |
| nin | Input shaft speed | RPM | RPM |
Worked Example: Cycloidal Drive in an automated brick-laying robot arm
Spec the wrist-axis reducer on an automated brick-laying robot arm. The servomotor delivers 3000 RPM at 2.5 Nm continuous, and you need the wrist to rotate at roughly 50 RPM for placement, with peak holding torque around 150 Nm when the gripper holds a 4 kg paver at full extension. You're choosing a cycloidal reducer with 60 ring pins and a 59-lobe disc.
Given
- Np = 60 pins
- NL = 59 lobes
- nin = 3000 RPM
- Tin = 2.5 Nm
- η = 0.90 dimensionless
Solution
Step 1 — calculate the reduction ratio from pin and lobe counts:
Step 2 — at nominal 3000 RPM input, calculate the output speed:
Step 3 — at the low end of the typical input range, say 1500 RPM during slow approach moves:
That gives the brick a smooth 5-second rotation onto the mortar bed — slow enough that the operator can verify alignment on the HMI without pausing the cycle. At the high end, 4500 RPM input during return-to-home moves:
Step 4 — calculate output torque at nominal input, accounting for 90% efficiency:
That's a touch under your 150 Nm peak holding requirement, which means you'll lean on the cycloidal's 500% shock rating during the brief peak — the drive is rated for it, but you should size the next frame up if peak holding is sustained for more than a few seconds per cycle.
Result
The 60:1 cycloidal reducer gives a nominal output of 50 RPM at 135 Nm — exactly the placement speed the robot programmer asked for, with continuous torque just below your peak holding spec. At the slow-approach extreme of 25 RPM the brick moves at hand-placement pace and gives the operator visual verification time; at the 75 RPM return-home end the wrist snaps back fast enough to keep cycle time under 4 seconds, which is where the sweet spot of a brick-laying duty cycle sits. If your measured output torque comes in 15-20% below the predicted 135 Nm, check three things in order: (1) eccentric bearing preload — a collapsed needle bearing on the cam adds drag that masquerades as efficiency loss, (2) ring pin lubrication — dry or contaminated grease drops efficiency from 90% to under 75% within hours, and (3) output-roller hole clearance, where excess clearance from a worn disc lets the drive lose a measurable percentage of its torque to lost motion before the load actually moves.
Choosing the Cycloidal Drive: Pros and Cons
Cycloidal drives compete most often against harmonic drives and planetary gearboxes for the same job. The right pick depends on whether you're optimizing for torque density, positioning accuracy, shock survival, or cost.
| Property | Cycloidal Drive | Harmonic Drive | Planetary Gearbox |
|---|---|---|---|
| Single-stage ratio range | 10:1 to 200:1 | 30:1 to 320:1 | 3:1 to 10:1 |
| Backlash (arc-min) | ≤1 arc-min | ≤0.5 arc-min | 3-15 arc-min |
| Efficiency at rated load | 85-93% | 65-85% | 94-98% |
| Shock load capacity | 500% of rated | 300% of rated | 200% of rated |
| Maximum input RPM | 3000-6000 RPM | 3500-7000 RPM | 5000-10000 RPM |
| Relative cost (per Nm output) | Medium-high | High | Low |
| Service life (L10, hours) | 20,000-30,000 | 10,000-15,000 | 20,000-40,000 |
| Best application fit | Robotics, conveyors, indexing under shock | Precision robotics, semiconductor | High-speed continuous duty, low ratio |
Frequently Asked Questions About Cycloidal Drive
True zero-backlash only holds when the ring pins, disc lobes and eccentric are all at their nominal manufactured dimensions and the eccentric bearing has zero radial play. As the eccentric needle bearing wears — typically after 8,000-12,000 hours in a duty-cycle application — the cam can shift radially by 0.01-0.03 mm, and that shows up at the output as 2-4 arc-minutes of lost motion.
The diagnostic check: lock the input shaft, apply alternating ±10% rated torque at the output, and measure angular deflection with a dial indicator on the output flange. If you see more than 1 arc-min of hysteresis, replace the eccentric bearing before chasing anything else.
Pick cycloidal when the joint sees impact loads, emergency stops with inertia, or a payload that can swing — the 500% shock rating is the deciding factor. Pick harmonic when the application is precision-dominated and shock is rare, like semiconductor wafer handling, because harmonic drives give you slightly tighter backlash and lower weight per Nm.
Rule of thumb: if the joint will ever drop a payload or hit a hard stop, go cycloidal. Harmonic drive flex-splines crack from repeated shock; cycloidal discs don't.
Catalogue temperature rise assumes the correct grease, correct fill volume, and rated input speed. The most common cause of excess heat is overfilling — operators often pack the housing, but cycloidal drives are specified at 30-50% fill by volume. Overfilled grease churns inside the cam orbit and dumps the work in as heat.
The second cause is wrong grease grade: if someone substituted NLGI 0 or 1 for the specified NLGI 2 EP, the lubricant film sheared at the pin contacts and viscous losses jumped. Drain, refill to spec, and re-measure after a 2-hour run-in.
Yes, cycloidal drives back-drive freely because the contact is rolling and the lead angle of the cycloidal profile is non-self-locking. Back-drive efficiency runs 75-85%, lower than forward drive because of seal drag and the eccentric bearing reversal.
One catch: at ratios above 100:1 the static back-drive torque required is high enough that the joint feels stiff to a human operator. For collaborative-robot applications where you want gravity compensation and easy hand-guiding, stay below a 60:1 ratio per stage.
Single-stage 30:1 cycloidal almost always wins for ratios in this range when shock or zero-backlash matters. You get one set of bearings, one input seal, one mounting interface, and combined backlash under 1 arc-min. Cascaded planetaries stack backlash — two 6:1 stages typically sum to 6-15 arc-min total.
Cascaded planetary wins on raw efficiency (96% × 96% = 92%, similar to one cycloidal stage) and on cost per Nm. If the application is continuous-duty pumping or a fan drive where positioning accuracy doesn't matter, cascade the planetaries and save the money.
That vibration signature points directly at the eccentric cam, not the output side. The disc orbits once per input revolution, so any imbalance, eccentricity error, or worn cam bearing produces a force at input frequency that radiates through the housing. Output-frequency vibration would point at disc lobe profile errors or pin spacing — different problem entirely.
Check the cam-to-disc fit first. Disassemble and measure the eccentric: if it has worn more than 0.01 mm out of round, replace it. The second-most common cause is a counterweight that shifted on its keyway — these are pressed-fit on cheaper drives and can creep over the first 500 hours of operation.
References & Further Reading
- Wikipedia contributors. Cycloidal drive. Wikipedia
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