Cycloidal Drive

How a cycloidal drive works

Start with a ring of round steel pins arranged in a circle, like the studs around a clock face. Now drop a disc inside that ring, but cut the disc's edge into smooth bulging lobes — and give it one fewer lobe than there are pins. The disc is mounted on an eccentric: a section of the input shaft that is machined off-center by a small distance e, the eccentricity. As the input shaft spins, the eccentric shoves the disc sideways so its lobes press into the pins on one side while pulling away on the other. The disc cannot spin freely with the shaft — the pins won't let it — so instead it wobbles, rolling around the inside of the pin ring like a coin rolling around the inside of a cup.

Here is the trick that produces the huge reduction. Because the disc has one fewer lobe than there are pins, after the eccentric has carried the contact point all the way around once (one full input turn), the disc has not returned to its starting orientation — it has slipped backward by exactly one lobe. The disc therefore turns very slowly, and in the opposite direction to the input. That slow disc rotation is the output. The motion of the lobe profile against the pins traces an epicycloid curve, which is where the drive gets its name.

The disc does two things at once: a slow rotation about the center, plus a small orbit of radius e around that center. We only want the rotation. So the disc carries a ring of output holes, each larger than an output roller that passes through it. The hole-to-roller clearance is set to exactly 2e, so the disc can orbit freely while the rollers feel only its rotation — the same offset-shaft trick an Oldham coupling uses. The rollers carry the slow rotation to the output flange.

The governing math

The reduction ratio is set entirely by the count of pins and lobes — there is no small driven gear:

Let  N  = number of ring pins (fixed)
     L  = number of disc lobes = N − 1
     e  = eccentricity of the cam (mm)
     R  = pitch radius of the pin circle (mm)

Reduction ratio (pins fixed, disc = output):
     i = L / (N − L) = (N − 1) / 1 = N − 1 : 1

Output direction: opposite to input.
Disc orbit radius = e   (a small circle, e.g. 1–3 mm)

Example: N = 40 pins, L = 39 lobes  →  i = 39 : 1

Two design quantities matter as much as the ratio. First, the eccentricity sets how deep the lobes bite the pins; the lobe profile is the epicycloid (or, in practice, an equidistant offset of it for the roller pin radius) generated by rolling a circle of radius e·N appropriately. Second, the load is shared. Under torque, roughly half the lobes — on the loaded side of the disc — press against pins at the same time:

Output torque from tangential pin forces:
     T_out ≈ Σ ( F_i · r_i )   over the loaded contacts (≈ N/2 of them)

Single-stage efficiency:
     η ≈ 0.85 to 0.93   (falls at very high ratio due to pin sliding)

Torque amplification (ideal):
     T_out = i · T_in · η

Because many contacts share the load, the contact force per pin is a fraction of what a single meshing gear tooth would carry at the same torque — this is the root of the cycloidal drive's shock tolerance. A momentary overload is spread across a dozen-plus rolling contacts instead of being dumped onto one tooth root.

Worked example: a robot-joint RV reducer

Take a mid-size industrial robot's second-axis (shoulder) reducer, a two-stage RV-style cycloidal unit, and run the numbers. RV reducers put a spur-gear pre-stage in front of the cycloidal stage to share input load and add ratio:

Spur pre-stage ratio:   i1 = 3 : 1   (input pinion → eccentric shafts)
Cycloidal stage:        N = 40 pins, L = 39 lobes → i2 = 39 : 1
Overall ratio:          i = i1 · i2 = 3 × 39 = 117 : 1

Input (servo):          3000 rpm, 3.2 N·m rated torque
Output speed:           3000 / 117 = 25.6 rpm
Output torque (η≈0.85): 3.2 × 117 × 0.85 ≈ 318 N·m rated
Allowable peak / shock: often 2.5× rated ≈ 800 N·m momentary

Now the precision side. With backlash held under 1 arc-minute, the angular play at the output is tiny:

Backlash = 1 arc-min = 1/60 degree = 0.000291 rad
At a 1.0 m robot reach, tool-tip play from backlash:
     Δx = 1.0 m × 0.000291 rad ≈ 0.29 mm

Torsional stiffness (typical RV-40 class): ~150–300 N·m / arc-min,
so a 100 N·m load deflects the output only a fraction of an arc-minute.

That combination — over 100:1 in a flat package, a few tenths of a millimeter of play at the tool, hundreds of N·m of capacity, and the ability to eat a hard stop without stripping a tooth — is exactly why nearly every large six-axis industrial robot uses cycloidal (RV) reducers in its base and shoulder joints, where loads and shock are highest.

Real-world examples and specs

Application	Type	Typical ratio	Notes
Industrial robot base & shoulder joints	RV (two-stage cycloidal)	40:1 to 200:1	Nabtesco RV series dominates; high shock tolerance, < 1 arc-min
Robot wrist / lighter axes	Single-stage cycloidal or harmonic	30:1 to 120:1	Cycloidal where stiffness and shock matter more than weight
Positioner & index tables, rotary stages	Single-stage cycloidal	30:1 to 87:1	Low backlash holds index position under load
Heavy gearmotors, conveyors, mixers	Cyclo-style (Sumitomo Cyclo)	11:1 to 119:1 (single), up to 7569:1 (double)	Rugged, overload-tolerant, long service intervals
Wind-turbine yaw & pitch drives	Cycloidal + planetary combos	1000:1+ combined	Shock from gusts handled by load sharing
Track-laying / printing / packaging drives	Cyclo gearmotor	up to ~119:1	Trochoidal/cycloidal element, sealed in oil or grease

Representative single-stage geometry for an RV-40 class unit: pin-circle pitch radius around 70–90 mm, eccentricity roughly 1.5–2.5 mm, 40 pins, 39 lobes on each of two discs set 180° apart, all in case-hardened and ground alloy steel (commonly carburized SAE 8620 or through-hardened bearing steel for the pins). Rated output torque is in the few-hundred N·m range with peak ratings 2–3× higher.

Cycloidal vs other reducers

	Cycloidal (RV)	Harmonic (strain wave)	Planetary (spur)	Worm
Single-stage ratio	30:1 to 200:1	30:1 to 320:1	3:1 to 10:1	5:1 to 100:1
Backlash (new)	< 1 arc-min	~0 (zero backlash)	3 to 15 arc-min	moderate, can adjust
Efficiency	~85 to 93%	~70 to 85%	~97 to 99% per stage	~50 to 90%
Shock / overload tolerance	Excellent (rigid disc, many contacts)	Moderate (thin flexspline)	Good	Good
Torsional stiffness	High	Moderate (flexes)	High	Moderate
Mass for given torque	Heavy (solid steel)	Light	Moderate	Moderate
Load sharing	~half the lobes at once	~30% of teeth at once	3 to 5 planets	1 to 2 thread contacts
Typical home	Robot base/shoulder, positioners	Robot wrist, aerospace, semicon	Gearmotors, e-axles	Lifts, conveyors, jacks

Design tradeoffs and when to use one

• Choose cycloidal when shock and stiffness dominate. The rigid disc and many-contact load path shrug off the hard stops, collisions, and inertial slams that a robot base joint or a heavy index table sees. A harmonic drive's thin flexspline is the weaker link under those loads.
• Choose it for compact, high single-stage ratio with low backlash. A 100:1 planetary needs three or four spur stages and accumulates backlash at each; a cycloidal unit does it in one (or, as RV, two) compact stages and holds under an arc-minute.
• Accept the weight and efficiency cost. Solid steel discs and a full set of pins make a cycloidal reducer heavier than a harmonic drive of similar capacity, and pin sliding drops efficiency below a clean planetary's. At extreme ratios efficiency falls further.
• Balance is not optional at speed. A single eccentric disc is unbalanced; serious designs use two discs 180° apart (or counterweights) to cancel the rotating inertial force, or vibration grows with input speed.
• Pick something else when you need near-perfect zero backlash and minimum mass (harmonic drive), when efficiency is paramount and ratio is modest (planetary), or when a self-locking right-angle reduction is wanted (self-locking worm).

Common failure modes and pitfalls

• Lobe and pin pitting (contact fatigue). The dominant wear-out mode. Load is carried by rolling-and-sliding line contact between the lobe flanks and the pins, so Hertzian contact stress cycles every revolution and eventually spalls pits from the surfaces. Hardened and ground steel plus clean lubricant pushes this out to tens of thousands of hours; contamination or under-lubrication brings it forward fast.
• Transmission error (periodic angular ripple). Manufacturing deviations in the lobe profile, pin spacing, and eccentricity produce a small angular error that repeats once per output turn — a few arc-seconds to about an arc-minute in good units. It is not backlash (which is play), but it limits absolute positioning and shows up as torque ripple. Tighter grinding and profile correction reduce it.
• Eccentricity / bearing tolerance drift. The cam runs on a needle bearing inside the disc. As that bearing wears, effective eccentricity and clearances change, contact patterns shift, and backlash and ripple grow. The eccentricity must be held to tight tolerance at build, since the output-hole-to-roller clearance is keyed to exactly 2e.
• Imbalance vibration. A single-disc design, or a twin-disc design with mismatched discs, leaves an uncanceled rotating force that shakes the housing at input speed and accelerates bearing wear. The fix is matched twin discs 180° apart.
• Lubricant starvation and heat. Efficiency losses (the 7–15% that doesn't reach the output) turn to heat at the sliding contacts. Sealed grease or oil with the right film strength is essential; running dry or overloaded scuffs the lobe flanks like any other gear contact.
• Misapplication for ultra-precision positioning. Where sub-arc-second repeatability with zero backlash is mandatory (some semiconductor and metrology stages), a harmonic drive's true zero backlash can beat a cycloidal unit's small but nonzero transmission error — choosing cycloidal there trades the wrong way.