How does a cycloidal drive work?

An eccentric on the input shaft makes a lobed disc orbit inside a ring of pins. Because the disc has one lobe fewer than there are pins, it rotates backward by one lobe per input turn, giving (N − 1):1; output pins in oversized holes take that slow rotation off the disc.

How do you calculate cycloidal drive ratio?

Divide the lobe count by the lobe difference, which is 1 for a standard disc: ratio = (N − 1):1. Twelve ring pins and an 11-lobe disc give 11:1 with the output turning opposite the input.

Why do cycloidal drives use two discs?

A single disc orbits off-center and shakes the drive. Two discs 180° apart cancel most of that imbalance and share the load between twice as many pin contacts.

How do I choose the eccentricity?

Keep E·N/R below 1, and in practice well below it; the default 1.5 mm on 12 pins and a 40 mm radius gives 0.45. Larger E makes deeper lobes and bigger output holes, while E close to R/N makes pointed lobes.

Why are the output holes larger than the output pins?

The disc orbits by E, so each hole must be the output pin diameter plus 2E. With 6 mm pins and E = 1.5 mm the holes are 9 mm.

What can I use for the ring pins?

Dowel pins, shoulder bolts, or pins with rollers or bushings over them. Rolling pins cut friction and wear; the generated pin ring plate has N holes sized for the pin diameter you enter.

Is a laser-cut cycloidal drive suitable for a robot joint?

It suits prototypes, educational builds, and low to moderate speed and load joints. Backlash depends on clearance, pin fit, and bearings, so critical or high-load drives need engineering review.

Power transmission calculator

Cycloidal Drive Generator

Design a cycloidal reducer from ring pin count, pin circle, pin size, and eccentricity, and export the disc, pin ring plate, and output plate as STEP, DXF, or SVG.

Design a laser-cut cycloidal drive

Set the ring pins and eccentricity, size the output pins, then choose the plates and material.

Units

Presets

Ring pins and disc

Ring pins11:1 reduction

Pin circle diameter

Pin diameter

EccentricityCrank offset

Profile clearanceRunning gap

Discs

Output pins

Disc center boreEccentric bearing OD

Output pins

Output pin circle diameter

Output pin diameter

Output hole clearanceAdded to each disc hole

Pin hole allowanceAdded to plate pin holes

Plates, holes, and material

Plate diameterAuto

QuantityOne each side of the disc

Bore

Bore diameter

Mounting holes

Holes

Hole circle diameter

Hole diameter

Rotation

Fabworks plate material

Plate thicknessMin. feature 0.050 in · 1.27 mm

Drive dimensions

Reduction ratio Output turns opposite the input: 11 : 1
Disc lobes: 11
Disc lobe diameter: 74.9 mm
Disc valley diameter: 68.9 mm
Output hole diameter Output pin + 2 × eccentricity + clearance: 9.1 mm
Curtate ratio Eccentricity × pins ÷ pin circle radius: 0.45
Pin spacing Center to center: 20.706 mm

Drive preview

The disc profile is the envelope of the ring pins as the disc rolls around them on the eccentric. Run it to watch the output pins turn once for every 11 turns of the input. The dashed circle is the pin circle.

True generated disc profile

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Cycloidal disc
73.8 mm × 74.3 mm
Pin ring plate
⌀ 116.0 mm · qty 2
Output plate
⌀ 64.0 mm

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Quick answer

How this cycloidal drive calculator works

A cycloidal drive with N ring pins and a disc of N − 1 lobes reduces speed by (N − 1):1 with the output reversed, so 12 pins give 11:1. Enter pin count, pin circle diameter, pin diameter, eccentricity, and clearance to generate the cycloidal disc, the pin ring plate, and the output plate, with checks for undercut lobes, overlapping pins, and thin webs. Files are generated in the browser and download as STEP, DXF, or SVG, or go straight into a Fabworks quote.

How to use the calculator

1Enter the ring pin count N; the disc gets N − 1 lobes and the reduction is (N − 1):1.
2Enter the pin circle diameter, pin diameter, and eccentricity E, keeping E·N/R below 1.
3Set profile clearance so the disc runs freely on real pins.
4Define the output pins (count, diameter, circle); the disc holes are sized to output pin diameter + 2E.
5Choose a Fabworks material and thickness and clear any web or minimum-feature warnings.
6Download the disc, pin ring plate, and output plate, or send them to a Fabworks quote. Most builds use two discs 180° apart.

Key formulas

Cycloidal drive formulas

Reduction ratio: i = (N − 1) : 1, output reversed; N is the number of ring pins; the disc has N − 1 lobes.
Disc profile, x: x = R·cos t − Rr·cos(t + ψ) − E·cos(N·t); R is the pin circle radius, Rr the pin radius, E the eccentricity, t from 0 to 2π.
Disc profile, y: y = −R·sin t + Rr·sin(t + ψ) + E·sin(N·t); Same parameters as x.
Contact angle term: ψ = atan2(sin((1 − N)·t), R ÷ (E·N) − cos((1 − N)·t)); Offsets the pin-center path by the pin radius along its normal.
Disc radius range: R − E − Rr ≤ r ≤ R + E − Rr; 34.5 to 37.5 mm for R = 40, E = 1.5, Rr = 4.
Shape condition: E·N ÷ R < 1; Above 1 the lobes loop and the profile self-intersects.
Output hole diameter: D_hole = d_output pin + 2E; The holes orbit the output pins by the eccentricity.
Pin spacing: s = 2R·sin(180°/N) > pin diameter; Center-to-center distance between neighboring ring pins.

Step by step

How to draw a cycloidal disc profile

1Choose N, R, Rr, and E, and confirm E·N/R < 1 and 2R·sin(180°/N) > 2Rr.
2Sample t from 0 to 2π in small steps.
3At each t compute ψ = atan2(sin((1 − N)t), R/(E·N) − cos((1 − N)t)).
4Compute x = R cos t − Rr cos(t + ψ) − E cos(Nt) and y = −R sin t + Rr sin(t + ψ) + E sin(Nt).
5Join the points into a closed curve with N − 1 lobes, then offset it inward by the running clearance.
6Add the eccentric-bearing bore at the disc center.
7Add output holes of diameter d_pin + 2E on the output pin circle.
8Make a second disc rotated 180° about the input shaft for balance.

Worked example

12-pin, 11:1 cycloidal drive

Inputs: N = 12 pins on an 80 mm pin circle (R = 40 mm), 8 mm pins (Rr = 4 mm), E = 1.5 mm, six 6 mm output pins on a 40 mm circle.
Result: Reduction 11:1 with the output reversed, disc profile from 69 mm to 75 mm diameter, output holes 9 mm, E·N/R = 0.45.

The disc has 11 lobes and advances one lobe per input turn. Its radius runs from R − E − Rr = 34.5 mm to R + E − Rr = 37.5 mm, and each output hole is 6 + 2 × 1.5 = 9 mm.

Common questions

What to know before using the result

How does a cycloidal drive work?: An eccentric on the input shaft makes a lobed disc orbit inside a ring of pins. Because the disc has one lobe fewer than there are pins, it rotates backward by one lobe per input turn, giving (N − 1):1; output pins in oversized holes take that slow rotation off the disc.
How do you calculate cycloidal drive ratio?: Divide the lobe count by the lobe difference, which is 1 for a standard disc: ratio = (N − 1):1. Twelve ring pins and an 11-lobe disc give 11:1 with the output turning opposite the input.
Why do cycloidal drives use two discs?: A single disc orbits off-center and shakes the drive. Two discs 180° apart cancel most of that imbalance and share the load between twice as many pin contacts.
How do I choose the eccentricity?: Keep E·N/R below 1, and in practice well below it; the default 1.5 mm on 12 pins and a 40 mm radius gives 0.45. Larger E makes deeper lobes and bigger output holes, while E close to R/N makes pointed lobes.
Why are the output holes larger than the output pins?: The disc orbits by E, so each hole must be the output pin diameter plus 2E. With 6 mm pins and E = 1.5 mm the holes are 9 mm.
What can I use for the ring pins?: Dowel pins, shoulder bolts, or pins with rollers or bushings over them. Rolling pins cut friction and wear; the generated pin ring plate has N holes sized for the pin diameter you enter.
Is a laser-cut cycloidal drive suitable for a robot joint?: It suits prototypes, educational builds, and low to moderate speed and load joints. Backlash depends on clearance, pin fit, and bearings, so critical or high-load drives need engineering review.

Reference

Cycloidal reduction by ring pin count

One-lobe-difference disc on an 80 mm pin circle (R = 40 mm). E·N/R must stay below 1, so at E = 1.5 mm a 30-pin ring needs a smaller eccentricity.

Ring pins N	Disc lobes	Reduction	Pin spacing (mm)	E·N/R at E = 1.5 mm	Max E (mm)
8	7	7:1	30.61	0.300	5.00
10	9	9:1	24.72	0.375	4.00
12	11	11:1	20.71	0.450	3.33
16	15	15:1	15.61	0.600	2.50
20	19	19:1	12.51	0.750	2.00
24	23	23:1	10.44	0.900	1.67
30	29	29:1	8.36	1.125	1.33

Formula

i = (N − 1) : 1 · r = R ± E − R_r

A disc with N − 1 lobes inside N ring pins reduces speed by (N − 1):1 and reverses the output. The disc profile is the pin-center path offset by the pin radius, x = R cos t − R_r cos(t + ψ) − E cos(Nt) and y = −R sin t + R_r sin(t + ψ) + E sin(Nt).

Engineering references

Assumptions and limits

The disc has one fewer lobe than there are ring pins.
E·N/R must be below 1 and ring pins must not overlap.
Output holes are sized to output pin diameter plus 2E.
Profile clearance is a uniform inward offset of the theoretical profile.
Two discs 180° apart are recommended for balance; bearings and pins are not included.

Educational estimate

Use this result for learning and early design exploration. Verify safety-critical or production decisions with the governing standard, material data, real tooling, and a qualified engineer.

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