Power transmission calculator

Cycloidal Disc Generator

Generate a cycloidal disc profile from pin count, pin circle, pin diameter, and eccentricity, and export the disc 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

11:1 reduction
mm
mm
Crank offset
mm
Running gap
mm

Output pins

Eccentric bearing OD
mm
mm
mm
Added to each disc hole
mm
Added to plate pin holes
mm

Plates, holes, and material

Auto
mm
One each side of the disc
mm
mm
mm
°
Min. 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

Download the manufacturing files

100% in-browser

STEP solids are built and checked in your browser. DXF and SVG drawings use lines and true arcs at full scale. Nothing is uploaded until you order.

  • 73.8 mm × 74.3 mm

  • ⌀ 116.0 mm · qty 2

  • ⌀ 64.0 mm

Laser cut it at Fabworks

We generate the STEP files, add them to a new quote, and open it in a new tab where you can review material, finish, and quantity.

Quick answer

How this cycloidal disc generator calculator works

A cycloidal disc profile is x = R cos t − Rr cos(t + ψ) − E cos(Nt), y = −R sin t + Rr sin(t + ψ) + E sin(Nt), with N ring pins of radius Rr on radius R and eccentricity E; it has N − 1 lobes. Enter those values to generate the disc with its bearing bore and output holes, plus the pin ring and output plates.

How to use the calculator

  1. 1Enter ring pin count N, pin circle diameter 2R, and pin diameter 2Rr.
  2. 2Enter eccentricity E, keeping E·N/R below 1.
  3. 3Set clearance and the output pin pattern; output holes are sized to pin diameter + 2E.
  4. 4Download the disc (and a second disc rotated 180°) as STEP, DXF, or SVG, or send it to a Fabworks quote.

Key formulas

Cycloidal disc generator formulas

Disc profile, x
x = R·cos t − Rr·cos(t + ψ) − E·cos(N·t)
Disc profile, y
y = −R·sin t + Rr·sin(t + ψ) + E·sin(N·t)
Contact angle term
ψ = atan2(sin((1 − N)·t), R ÷ (E·N) − cos((1 − N)·t))
Shape condition
E·N ÷ R < 1
Output hole diameter
D_hole = d_output pin + 2E

Step by step

How to draw a cycloidal disc in CAD

  1. 1Choose N, R, Rr, and E, and confirm E·N/R < 1.
  2. 2Evaluate ψ, x, and y for t from 0 to 2π in small steps (a few thousand points).
  3. 3Join the points with a closed curve; it should show N − 1 lobes.
  4. 4Offset the curve inward by the running clearance.
  5. 5Add the center bore for the eccentric bearing and output holes of d_pin + 2E.
  6. 6Copy the disc and rotate the copy 180° about the input shaft for the second disc.

Worked example

11-lobe disc for 12 pins

Inputs
N = 12, R = 40 mm, Rr = 4 mm, E = 1.5 mm.
Result
11 lobes, disc profile from 69 mm to 75 mm diameter, ratio 11:1.

The profile radius ranges from R − E − Rr = 34.5 mm to R + E − Rr = 37.5 mm. E·N/R = 0.45, well inside the limit of 1.

Common questions

What to know before using the result

How do you draw a cycloidal disc?
Plot the parametric equations for x and y with ψ over t from 0 to 2π, join the points into a closed curve, and offset for clearance. The generator does this and exports clean arcs within 0.005 mm of the curve.
How many lobes does a cycloidal disc have?
One fewer than the number of ring pins, N − 1. Twelve pins need an 11-lobe disc and give an 11:1 reduction.
What limits the eccentricity?
E·N/R must stay below 1 or the lobes self-intersect. For R = 40 mm and 12 pins, E must be under 3.33 mm; the default 1.5 mm gives 0.45.
How big is the cycloidal disc?
Its profile radius runs from R − E − Rr to R + E − Rr. For R = 40, E = 1.5, and Rr = 4 mm, that is 34.5 to 37.5 mm, or 69 to 75 mm in diameter.
Can I export the disc as DXF?
Yes. The disc, pin ring plate, and output plate export as STEP, DXF in millimeters, or SVG, and Order sends the STEP files to a Fabworks quote.

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 NDisc lobesReductionPin spacing (mm)E·N/R at E = 1.5 mmMax E (mm)
877:130.610.3005.00
1099:124.720.3754.00
121111:120.710.4503.33
161515:115.610.6002.50
201919:112.510.7502.00
242323:110.440.9001.67
302929:18.361.1251.33

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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