Power transmission calculator
Lantern Gear Generator
Generate a lantern gear pin wheel and its mating toothed gear from pin count, pin pitch, and pin diameter, ready for laser cutting.
Design a laser-cut pin gear
Set the pins and their pitch, choose a pin wheel or a pin rack, then add bores, holes, and a plate.
Pin wheel plate
Hub, holes, and plate
Gear dimensions
- Gear pitch diameter
- 45.837 mm
- Gear outside diameter Tips trimmed flat
- 56.201 mm
- Gear root diameter
- 39.637 mm
- Pin circle diameter
- 114.592 mm
- Center distance
- 80.214 mm
- Gear ratio Gear turns per wheel turn, in the opposite direction
- 2.5 : 1
Mesh preview
Each tooth space is the path a round pin sweeps as the wheel rolls past the gear, plus the running clearance. Dashed circles are pitch circles.
Download the manufacturing files
100% in-browserSTEP 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.
⌀ 54.7 mm
⌀ 132.6 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 lantern gear calculator works
A lantern gear is a pin wheel whose pins sit on a circle of diameter D = Np·p/π, meshing with a toothed gear of pitch diameter d = z·p/π; 30 pins at a 12 mm pitch give D = 114.59 mm. The generator makes the pin wheel plate with Np holes and the mating gear, whose teeth are offset epicycloids of the pin path.
How to use the calculator
- 1Choose pin wheel as the carrier.
- 2Enter the pin count, pin pitch, and pin diameter of your dowels, bolts, or bearings.
- 3Enter the gear tooth count and clearance, then review center distance and ratio.
- 4Download the gear and pin wheel plate or send them to a Fabworks quote.
Key formulas
Lantern gear formulas
- Pin circle diameter
- D = Np·p ÷ π
- Gear pitch diameter
- d = z·p ÷ π
- Center distance
- a = (D + d) ÷ 2
- Ratio
- i = Np ÷ z
Worked example
30-pin lantern wheel and 12-tooth gear
- Inputs
- 30 pins of 6 mm diameter at a 12 mm pitch; 12-tooth gear.
- Result
- Pin circle 114.59 mm, gear pitch diameter 45.84 mm, center distance 80.21 mm, ratio 2.5:1.
D = 30 × 12 ÷ π, d = 12 × 12 ÷ π, and a = (D + d)/2.
Common questions
What to know before using the result
- What is a lantern gear?
- A lantern gear is a wheel of round pins held between plates, used in place of a toothed gear. Historic mills and clocks used them, and they are easy to build from a laser-cut plate and standard pins.
- How do you size a lantern gear?
- Pick a pin pitch and count; the pin circle is D = Np·p/π. Thirty pins at 12 mm pitch sit on a 114.59 mm circle.
- What tooth shape meshes with the pins?
- The mating gear’s flanks are the path of each pin center relative to the gear, an epicycloid, offset inward by the pin radius. The generator also trims tips to keep a minimum land.
- What should I use as pins?
- Dowel pins, shoulder bolts, or small bearings. Bearings roll on the gear teeth and reduce friction; a pin diameter near half the pitch, such as 6 mm on 12 mm, is a good start.
- Can I make the pin wheel larger than the gear?
- Yes, and that is the usual arrangement for reduction. A 30-pin wheel driven by a 12-tooth gear gives 2.5:1.
Reference
Pin gear pitch diameter by pin pitch and tooth count (mm)
d = z·p ÷ π. The same formula gives the pin circle diameter of a pin wheel when z is the pin count. On a pin rack, travel per gear revolution is z·p.
| Pin pitch p | 10 teeth | 12 teeth | 16 teeth | 20 teeth | 24 teeth |
|---|---|---|---|---|---|
| 6 | 19.10 | 22.92 | 30.56 | 38.20 | 45.84 |
| 8 | 25.46 | 30.56 | 40.74 | 50.93 | 61.12 |
| 10 | 31.83 | 38.20 | 50.93 | 63.66 | 76.39 |
| 12 | 38.20 | 45.84 | 61.12 | 76.39 | 91.67 |
| 15 | 47.75 | 57.30 | 76.39 | 95.49 | 114.59 |
| 20 | 63.66 | 76.39 | 101.86 | 127.32 | 152.79 |
Formula
d = z·p ÷ π · D = N_p·p ÷ π · a = (D + d) ÷ 2
Gear pitch diameter d and pin circle diameter D come from tooth count z, pin count Nₚ, and pin pitch p, and their center distance is (D + d)/2. Tooth flanks are the epicycloid (pin wheel) or involute (pin rack) path of the pin centers, offset by the pin radius plus clearance.
Engineering references
Assumptions and limits
- Pins are round and of uniform diameter, such as dowels, shoulder bolts, or bearings.
- Pin pitch is measured along the pitch circle or pitch line.
- Tooth tips are trimmed to keep a minimum land.
- Running clearance is applied as a uniform offset of the tooth flanks.
- Laser-cut pin gears suit low to moderate speed and load; critical drives need engineering review.
Keep designing
Fabworks resources
Related calculators
Order Sheet Metal Parts
Upload a 2D DXF or 3D STEP file for an instant laser cutting quote. Quote in seconds, order in minutes, receive parts in days.
or drag and drop
STEP / DXF up to 24MB
Your files are safe, secure, and retain all intellectual rights.