A pin gear is a toothed gear that meshes with round pins instead of another set of teeth. The pins sit in a pin wheel (on a circle) or a pin rack (in a line), and can be dowels, shoulder bolts, or bearings.

What is a lantern gear?

A lantern gear is a pin wheel: round pins held between one or two plates, like the bars of a lantern. It was common in mills and clocks and is easy to build today from a laser-cut plate and off-the-shelf pins.

How do you calculate pin gear pitch diameter?

Use d = z·p/π, where p is the pin pitch measured along the pitch circle. A 12-tooth gear on a 12 mm pitch is 45.84 mm, and a 30-pin wheel on the same pitch has a 114.59 mm pin circle.

What pin diameter should I use?

About half the pin pitch is a good starting point, which leaves room for a solid gear tooth between pins. The default uses 6 mm pins on a 12 mm pitch.

Why use pins instead of a second gear?

Pins are cheap, replaceable, and easy to source, and a pin wheel or pin rack can be very large or long without a large machined gear. Bearings as pins roll instead of slide, which cuts friction.

Can the pins be on a straight rack?

Yes. Choose pin rack to get a bar with holes in a line and a gear that drives it. Travel per gear revolution is z·p, so 12 teeth at 12 mm pitch move 144 mm per turn.

Are laser-cut pin gears suitable for machinery?

Yes, for low to moderate speed and load. Laser-cut plate parts suit prototypes, robots, fixtures, and light machinery; critical, high-speed, or high-load drives need engineering review of material, thickness, hub attachment, alignment, lubrication, and wear.

Power transmission calculator

Pin Gear & Lantern Gear Generator

Generate a gear that meshes with round pins on a laser-cut pin wheel or pin rack, with pitch diameters, center distance, and ratio, then export STEP, DXF, or SVG or order it.

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.

Units

Presets

Pins on

Gear teeth

Wheel pins

Pin pitchCenter to center

Pin diameter

ClearanceRunning gap at the teeth

Pin wheel plate

Plate diameterAuto

Pin hole allowanceAdded to pin diameter

Hub, holes, and plate

Bore

Bore diameter

Mounting holes

Lightening holes

Fabworks plate material

Plate thicknessMin. feature 0.050 in · 1.27 mm

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.

True generated tooth form

Tooth tips trimmed to keep a flat land, as on a lantern gear.

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.

Pin gear
⌀ 54.7 mm
Pin wheel
⌀ 132.6 mm

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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 pin gear calculator works

A pin gear’s pitch diameter is d = z·p/π and its pin wheel’s pin circle is D = Np·p/π, where p is the pin pitch; 12 teeth at a 12 mm pitch give d = 45.84 mm. This generator makes the toothed gear plus a laser-cut pin wheel or pin rack that holds dowels, shoulder bolts, or bearings as the mating teeth. 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

1Choose the pin carrier: a pin wheel (pins on a circle, a lantern gear) or a pin rack (pins in a line).
2Enter the pin count, pin pitch, and pin diameter for the pins you will use.
3Enter the gear tooth count and running clearance.
4Review pitch diameters, center distance, and ratio; tooth tips are trimmed to keep a minimum land.
5Choose a Fabworks material and thickness for the gear and the carrier plate.
6Download the gear and the pin wheel plate or pin rack bar, or send them to a Fabworks quote.

Key formulas

Pin gear formulas

Gear pitch diameter: d = z·p ÷ π; z is the gear tooth count and p the pin pitch along the pitch circle.
Pin circle diameter: D = Np·p ÷ π; Np is the number of pins on the pin wheel.
Center distance: a = (D + d) ÷ 2; For a pin rack, the gear center sits d/2 from the line of pin centers.
Ratio: i = Np ÷ z; Speed ratio between the gear and the pin wheel.
Pin rack travel per gear revolution: s = z·p; 12 teeth at 12 mm pin pitch move the rack 144 mm per turn.
Pin-center path on a pin wheel (epicycloid): x = (rg + rw)·cos θ − rw·cos(((rg + rw)/rw)·θ), y = (rg + rw)·sin θ − rw·sin(((rg + rw)/rw)·θ); rg = d/2 and rw = D/2. The tooth flank is this path offset inward by the pin radius plus clearance.
Pin-center path on a pin rack (involute): x = rg·(cos θ + θ·sin θ), y = rg·(sin θ − θ·cos θ); The line of pins rolls on the gear pitch circle; offset by the pin radius for the flank.

Step by step

How to draw a pin gear (lantern gear) profile

1Pick the pin pitch p, pin diameter, pin count Np, and gear teeth z; pin diameter is usually about half the pitch.
2Calculate d = z·p/π and D = Np·p/π and place the centers (D + d)/2 apart.
3Trace the path of one pin center relative to the gear: an epicycloid for a pin wheel, an involute of the pitch circle for a pin rack.
4Offset that path inward by the pin radius plus running clearance to get one tooth flank.
5Mirror the flank about the tooth centerline, half a pitch from the neighboring flank.
6Trim the tooth tips to leave a land at least as wide as the minimum feature size.
7Pattern the tooth z times and add the bore.
8Draw the pin wheel or pin rack with Np pin holes on the pitch circle or line, spaced p apart.

Worked example

30-pin wheel driving a 12-tooth gear

Inputs: Pin wheel with 30 pins, 6 mm pin diameter, 12 mm pin pitch, mating gear with 12 teeth.
Result: Pin circle D = 114.59 mm, gear pitch diameter d = 45.84 mm, center distance 80.21 mm, ratio 2.5:1.

D = 30 × 12 ÷ π and d = 12 × 12 ÷ π. The center distance is (D + d)/2 and the ratio is 30 ÷ 12.

Common questions

What to know before using the result

What is a pin gear?: A pin gear is a toothed gear that meshes with round pins instead of another set of teeth. The pins sit in a pin wheel (on a circle) or a pin rack (in a line), and can be dowels, shoulder bolts, or bearings.
What is a lantern gear?: A lantern gear is a pin wheel: round pins held between one or two plates, like the bars of a lantern. It was common in mills and clocks and is easy to build today from a laser-cut plate and off-the-shelf pins.
How do you calculate pin gear pitch diameter?: Use d = z·p/π, where p is the pin pitch measured along the pitch circle. A 12-tooth gear on a 12 mm pitch is 45.84 mm, and a 30-pin wheel on the same pitch has a 114.59 mm pin circle.
What pin diameter should I use?: About half the pin pitch is a good starting point, which leaves room for a solid gear tooth between pins. The default uses 6 mm pins on a 12 mm pitch.
Why use pins instead of a second gear?: Pins are cheap, replaceable, and easy to source, and a pin wheel or pin rack can be very large or long without a large machined gear. Bearings as pins roll instead of slide, which cuts friction.
Can the pins be on a straight rack?: Yes. Choose pin rack to get a bar with holes in a line and a gear that drives it. Travel per gear revolution is z·p, so 12 teeth at 12 mm pitch move 144 mm per turn.
Are laser-cut pin gears suitable for machinery?: Yes, for low to moderate speed and load. Laser-cut plate parts suit prototypes, robots, fixtures, and light machinery; critical, high-speed, or high-load drives need engineering review of material, thickness, hub attachment, alignment, lubrication, and wear.

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.

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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