Power transmission calculator
Pin Rack and Pinion Generator
Generate a pin rack bar and its mating roller pinion from pin pitch, pin diameter, and tooth count, with travel per revolution.
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 rack bar
Hub, holes, and plate
Gear dimensions
- Gear pitch diameter
- 45.837 mm
- Gear outside diameter Tips trimmed flat
- 56.684 mm
- Gear root diameter
- 39.637 mm
- Gear center to pin row
- 22.918 mm
- Travel per gear turn
- 144 mm
- Rack length
- 240 mm
Mesh preview
Each tooth space is the path a round pin sweeps as the rack rolls past the gear, plus the running clearance. Dashed circles are pitch circles.
Download the manufacturing files
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⌀ 55.1 mm
240.0 mm × 18.0 mm
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Quick answer
How this pin rack calculator works
A pin rack moves z·p per pinion revolution, where z is the pinion teeth and p the pin pitch; 12 teeth on a 12 mm pin pitch travel 144 mm per turn. The generator makes the rack bar with a straight row of pin holes and the pinion, whose teeth are offset involutes of the pin path, for dowels, shoulder bolts, or rollers.
How to use the calculator
- 1Choose pin rack as the carrier.
- 2Enter pin pitch, pin diameter, and the number of pins along the rack.
- 3Enter the pinion tooth count and clearance, then review travel and pinion position.
- 4Download the pinion and rack bar or send them to a Fabworks quote.
Key formulas
Pin rack formulas
- Travel per revolution
- s = z·p
- Pinion pitch diameter
- d = z·p ÷ π
- Pinion center to pin line
- h = d ÷ 2
- Rack length
- L ≈ (Np − 1)·p + end margins
Worked example
12-tooth pinion on a 12 mm pin rack
- Inputs
- 6 mm pins at 12 mm pitch; 12-tooth pinion.
- Result
- Travel 144 mm per revolution; pinion pitch diameter 45.84 mm, so its center sits 22.92 mm from the line of pin centers.
Travel = 12 × 12 mm. d = 12 × 12 ÷ π = 45.84 mm.
Common questions
What to know before using the result
- What is a pin rack?
- A pin rack is a straight bar holding round pins at a fixed pitch, driven by a toothed pinion. It works like a gear rack but uses off-the-shelf pins or rollers as teeth.
- How far does a pin rack move per revolution?
- Travel is z·p. A 12-tooth pinion on a 12 mm pin pitch moves 144 mm per turn.
- What is a roller pinion?
- A roller pinion carries the pins and meshes with a toothed rack; here the arrangement is reversed, with pins in the rack and teeth on the pinion. Both rely on the same pin-path geometry.
- Why use a pin rack instead of a gear rack?
- Pins are cheap and replaceable, the rack bar is a simple row of holes, and long racks join easily by keeping the pin pitch across the joint. Rollers or bearings as pins reduce sliding friction.
- Are laser-cut pin racks suitable for machines?
- 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.
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