Xem Studiomeasured geometryLibrary › Mechanisms › Gears ·
Rack and pinion, module 1 (20 T pinion, 120 mm rack)
How far does a rack move per turn of the pinion? · Hardware · basis: Xem Studio design following Brown No. 113 (1868)
Also called: rack and pinion, gear rack, rack pinion linear motion, piñón y cremallera, Zahnstangengetriebe
Exact dimensions. True size, with no printing tolerance added.
- sizes
- 5 in table
Notes
- A pinion turning on a fixed axis drives a straight toothed rack: one turn moves the rack π·m·N = 62.83 mm for a 20-tooth module 1 pinion (its pitch circumference). Either part can drive.
- The rack is the basic rack of the involute system (straight 20° flanks), so it meshes with every module 1 gear; the pinion's axis sits exactly one pitch radius (10 mm) above the rack's pitch line.
- Brown's No. 113: circular motion to straight-line motion and back.
- Parts (each has its own page): spur-gears-module-1, gear-rack-m1-120-full-depth.
- Brown's movement No. 113 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.
Rack and pinion, module 1 size chart
| parameter | value |
|---|---|
| module | 1 |
| pinion | 20 T, pitch Ø20 |
| rack | 120 mm |
| travel per turn | 62.83 mm |
| pinion axis above pitch line | 10 mm |
Where the files are
Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.
| Henry T. Brown (1868, public domain) | Five Hundred and Seven Mechanical Movements — scan on archive.org | web | Publisher's page; dimensions are facts |
| 507movements.com | Brown's movement No. 113: figure, his text and an animation | web | Publisher's page; dimensions are facts |
Free files
★ Free files 1 parts. Generated by Xem Studio from the standard; threads are plain cylinders at major diameter. CC BY 4.0. index.json
| rack-and-pinion-mechanism-assembly | Assembled mechanism, all parts placed at one pose (STEP keeps each part separate) | STEP · STL |
https://xemstudio.com/mcp to Claude, ChatGPT, Cursor or any MCP client (free, no account, one minute) and it can look up exact sizes, mating fits and free STEP/STL from every chat.Plain text: sheet.txt · JSON: /api/geometry?object=rack-and-pinion-mechanism
Fits with
Questions
How far does a rack move per turn of the pinion?
A pinion turning on a fixed axis drives a straight toothed rack: one turn moves the rack π·m·N = 62.83 mm for a 20-tooth module 1 pinion (its pitch circumference). Either part can drive.
How far does a rack move per pinion revolution?
Pitch circumference: π × module × teeth (62.83 mm for module 1, 20 teeth).