{
 "version": "2026-10-20",
 "license": "Dimension sheets are written by Xem Studio from the cited sources and are free to use (CC BY 4.0, attribute 'Xem Studio'). Linked files belong to their publishers under the license shown; Xem Studio does not host them. 'license_verified: false' means the license shown is from memory or the publisher's page as last read and should be confirmed at the link before commercial use.",
 "slug": "rack-and-pinion-mechanism",
 "name": "Rack and pinion, module 1 (20 T pinion, 120 mm rack)",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How far does a rack move per turn of the pinion?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "rack and pinion",
  "gear rack",
  "rack pinion linear motion",
  "piñón y cremallera",
  "Zahnstangengetriebe"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": false,
 "free_files": 1,
 "url": "https://xemstudio.com/objects/rack-and-pinion-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/rack-and-pinion-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 113 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "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."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "module",
     "1"
    ],
    [
     "pinion",
     "20 T, pitch Ø20"
    ],
    [
     "rack",
     "120 mm"
    ],
    [
     "travel per turn",
     "62.83 mm"
    ],
    [
     "pinion axis above pitch line",
     "10 mm"
    ]
   ]
  }
 },
 "sheet_text": "Rack and pinion, module 1 (20 T pinion, 120 mm rack) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/rack-and-pinion-mechanism/  (CC BY 4.0)\nBasis: Xem Studio design following Brown No. 113 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- 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.\n- 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.\n- Brown's No. 113: circular motion to straight-line motion and back.\n- Parts (each has its own page): spur-gears-module-1, gear-rack-m1-120-full-depth.\n- Brown's movement No. 113 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nmodule  1\npinion  20 T, pitch Ø20\nrack  120 mm\ntravel per turn  62.83 mm\npinion axis above pitch line  10 mm\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\n- Henry T. Brown (1868, public domain): Five Hundred and Seven Mechanical Movements — scan on archive.org — web — Publisher's page; dimensions are facts — https://archive.org/details/fivehundredseven00browiala\n- 507movements.com: Brown's movement No. 113: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_113.html\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/rack-and-pinion-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=rack-and-pinion-mechanism\n",
 "sources": [
  {
   "publisher": "Henry T. Brown (1868, public domain)",
   "title": "Five Hundred and Seven Mechanical Movements — scan on archive.org",
   "url": "https://archive.org/details/fivehundredseven00browiala",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "507movements.com",
   "title": "Brown's movement No. 113: figure, his text and an animation",
   "url": "https://507movements.com/mm_113.html",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  }
 ],
 "xem": {
  "status": "free-files",
  "sheet_free": true,
  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "spur-gears-module-1",
  "gear-rack-m1-120-full-depth"
 ],
 "fits": [],
 "dimensions": "exact (nominal, no printing tolerance)",
 "dimension_rule": "All geometry on Xem Studio is exact (nominal, true size) with no printing tolerance. Where a part meets another part, the object lists its mating features (feature, exact size, what it mates with, fit class: press, slide, run, socket, clamp or designed). Apply your process's allowance to those features only; 'designed' gaps are part of the design and stay as drawn.",
 "mating": [],
 "faq": [
  {
   "q": "How far does a rack move per turn of the pinion?",
   "a": "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."
  },
  {
   "q": "How far does a rack move per pinion revolution?",
   "a": "Pitch circumference: π × module × teeth (62.83 mm for module 1, 20 teeth)."
  }
 ],
 "files_license": null,
 "offers": [
  {
   "file": "rack-and-pinion-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/rack-and-pinion-mechanism/rack-and-pinion-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/rack-and-pinion-mechanism/rack-and-pinion-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/rack-and-pinion-mechanism/index.md"
}