{
 "version": "2026-10-20",
 "license": "Dimension sheets: CC BY 4.0. Standard and published-size files: CC BY 4.0. Xem Studio's own designs (files_license = Xem Studio Design License): free to use and sell things from, not to redistribute as files — https://xemstudio.com/license/. Other publishers' files: their own license, linked beside them.",
 "slug": "mutilated-gear-spring-rack-mechanism",
 "name": "Mutilated spur gear moving a rack, a spring bringing it back",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Intermittent motion",
 "year": null,
 "question": "How does a part-toothed gear and a spring make a rack go back and forth?",
 "tags": [
  "mechanism",
  "intermittent motion",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "mutilated gear rack",
  "spring return rack",
  "intermittent rack drive",
  "engranaje mutilado con cremallera y muelle",
  "Teilzahnrad mit Zahnstange und Rückholfeder"
 ],
 "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/mutilated-gear-spring-rack-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/mutilated-gear-spring-rack-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 81 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "A spur gear with teeth on half its rim turns continuously above a rack: while its teeth are in mesh it drives the rack one way and compresses a spring; when the toothless half comes round the spring pushes the rack back.",
   "Catalog parts: the module 1, 20-tooth mutilated pinion (10 teeth) and the 120 mm full-depth rack; stroke = 10 × π = 31.42 mm. The rack slides on a base against a side rail; an Ø8 spring between the rack's end and the base's end wall returns it. Drawn in mesh.",
   "Brown's No. 81 (mutilated spur gear giving alternate rectilinear motion to a rack rod, a spring returning it).",
   "Parts (each has its own page): mutilated-pinion-m1-20t-half, gear-rack-m1-120-full-depth, compression-spring-od8-wire1-l30, rack-guide-base-170-spring-seat, dowel-pins-metric.",
   "Brown's movement No. 81 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "pinion",
     "module 1, 10 of 20 teeth"
    ],
    [
     "stroke",
     "31.42 mm"
    ],
    [
     "spring",
     "OD8 × Ø1 wire"
    ]
   ]
  }
 },
 "sheet_text": "Mutilated spur gear moving a rack, a spring bringing it back — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/mutilated-gear-spring-rack-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 81 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- A spur gear with teeth on half its rim turns continuously above a rack: while its teeth are in mesh it drives the rack one way and compresses a spring; when the toothless half comes round the spring pushes the rack back.\n- Catalog parts: the module 1, 20-tooth mutilated pinion (10 teeth) and the 120 mm full-depth rack; stroke = 10 × π = 31.42 mm. The rack slides on a base against a side rail; an Ø8 spring between the rack's end and the base's end wall returns it. Drawn in mesh.\n- Brown's No. 81 (mutilated spur gear giving alternate rectilinear motion to a rack rod, a spring returning it).\n- Parts (each has its own page): mutilated-pinion-m1-20t-half, gear-rack-m1-120-full-depth, compression-spring-od8-wire1-l30, rack-guide-base-170-spring-seat, dowel-pins-metric.\n- Brown's movement No. 81 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\npinion  module 1, 10 of 20 teeth\nstroke  31.42 mm\nspring  OD8 × Ø1 wire\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. 81: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_081.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/mutilated-gear-spring-rack-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=mutilated-gear-spring-rack-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. 81: figure, his text and an animation",
   "url": "https://507movements.com/mm_081.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": [
  "mutilated-pinion-m1-20t-half",
  "gear-rack-m1-120-full-depth",
  "compression-spring-od8-wire1-l30",
  "rack-guide-base-170-spring-seat",
  "dowel-pins-metric"
 ],
 "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 does a part-toothed gear and a spring make a rack go back and forth?",
   "a": "A spur gear with teeth on half its rim turns continuously above a rack: while its teeth are in mesh it drives the rack one way and compresses a spring; when the toothless half comes round the spring pushes the rack back."
  }
 ],
 "files_license": {
  "name": "Xem Studio Design License",
  "holder": "Xem Studio",
  "url": "https://xemstudio.com/license/",
  "note": "Xem Studio's own design: free to use, print, modify and sell things made from it; not to be republished or redistributed as files."
 },
 "offers": [
  {
   "file": "mutilated-gear-spring-rack-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/mutilated-gear-spring-rack-mechanism/mutilated-gear-spring-rack-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/mutilated-gear-spring-rack-mechanism/mutilated-gear-spring-rack-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/mutilated-gear-spring-rack-mechanism/index.md"
}