{
 "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": "pinion-between-racks-doubler-mechanism",
 "name": "Pinion between a fixed and a free rack (travel doubler)",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How does a pinion between two racks double a stroke?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "rack doubler",
  "pinion between two racks",
  "stroke doubling rack",
  "piñón entre cremallera fija y móvil",
  "Ritzel zwischen fester und loser Zahnstange"
 ],
 "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/pinion-between-racks-doubler-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/pinion-between-racks-doubler-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 118 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "A pinion turns on an axle carried by a rod. Below it is a fixed rack, above it a rack free to slide. Moving the axle a distance d rolls the pinion on the fixed rack, and its top, moving at twice the axle's speed, carries the free rack 2d: the stroke is doubled with no gearing ratio.",
   "Module 1, 20-tooth pinion, racks with pitch lines 20 mm apart (one pitch diameter); drawn with the axle 6.28 mm (two pitches) along and the free rack 12.57 mm along. The free rack's own guide is not drawn.",
   "Brown's No. 118 (pinion on the connecting rod between a fixed and a movable rack).",
   "Parts (each has its own page): gear-rack-m1-120-full-depth, spur-gears-module-1, pinion-carrier-rod-100-bore6, dowel-pins-metric.",
   "Brown's movement No. 118 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "pinion",
     "20 T, module 1"
    ],
    [
     "racks",
     "2 × 120 mm, pitch lines 20 mm apart"
    ],
    [
     "ratio",
     "free rack = 2 × axle travel"
    ],
    [
     "rod",
     "100 mm"
    ]
   ]
  }
 },
 "sheet_text": "Pinion between a fixed and a free rack (travel doubler) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/pinion-between-racks-doubler-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 118 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- A pinion turns on an axle carried by a rod. Below it is a fixed rack, above it a rack free to slide. Moving the axle a distance d rolls the pinion on the fixed rack, and its top, moving at twice the axle's speed, carries the free rack 2d: the stroke is doubled with no gearing ratio.\n- Module 1, 20-tooth pinion, racks with pitch lines 20 mm apart (one pitch diameter); drawn with the axle 6.28 mm (two pitches) along and the free rack 12.57 mm along. The free rack's own guide is not drawn.\n- Brown's No. 118 (pinion on the connecting rod between a fixed and a movable rack).\n- Parts (each has its own page): gear-rack-m1-120-full-depth, spur-gears-module-1, pinion-carrier-rod-100-bore6, dowel-pins-metric.\n- Brown's movement No. 118 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\npinion  20 T, module 1\nracks  2 × 120 mm, pitch lines 20 mm apart\nratio  free rack = 2 × axle travel\nrod  100 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. 118: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_118.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/pinion-between-racks-doubler-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=pinion-between-racks-doubler-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. 118: figure, his text and an animation",
   "url": "https://507movements.com/mm_118.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": [
  "gear-rack-m1-120-full-depth",
  "spur-gears-module-1",
  "pinion-carrier-rod-100-bore6",
  "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 pinion between two racks double a stroke?",
   "a": "A pinion turns on an axle carried by a rod. Below it is a fixed rack, above it a rack free to slide. Moving the axle a distance d rolls the pinion on the fixed rack, and its top, moving at twice the axle's speed, carries the free rack 2d: the stroke is doubled with no gearing ratio."
  }
 ],
 "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": "pinion-between-racks-doubler-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/pinion-between-racks-doubler-mechanism/pinion-between-racks-doubler-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/pinion-between-racks-doubler-mechanism/pinion-between-racks-doubler-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/pinion-between-racks-doubler-mechanism/index.md"
}