{
 "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": "elliptical-gear-m1-5-31t-e0-5-focus-bore",
 "name": "Elliptical gear, module 1.5, 31 teeth, eccentricity 0.5, bore at a focus",
 "kind": "modern",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How are elliptical gears made?",
 "tags": [
  "mechanism part",
  "507 mechanical movements"
 ],
 "aliases": [
  "elliptical gear",
  "oval gear",
  "non circular gear",
  "engranaje elíptico",
  "elliptisches Zahnrad"
 ],
 "overall_mm": {
  "length": 52.67,
  "width": 46.09,
  "height": 12
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": false,
 "free_files": 1,
 "url": "https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/",
 "sheet_txt": "https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown's figure (1868); true size, no printing allowance",
  "overall_mm": {
   "length": 52.67,
   "width": 46.09,
   "height": 12
  },
  "notes": [
   "Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm.",
   "31 teeth (odd): a pair pivoted at their foci 49.77 mm apart (the major axis) meets tooth-to-space at both ends of the major axis. 12 mm face.",
   "Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features)."
  ],
  "table": {
   "columns": [
    "dimension",
    "value"
   ],
   "rows": [
    [
     "module",
     "1.5"
    ],
    [
     "teeth",
     "31"
    ],
    [
     "pitch ellipse",
     "49.77 × 43.11 mm"
    ],
    [
     "eccentricity",
     "0.5"
    ],
    [
     "bore",
     "Ø8 at a focus"
    ],
    [
     "face",
     "12 mm"
    ]
   ]
  }
 },
 "sheet_text": "Elliptical gear, module 1.5, 31 teeth, eccentricity 0.5, bore at a focus — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown's figure (1868); true size, no printing allowance\nCatalog version: 2026-10-20\n\nOverall (mm): length 52.67, width 46.09, height 12.0\n- Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm.\n- 31 teeth (odd): a pair pivoted at their foci 49.77 mm apart (the major axis) meets tooth-to-space at both ends of the major axis. 12 mm face.\n- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).\n\ndimension  value\nmodule  1.5\nteeth  31\npitch ellipse  49.77 × 43.11 mm\neccentricity  0.5\nbore  Ø8 at a focus\nface  12 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. 33: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_033.html\n- Xem Studio: drawing — web — Publisher's page; dimensions are facts — https://xemstudio.com/objects/elliptical-gears-focus-mechanism/\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/index.json\nAPI: https://xemstudio.com/api/geometry?object=elliptical-gear-m1-5-31t-e0-5-focus-bore\n",
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   "license": "Publisher's page; dimensions are facts",
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   "title": "drawing",
   "url": "https://xemstudio.com/objects/elliptical-gears-focus-mechanism/",
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   "license": "Publisher's page; dimensions are facts",
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 "related": [
  "elliptical-gears-focus-mechanism"
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 "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 are elliptical gears made?",
   "a": "Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm."
  }
 ],
 "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."
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   "note": "gear, bore (focus) on the Z axis, near vertex on +X, z 0..12"
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 ],
 "markdown": "https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/index.md"
}