{
 "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": "mitre-gear-m2-24t-bore5",
 "name": "Mitre (bevel) gear, module 2, 24 teeth, Ø5 bore, spherical involute (spline flanks)",
 "kind": "modern",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "What are the dimensions of a module 2, 24-tooth mitre gear?",
 "tags": [
  "mechanism part",
  "507 mechanical movements"
 ],
 "aliases": [
  "mitre gear",
  "miter gear",
  "bevel gear",
  "spherical involute bevel gear",
  "module 2 mitre gear",
  "engranaje cónico de inglete",
  "Kegelrad (Tellerrad 1:1)"
 ],
 "overall_mm": {
  "length": 50.74,
  "width": 50.74,
  "height": 26.9
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": false,
 "free_files": 1,
 "url": "https://xemstudio.com/objects/mitre-gear-m2-24t-bore5/",
 "sheet_txt": "https://xemstudio.com/objects/mitre-gear-m2-24t-bore5/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown's figure (1868); true size, no printing allowance",
  "overall_mm": {
   "length": 50.74,
   "width": 50.74,
   "height": 26.9
  },
  "notes": [
   "Straight bevel gear for a 90° shaft angle with an equal mate (a mitre gear): module 2 at the large end, 24 teeth, pitch cone angle 45°, cone distance 33.94 mm, pitch Ø48, tip Ø50.74, face width 11.3 mm, Ø5 bore, Ø35.16 hub, 41.94 mm from the apex to the back of the hub.",
   "Teeth are exact spherical involutes (base cone sin γb = sin δ · cos 20°), converging to the pitch apex: each flank is one ruled face — a cone from the apex over the spherical involute — so two such gears roll with line contact at every position; ends are spheres about the apex (radii A0 and A0 − F). Addendum m, dedendum 1.25 m at the large end. Drawn with one spline per flank instead of a facetted polyline, so three of them fit an assembly STEP under 20 MB.",
   "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 (large end)",
     "2"
    ],
    [
     "teeth",
     "24"
    ],
    [
     "shaft angle",
     "90° (mate: same gear)"
    ],
    [
     "pitch cone",
     "45°"
    ],
    [
     "cone distance A0",
     "33.94 mm"
    ],
    [
     "face width",
     "11.3 mm"
    ],
    [
     "pitch Ø",
     "48 mm"
    ],
    [
     "tip Ø",
     "50.74 mm"
    ],
    [
     "bore",
     "Ø5"
    ],
    [
     "apex to back of hub",
     "41.94 mm"
    ]
   ]
  }
 },
 "sheet_text": "Mitre (bevel) gear, module 2, 24 teeth, Ø5 bore, spherical involute (spline flanks) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/mitre-gear-m2-24t-bore5/  (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 50.74, width 50.74, height 26.9\n- Straight bevel gear for a 90° shaft angle with an equal mate (a mitre gear): module 2 at the large end, 24 teeth, pitch cone angle 45°, cone distance 33.94 mm, pitch Ø48, tip Ø50.74, face width 11.3 mm, Ø5 bore, Ø35.16 hub, 41.94 mm from the apex to the back of the hub.\n- Teeth are exact spherical involutes (base cone sin γb = sin δ · cos 20°), converging to the pitch apex: each flank is one ruled face — a cone from the apex over the spherical involute — so two such gears roll with line contact at every position; ends are spheres about the apex (radii A0 and A0 − F). Addendum m, dedendum 1.25 m at the large end. Drawn with one spline per flank instead of a facetted polyline, so three of them fit an assembly STEP under 20 MB.\n- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).\n\ndimension  value\nmodule (large end)  2\nteeth  24\nshaft angle  90° (mate: same gear)\npitch cone  45°\ncone distance A0  33.94 mm\nface width  11.3 mm\npitch Ø  48 mm\ntip Ø  50.74 mm\nbore  Ø5\napex to back of hub  41.94 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. 7: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_007.html\n- Xem Studio: drawing — web — Publisher's page; dimensions are facts — https://xemstudio.com/objects/bevel-reversing-gear-fast-loose-pulleys-mechanism/\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/index.json\nAPI: https://xemstudio.com/api/geometry?object=mitre-gear-m2-24t-bore5\n",
 "sources": [
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   "publisher": "Henry T. Brown (1868, public domain)",
   "title": "Five Hundred and Seven Mechanical Movements — scan on archive.org",
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   "formats": [
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   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
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  {
   "publisher": "507movements.com",
   "title": "Brown's movement No. 7: figure, his text and an animation",
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   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
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  "status": "free-files",
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  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "bevel-reversing-gear-fast-loose-pulleys-mechanism",
  "opposed-ratchets-bevel-gears-rocking-mechanism"
 ],
 "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": "What are the dimensions of a module 2, 24-tooth mitre gear?",
   "a": "Straight bevel gear for a 90° shaft angle with an equal mate (a mitre gear): module 2 at the large end, 24 teeth, pitch cone angle 45°, cone distance 33.94 mm, pitch Ø48, tip Ø50.74, face width 11.3 mm, Ø5 bore, Ø35.16 hub, 41.94 mm from the apex to the back of the hub."
  }
 ],
 "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": "mitre-gear-m2-24t-bore5",
   "formats": [
    "step",
    "stl"
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   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/mitre-gear-m2-24t-bore5.step",
   "stl": "https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/mitre-gear-m2-24t-bore5.stl",
   "note": "gear, pitch apex at the origin, axis +Z, a tooth on +X"
  }
 ],
 "markdown": "https://xemstudio.com/objects/mitre-gear-m2-24t-bore5/index.md"
}