{
 "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": "bevel-gears-mechanism",
 "name": "Bevel gears, module 1.5, 20 : 40, shafts at 90°",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How do bevel gears turn motion through an angle?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "bevel gears",
  "bevel gear pair",
  "mitre gears",
  "right angle gears",
  "conical gears",
  "engranajes cónicos",
  "Kegelradgetriebe"
 ],
 "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/bevel-gears-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/bevel-gears-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 25 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Two cone-shaped gears whose pitch cones share an apex roll on each other like friction cones: the shafts meet at the apex at any angle (90° here) and the ratio is the tooth ratio, 40 : 20 = 2 : 1. Equal gears at 90° are mitre gears.",
   "Pitch cone angles from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ): 26.57° and 63.43°; cone distance 33.54 mm, face 11.2 mm. The teeth are exact spherical involutes, generated on a sphere about the apex, so the mesh is conjugate at every position; drawn turned 4°.",
   "Brown's No. 25 (bevel gears for shafts at an angle; mitre gears when the two are equal).",
   "Parts (each has its own page): bevel-gear-m1-5-20t-for-40t-90deg, bevel-gear-m1-5-40t-for-20t-90deg, linear-shafts-h6.",
   "Brown's movement No. 25 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "module (large end)",
     "1.5"
    ],
    [
     "teeth",
     "20 / 40"
    ],
    [
     "ratio",
     "2 : 1"
    ],
    [
     "shaft angle",
     "90°"
    ],
    [
     "pitch cones",
     "26.57° / 63.43°"
    ],
    [
     "cone distance",
     "33.54 mm"
    ]
   ]
  }
 },
 "sheet_text": "Bevel gears, module 1.5, 20 : 40, shafts at 90° — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/bevel-gears-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 25 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Two cone-shaped gears whose pitch cones share an apex roll on each other like friction cones: the shafts meet at the apex at any angle (90° here) and the ratio is the tooth ratio, 40 : 20 = 2 : 1. Equal gears at 90° are mitre gears.\n- Pitch cone angles from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ): 26.57° and 63.43°; cone distance 33.54 mm, face 11.2 mm. The teeth are exact spherical involutes, generated on a sphere about the apex, so the mesh is conjugate at every position; drawn turned 4°.\n- Brown's No. 25 (bevel gears for shafts at an angle; mitre gears when the two are equal).\n- Parts (each has its own page): bevel-gear-m1-5-20t-for-40t-90deg, bevel-gear-m1-5-40t-for-20t-90deg, linear-shafts-h6.\n- Brown's movement No. 25 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nmodule (large end)  1.5\nteeth  20 / 40\nratio  2 : 1\nshaft angle  90°\npitch cones  26.57° / 63.43°\ncone distance  33.54 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. 25: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_025.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/bevel-gears-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=bevel-gears-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. 25: figure, his text and an animation",
   "url": "https://507movements.com/mm_025.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": [
  "bevel-gear-m1-5-20t-for-40t-90deg",
  "bevel-gear-m1-5-40t-for-20t-90deg",
  "linear-shafts-h6"
 ],
 "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 do bevel gears turn motion through an angle?",
   "a": "Two cone-shaped gears whose pitch cones share an apex roll on each other like friction cones: the shafts meet at the apex at any angle (90° here) and the ratio is the tooth ratio, 40 : 20 = 2 : 1. Equal gears at 90° are mitre gears."
  },
  {
   "q": "What is the pitch cone angle of a 20 and 40 tooth bevel pair at 90°?",
   "a": "tan δ = 20/40: 26.57° for the pinion and 63.43° for the wheel."
  },
  {
   "q": "Why are bevel teeth spherical involutes?",
   "a": "Every point of a bevel gear moves on a sphere about the apex; the tooth shape that rolls conjugately on that sphere is the spherical involute (Tredgold's back-cone method approximates it)."
  }
 ],
 "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": "bevel-gears-mechanism-assembly",
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    "stl"
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   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/bevel-gears-mechanism/bevel-gears-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/bevel-gears-mechanism/bevel-gears-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/bevel-gears-mechanism/index.md"
}