{
 "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": "conoid-pulleys-mechanism",
 "name": "Conoid (curved cone) pulleys: varied speed with a belt of constant length",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Belt and friction drives",
 "year": null,
 "question": "Why are the cones curved?",
 "tags": [
  "mechanism",
  "belt and friction drives",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "conoid pulleys",
  "curved speed cones",
  "variable speed cone pulleys",
  "poleas conoides",
  "gewölbte Kegelscheiben"
 ],
 "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/conoid-pulleys-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/conoid-pulleys-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 10 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Two straight cones head to tail keep r₁ + r₂ constant, which keeps a CROSSED belt the same length but not an open one: an open belt goes slack away from the middle. Curving the cones by the right amount makes the open-belt length exactly constant.",
   "Here Ø24–Ø56 × 64 conoids at 110 mm; at 20 mm along, Ø27.9 drives Ø51.9, ratio 0.54. The belt length 346.65 mm is the same at every position (straight cones of the same size lose -4.64 mm near the ends).",
   "Brown's No. 10 (cone pulleys of curved outline for gradually varying speed).",
   "Parts (each has its own page): conoid-pulley-24-56x64-bore8, flat-belt-10x1-5-conoid-pulleys-c110.",
   "Brown's movement No. 10 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "pulleys",
     "2 × Ø24–Ø56 × 64 conoids, head to tail"
    ],
    [
     "centres",
     "110 mm"
    ],
    [
     "ratio range",
     "0.43 – 2.33 (approx.)"
    ],
    [
     "drawn at 20 mm",
     "ratio 0.54"
    ],
    [
     "belt",
     "10 × 1.5, 346.65 mm"
    ]
   ]
  }
 },
 "sheet_text": "Conoid (curved cone) pulleys: varied speed with a belt of constant length — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/conoid-pulleys-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 10 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Two straight cones head to tail keep r₁ + r₂ constant, which keeps a CROSSED belt the same length but not an open one: an open belt goes slack away from the middle. Curving the cones by the right amount makes the open-belt length exactly constant.\n- Here Ø24–Ø56 × 64 conoids at 110 mm; at 20 mm along, Ø27.9 drives Ø51.9, ratio 0.54. The belt length 346.65 mm is the same at every position (straight cones of the same size lose -4.64 mm near the ends).\n- Brown's No. 10 (cone pulleys of curved outline for gradually varying speed).\n- Parts (each has its own page): conoid-pulley-24-56x64-bore8, flat-belt-10x1-5-conoid-pulleys-c110.\n- Brown's movement No. 10 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\npulleys  2 × Ø24–Ø56 × 64 conoids, head to tail\ncentres  110 mm\nratio range  0.43 – 2.33 (approx.)\ndrawn at 20 mm  ratio 0.54\nbelt  10 × 1.5, 346.65 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. 10: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_010.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/conoid-pulleys-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=conoid-pulleys-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. 10: figure, his text and an animation",
   "url": "https://507movements.com/mm_010.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": [
  "conoid-pulley-24-56x64-bore8",
  "flat-belt-10x1-5-conoid-pulleys-c110"
 ],
 "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": "Why are the cones curved?",
   "a": "Two straight cones head to tail keep r₁ + r₂ constant, which keeps a CROSSED belt the same length but not an open one: an open belt goes slack away from the middle. Curving the cones by the right amount makes the open-belt length exactly constant."
  }
 ],
 "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": "conoid-pulleys-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/conoid-pulleys-mechanism/conoid-pulleys-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/conoid-pulleys-mechanism/conoid-pulleys-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/conoid-pulleys-mechanism/index.md"
}