{
 "version": "2026-10-20",
 "license": "Dimension sheets are written by Xem Studio from the cited sources and are free to use (CC BY 4.0, attribute 'Xem Studio'). Linked files belong to their publishers under the license shown; Xem Studio does not host them. 'license_verified: false' means the license shown is from memory or the publisher's page as last read and should be confirmed at the link before commercial use.",
 "slug": "universal-joint-mechanism",
 "name": "Universal (Hooke / Cardan) joint",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Couplings & joints",
 "year": null,
 "question": "Why does a universal joint not turn at constant speed?",
 "tags": [
  "mechanism",
  "couplings & joints",
  "kinematics"
 ],
 "aliases": [
  "universal joint",
  "cardan joint",
  "hooke joint",
  "u joint speed"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "not-scanned",
 "les": false,
 "free_files": 0,
 "url": "https://xemstudio.com/objects/universal-joint-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/universal-joint-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio drawing; classic mechanism (Brown No. 50)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Two yokes at 90° on a cross: shafts at an angle β turn together, but the output speed swings: ω₂/ω₁ = cos β / (1 − sin²β·cos²θ), between cos β and 1/cos β twice per turn.",
   "Two joints in phase with equal angles (a double Cardan or a drive shaft with both yokes aligned) cancel the swing.",
   "Brown shows two forms (Nos. 50 and 51). The 5 mm printable joint is its own page.",
   "Parts (each has its own page): universal-joint-5mm, clevis-pins. Brown's movement No. 50 shows it (1868)."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "angle β (max, printable joint)",
     "≈30°"
    ],
    [
     "speed swing at 30°",
     "0.866 – 1.155"
    ]
   ]
  }
 },
 "sheet_text": "Universal (Hooke / Cardan) joint — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/universal-joint-mechanism/  (CC BY 4.0)\nBasis: Xem Studio drawing; classic mechanism (Brown No. 50)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Two yokes at 90° on a cross: shafts at an angle β turn together, but the output speed swings: ω₂/ω₁ = cos β / (1 − sin²β·cos²θ), between cos β and 1/cos β twice per turn.\n- Two joints in phase with equal angles (a double Cardan or a drive shaft with both yokes aligned) cancel the swing.\n- Brown shows two forms (Nos. 50 and 51). The 5 mm printable joint is its own page.\n- Parts (each has its own page): universal-joint-5mm, clevis-pins. Brown's movement No. 50 shows it (1868).\n\nparameter  value\nangle β (max, printable joint)  ≈30°\nspeed swing at 30°  0.866 – 1.155\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\nXem Studio scan: not needed; this is a published standard. The sheet is the geometry.\nAPI: https://xemstudio.com/api/geometry?object=universal-joint-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
  }
 ],
 "xem": {
  "status": "not-scanned",
  "sheet_free": true,
  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "universal-joint-5mm",
  "clevis-pins"
 ],
 "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 does a universal joint not turn at constant speed?",
   "a": "Two yokes at 90° on a cross: shafts at an angle β turn together, but the output speed swings: ω₂/ω₁ = cos β / (1 − sin²β·cos²θ), between cos β and 1/cos β twice per turn."
  }
 ],
 "files_license": null,
 "offers": [],
 "markdown": "https://xemstudio.com/objects/universal-joint-mechanism/index.md"
}