{
 "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": "crown-wheel-spur-pinion-mechanism",
 "name": "Crown wheel and spur pinion at right angles (face gear, 3 : 1)",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How does a crown wheel mesh with an ordinary spur pinion?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "crown wheel and pinion",
  "face gear",
  "contrate wheel",
  "crown gear drive",
  "rueda de corona y piñón",
  "Kronenrad und Ritzel"
 ],
 "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/crown-wheel-spur-pinion-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 26 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Resize: multiply every length by one factor k and the motion stays identical: angles, ratios, timing and the formulas below do not change, because a mechanism's motion depends only on the ratios of its lengths. Here, scales with k: pinion axis height; stays the same: crown wheel, pinion, ratio; step to the nearest standard size (and redraw the hole or pocket it fits): shafts.",
   "Resize: Gears scale by the module m (pitch Ø = m·z, centre distance = m·(z₁ + z₂)/2): keep the tooth counts so the ratio stays, and choose a standard module (0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3).",
   "Resize: fit clearances stay in mm (a slide fit is the same gap at any size); keep every printed wall and pin at least two nozzle widths; mass grows with k³ but part strength only with k², so at k = 2 parts are about 8× heavier and 4× stronger: check pins and thin links when scaling up.",
   "A crown wheel (face gear) carries its teeth on its face; an ordinary spur pinion whose axis lies in the wheel's pitch plane meshes with them and turns the motion through 90° — the clockmaker's contrate wheel, the mill's crown-and-trundle. Ratio = tooth ratio, 54 : 18 = 3 : 1.",
   "For a true involute pinion the crown teeth cannot be drawn directly: they are generated by the pinion itself. Here each tooth is the envelope of the catalog 18-tooth module 1.5 pinion's teeth as the pair turns at 3 : 1, computed slice by slice across the 7 mm face (r 37.5–44.5) and lofted; the pinion sits with its axis 13.5 mm (its pitch radius) above the wheel's pitch plane, centred on the face. Checked at seven positions through a tooth passage: no overlap beyond contact.",
   "Brown's No. 26 (crown wheel and spur gear at right angles; little used in his day). Drawn turned 5° (pinion) / 1.67° (wheel).",
   "Parts (each has its own page): crown-wheel-m1-5-54t-for-18t-pinion, spur-gears-module-1-5, linear-shafts-h6.",
   "Brown's movement No. 26 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "crown wheel",
     "54 T, module 1.5, face r 37.5–44.5"
    ],
    [
     "pinion",
     "18 T spur (catalog)"
    ],
    [
     "ratio",
     "3 : 1"
    ],
    [
     "shafts",
     "90°, intersecting"
    ],
    [
     "pinion axis height",
     "13.5 mm above the pitch plane"
    ]
   ]
  }
 },
 "sheet_text": "Crown wheel and spur pinion at right angles (face gear, 3 : 1) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 26 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Resize: multiply every length by one factor k and the motion stays identical: angles, ratios, timing and the formulas below do not change, because a mechanism's motion depends only on the ratios of its lengths. Here, scales with k: pinion axis height; stays the same: crown wheel, pinion, ratio; step to the nearest standard size (and redraw the hole or pocket it fits): shafts.\n- Resize: Gears scale by the module m (pitch Ø = m·z, centre distance = m·(z₁ + z₂)/2): keep the tooth counts so the ratio stays, and choose a standard module (0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3).\n- Resize: fit clearances stay in mm (a slide fit is the same gap at any size); keep every printed wall and pin at least two nozzle widths; mass grows with k³ but part strength only with k², so at k = 2 parts are about 8× heavier and 4× stronger: check pins and thin links when scaling up.\n- A crown wheel (face gear) carries its teeth on its face; an ordinary spur pinion whose axis lies in the wheel's pitch plane meshes with them and turns the motion through 90° — the clockmaker's contrate wheel, the mill's crown-and-trundle. Ratio = tooth ratio, 54 : 18 = 3 : 1.\n- For a true involute pinion the crown teeth cannot be drawn directly: they are generated by the pinion itself. Here each tooth is the envelope of the catalog 18-tooth module 1.5 pinion's teeth as the pair turns at 3 : 1, computed slice by slice across the 7 mm face (r 37.5–44.5) and lofted; the pinion sits with its axis 13.5 mm (its pitch radius) above the wheel's pitch plane, centred on the face. Checked at seven positions through a tooth passage: no overlap beyond contact.\n- Brown's No. 26 (crown wheel and spur gear at right angles; little used in his day). Drawn turned 5° (pinion) / 1.67° (wheel).\n- Parts (each has its own page): crown-wheel-m1-5-54t-for-18t-pinion, spur-gears-module-1-5, linear-shafts-h6.\n- Brown's movement No. 26 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\ncrown wheel  54 T, module 1.5, face r 37.5–44.5\npinion  18 T spur (catalog)\nratio  3 : 1\nshafts  90°, intersecting\npinion axis height  13.5 mm above the pitch plane\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. 26: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_026.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=crown-wheel-spur-pinion-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. 26: figure, his text and an animation",
   "url": "https://507movements.com/mm_026.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": [
  "crown-wheel-m1-5-54t-for-18t-pinion",
  "spur-gears-module-1-5",
  "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 does a crown wheel mesh with an ordinary spur pinion?",
   "a": "A crown wheel (face gear) carries its teeth on its face; an ordinary spur pinion whose axis lies in the wheel's pitch plane meshes with them and turns the motion through 90° — the clockmaker's contrate wheel, the mill's crown-and-trundle. Ratio = tooth ratio, 54 : 18 = 3 : 1."
  },
  {
   "q": "Can any spur pinion run on a crown wheel?",
   "a": "Only the pinion it was generated for (module, pressure angle, tooth count and root form): the crown tooth form is the envelope of that pinion's teeth."
  },
  {
   "q": "Why is a face gear's face width so short?",
   "a": "The tooth form changes with radius: inside the nominal pitch radius the teeth are undercut, outside it they become pointed; only a few modules each way are usable (here 3 inside, 4 outside)."
  }
 ],
 "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": "crown-wheel-spur-pinion-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/crown-wheel-spur-pinion-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/crown-wheel-spur-pinion-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/index.md"
}