{
 "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": "helical-gears-mechanism",
 "name": "Helical (oblique-toothed) gears on parallel shafts, 20 : 30, helix 20°",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "Why are helical gears smoother than spur gears?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "helical gears",
  "oblique tooth gears",
  "helical gear pair",
  "engranajes helicoidales",
  "Schrägstirnräder"
 ],
 "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/helical-gears-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/helical-gears-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 40 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "The teeth are cut along a helix, so each tooth comes into mesh gradually from one end of the face to the other and more than one pair is always in contact: quieter, smoother and stronger than straight teeth, at the cost of an end thrust along the shafts.",
   "Normal module 1.5, helix 20° (right hand on the 20-tooth, left on the 30-tooth), 12 mm face: transverse module 1.6, centre distance 39.91 mm, transverse pressure angle 21.17°. Each transverse section is an exact involute spur mesh, twisted 15.68° over the face on the pinion.",
   "Brown's No. 40 (oblique-toothed gears, giving a more continuous bearing of the teeth).",
   "Parts (each has its own page): helical-gear-mn1-5-20t-beta20-rh-bore6, helical-gear-mn1-5-30t-beta20-lh-bore8, linear-shafts-h6.",
   "Brown's movement No. 40 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "normal module",
     "1.5"
    ],
    [
     "teeth",
     "20 / 30"
    ],
    [
     "helix",
     "20°, opposite hands"
    ],
    [
     "face",
     "12 mm"
    ],
    [
     "centre distance",
     "39.91 mm"
    ]
   ]
  }
 },
 "sheet_text": "Helical (oblique-toothed) gears on parallel shafts, 20 : 30, helix 20° — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/helical-gears-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 40 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- The teeth are cut along a helix, so each tooth comes into mesh gradually from one end of the face to the other and more than one pair is always in contact: quieter, smoother and stronger than straight teeth, at the cost of an end thrust along the shafts.\n- Normal module 1.5, helix 20° (right hand on the 20-tooth, left on the 30-tooth), 12 mm face: transverse module 1.6, centre distance 39.91 mm, transverse pressure angle 21.17°. Each transverse section is an exact involute spur mesh, twisted 15.68° over the face on the pinion.\n- Brown's No. 40 (oblique-toothed gears, giving a more continuous bearing of the teeth).\n- Parts (each has its own page): helical-gear-mn1-5-20t-beta20-rh-bore6, helical-gear-mn1-5-30t-beta20-lh-bore8, linear-shafts-h6.\n- Brown's movement No. 40 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nnormal module  1.5\nteeth  20 / 30\nhelix  20°, opposite hands\nface  12 mm\ncentre distance  39.91 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. 40: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_040.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/helical-gears-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=helical-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. 40: figure, his text and an animation",
   "url": "https://507movements.com/mm_040.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": [
  "helical-gear-mn1-5-20t-beta20-rh-bore6",
  "helical-gear-mn1-5-30t-beta20-lh-bore8",
  "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": "Why are helical gears smoother than spur gears?",
   "a": "The teeth are cut along a helix, so each tooth comes into mesh gradually from one end of the face to the other and more than one pair is always in contact: quieter, smoother and stronger than straight teeth, at the cost of an end thrust along the shafts."
  },
  {
   "q": "What is the centre distance of helical gears?",
   "a": "m_n (N₁ + N₂) / (2 cos β): 1.5 × 50 / (2 cos 20°) = 39.91 mm here."
  }
 ],
 "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": "helical-gears-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/helical-gears-mechanism/helical-gears-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/helical-gears-mechanism/helical-gears-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/helical-gears-mechanism/index.md"
}