{
 "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": "worm-and-worm-wheel-mechanism",
 "name": "Worm and worm wheel, module 1.5, 1-start, 30 : 1",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How do a worm and worm wheel work?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "worm gear",
  "worm and wheel",
  "endless screw",
  "worm drive",
  "worm gear set",
  "tornillo sin fin y rueda helicoidal",
  "Schneckengetriebe"
 ],
 "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/worm-and-worm-wheel-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 31 (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: centre distance; stays the same: worm, wheel, 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.",
   "An endless screw (the worm) on one shaft meshes with a toothed wheel on a shaft at right angles: each turn of the worm advances the wheel one tooth (one thread), so the ratio is the tooth count — 30 : 1 here — in a single, quiet stage. The same result as the face-spiral drive of Brown's No. 29, but simpler to make, so far more used.",
   "Worm: involute helicoid (ZI), axial module 1.5, single start, pitch Ø16, lead angle 5.36°. Wheel: 30-tooth involute helical gear with helix angle = lead angle, same hand — a non-throated worm wheel, so the pair is an exactly conjugate crossed-helical pair (point contact) at centre distance 30.5 mm. Checked at nine positions over 1.5 worm turns: no overlap beyond contact.",
   "With a lead angle of 5.36° (below ~6°) the drive is self-locking: the wheel cannot drive the worm. Brown's No. 31; drawn with the worm turned 30°.",
   "Parts (each has its own page): worm-zi-m1-5-1start-d16-l40-bore6, worm-wheel-helical-m1-5-30t-for-1start-d16, linear-shafts-h6.",
   "Brown's movement No. 31 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "worm",
     "module 1.5, 1-start, pitch Ø16, lead angle 5.36°"
    ],
    [
     "wheel",
     "30 T helical, helix 5.36°"
    ],
    [
     "ratio",
     "30 : 1"
    ],
    [
     "centre distance",
     "30.5 mm"
    ],
    [
     "shafts",
     "90°, non-intersecting"
    ]
   ]
  }
 },
 "sheet_text": "Worm and worm wheel, module 1.5, 1-start, 30 : 1 — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 31 (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: centre distance; stays the same: worm, wheel, 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- An endless screw (the worm) on one shaft meshes with a toothed wheel on a shaft at right angles: each turn of the worm advances the wheel one tooth (one thread), so the ratio is the tooth count — 30 : 1 here — in a single, quiet stage. The same result as the face-spiral drive of Brown's No. 29, but simpler to make, so far more used.\n- Worm: involute helicoid (ZI), axial module 1.5, single start, pitch Ø16, lead angle 5.36°. Wheel: 30-tooth involute helical gear with helix angle = lead angle, same hand — a non-throated worm wheel, so the pair is an exactly conjugate crossed-helical pair (point contact) at centre distance 30.5 mm. Checked at nine positions over 1.5 worm turns: no overlap beyond contact.\n- With a lead angle of 5.36° (below ~6°) the drive is self-locking: the wheel cannot drive the worm. Brown's No. 31; drawn with the worm turned 30°.\n- Parts (each has its own page): worm-zi-m1-5-1start-d16-l40-bore6, worm-wheel-helical-m1-5-30t-for-1start-d16, linear-shafts-h6.\n- Brown's movement No. 31 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nworm  module 1.5, 1-start, pitch Ø16, lead angle 5.36°\nwheel  30 T helical, helix 5.36°\nratio  30 : 1\ncentre distance  30.5 mm\nshafts  90°, non-intersecting\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. 31: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_031.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/worm-and-worm-wheel-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=worm-and-worm-wheel-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. 31: figure, his text and an animation",
   "url": "https://507movements.com/mm_031.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": [
  "worm-zi-m1-5-1start-d16-l40-bore6",
  "worm-wheel-helical-m1-5-30t-for-1start-d16",
  "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 a worm and worm wheel work?",
   "a": "An endless screw (the worm) on one shaft meshes with a toothed wheel on a shaft at right angles: each turn of the worm advances the wheel one tooth (one thread), so the ratio is the tooth count — 30 : 1 here — in a single, quiet stage. The same result as the face-spiral drive of Brown's No. 29, but simpler to make, so far more used."
  },
  {
   "q": "What is the ratio of a worm drive?",
   "a": "Wheel teeth divided by worm starts: a single-start worm and a 30-tooth wheel give 30 : 1 in one stage."
  },
  {
   "q": "Why is the worm wheel a helical gear here?",
   "a": "A worm is a helical gear with very few teeth; a helical gear of the same normal module and hand, with helix angle equal to the worm's lead angle, meshes with it conjugately on crossed axes. Throated (hobbed) wheels add line contact for power, at the cost of exact axial positioning."
  }
 ],
 "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": "worm-and-worm-wheel-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/worm-and-worm-wheel-mechanism/worm-and-worm-wheel-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/worm-and-worm-wheel-mechanism/worm-and-worm-wheel-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/index.md"
}