{
 "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-zi-m1-5-1start-d16-l40-bore6",
 "name": "Worm (involute helicoid, ZI), axial module 1.5, 1-start, pitch Ø16 × 40, Ø6 bore",
 "kind": "modern",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "What are the dimensions of a module 1.5, 1-start worm?",
 "tags": [
  "mechanism part",
  "507 mechanical movements"
 ],
 "aliases": [
  "worm",
  "endless screw",
  "involute helicoid worm",
  "ZI worm",
  "tornillo sin fin",
  "Schnecke (Evolventenschnecke)"
 ],
 "overall_mm": {
  "length": 19,
  "width": 19,
  "height": 40
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": false,
 "free_files": 1,
 "url": "https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/",
 "sheet_txt": "https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown's figure (1868); true size, no printing allowance",
  "overall_mm": {
   "length": 19,
   "width": 19,
   "height": 40
  },
  "notes": [
   "Right-hand involute-helicoid (ZI) worm: axial module 1.5, 1 start, pitch Ø16, lead 4.71 mm, lead angle γ = atan(m z₁ / d₁) = 5.36°, normal module 1.49, normal pressure angle 20°; tip Ø19, root Ø12.25 (addendum m, dedendum 1.25 m), thread thickness πm/2 on the pitch cylinder.",
   "Every transverse section is an involute of the base cylinder Ø3.97 (rb = r₁ cos αt, tan αt = tan 20° / sin γ, αt = 75.62°), swept helically along the 40 mm length (8.49 turns): the flank is an exact involute helicoid, the surface of a helical gear with 1 tooth, so it meshes conjugately with any involute helical gear of normal module 1.49 on crossed axes.",
   "Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features)."
  ],
  "table": {
   "columns": [
    "dimension",
    "value"
   ],
   "rows": [
    [
     "axial module",
     "1.5"
    ],
    [
     "starts",
     "1"
    ],
    [
     "pitch Ø",
     "16 mm"
    ],
    [
     "lead",
     "4.71 mm"
    ],
    [
     "lead angle",
     "5.36°"
    ],
    [
     "normal module",
     "1.49"
    ],
    [
     "tip / root Ø",
     "19 / 12.25 mm"
    ],
    [
     "length",
     "40 mm"
    ],
    [
     "bore",
     "Ø6"
    ]
   ]
  }
 },
 "sheet_text": "Worm (involute helicoid, ZI), axial module 1.5, 1-start, pitch Ø16 × 40, Ø6 bore — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown's figure (1868); true size, no printing allowance\nCatalog version: 2026-10-20\n\nOverall (mm): length 19.0, width 19.0, height 40.0\n- Right-hand involute-helicoid (ZI) worm: axial module 1.5, 1 start, pitch Ø16, lead 4.71 mm, lead angle γ = atan(m z₁ / d₁) = 5.36°, normal module 1.49, normal pressure angle 20°; tip Ø19, root Ø12.25 (addendum m, dedendum 1.25 m), thread thickness πm/2 on the pitch cylinder.\n- Every transverse section is an involute of the base cylinder Ø3.97 (rb = r₁ cos αt, tan αt = tan 20° / sin γ, αt = 75.62°), swept helically along the 40 mm length (8.49 turns): the flank is an exact involute helicoid, the surface of a helical gear with 1 tooth, so it meshes conjugately with any involute helical gear of normal module 1.49 on crossed axes.\n- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).\n\ndimension  value\naxial module  1.5\nstarts  1\npitch Ø  16 mm\nlead  4.71 mm\nlead angle  5.36°\nnormal module  1.49\ntip / root Ø  19 / 12.25 mm\nlength  40 mm\nbore  Ø6\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- Xem Studio: drawing — web — Publisher's page; dimensions are facts — https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/index.json\nAPI: https://xemstudio.com/api/geometry?object=worm-zi-m1-5-1start-d16-l40-bore6\n",
 "sources": [
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   "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"
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   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
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   "publisher": "507movements.com",
   "title": "Brown's movement No. 31: figure, his text and an animation",
   "url": "https://507movements.com/mm_031.html",
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    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
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   "title": "drawing",
   "url": "https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/",
   "formats": [
    "web"
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   "license": "Publisher's page; dimensions are facts",
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  "status": "free-files",
  "sheet_free": true,
  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "worm-and-worm-wheel-mechanism"
 ],
 "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": "What are the dimensions of a module 1.5, 1-start worm?",
   "a": "Right-hand involute-helicoid (ZI) worm: axial module 1.5, 1 start, pitch Ø16, lead 4.71 mm, lead angle γ = atan(m z₁ / d₁) = 5.36°, normal module 1.49, normal pressure angle 20°; tip Ø19, root Ø12.25 (addendum m, dedendum 1.25 m), thread thickness πm/2 on the pitch cylinder."
  }
 ],
 "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."
 },
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   "file": "worm-zi-m1-5-1start-d16-l40-bore6",
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   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/worm-zi-m1-5-1start-d16-l40-bore6.step",
   "stl": "https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/worm-zi-m1-5-1start-d16-l40-bore6.stl",
   "note": "worm, axis Z, z 0..40, a thread centred on +X at z = 0"
  }
 ],
 "markdown": "https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/index.md"
}