{
 "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": "tusi-couple-straight-line-mechanism",
 "name": "Tusi couple: straight line from a gear rolling inside a ring twice its size",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Gears",
 "year": null,
 "question": "How does a Tusi couple make exact straight-line motion?",
 "tags": [
  "mechanism",
  "gears",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "tusi couple",
  "cardan straight line",
  "hypocycloid straight line",
  "cardan gear",
  "par de Tusi",
  "Kardankreis (Tusi-Paar)"
 ],
 "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/tusi-couple-straight-line-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/tusi-couple-straight-line-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 329 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "A planet of half the ring's pitch diameter rolls inside it (30 T in 60 T, carrier 15 mm): any point on the planet's pitch circle moves on a straight line through the ring's centre, 4 × 15 = 60 mm long — exact, not approximate.",
   "At the drawn carrier angle 40° the planet has turned −40° and the tracer pin sits at x = 22.98, y = 0; x = 60/2 · cos θ.",
   "Brown's No. 329 uses it to guide a piston rod without slides (cog-wheel inside a fixed internal gear of twice its diameter).",
   "Parts (each has its own page): internal-ring-gear-m1-60t, spur-gears-module-1, tusi-carrier-15, tusi-tracer-arm-15, dowel-pins-metric.",
   "Brown's movement No. 329 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "ring",
     "60 T internal"
    ],
    [
     "planet",
     "30 T"
    ],
    [
     "carrier",
     "15 mm"
    ],
    [
     "stroke",
     "60 mm, straight"
    ]
   ]
  }
 },
 "sheet_text": "Tusi couple: straight line from a gear rolling inside a ring twice its size — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/tusi-couple-straight-line-mechanism/  (CC BY 4.0)\nBasis: Xem Studio design following Brown No. 329 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- A planet of half the ring's pitch diameter rolls inside it (30 T in 60 T, carrier 15 mm): any point on the planet's pitch circle moves on a straight line through the ring's centre, 4 × 15 = 60 mm long — exact, not approximate.\n- At the drawn carrier angle 40° the planet has turned −40° and the tracer pin sits at x = 22.98, y = 0; x = 60/2 · cos θ.\n- Brown's No. 329 uses it to guide a piston rod without slides (cog-wheel inside a fixed internal gear of twice its diameter).\n- Parts (each has its own page): internal-ring-gear-m1-60t, spur-gears-module-1, tusi-carrier-15, tusi-tracer-arm-15, dowel-pins-metric.\n- Brown's movement No. 329 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nring  60 T internal\nplanet  30 T\ncarrier  15 mm\nstroke  60 mm, straight\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. 329: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_329.html\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/tusi-couple-straight-line-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=tusi-couple-straight-line-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. 329: figure, his text and an animation",
   "url": "https://507movements.com/mm_329.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": [
  "internal-ring-gear-m1-60t",
  "spur-gears-module-1",
  "tusi-carrier-15",
  "tusi-tracer-arm-15",
  "dowel-pins-metric"
 ],
 "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 Tusi couple make exact straight-line motion?",
   "a": "A planet of half the ring's pitch diameter rolls inside it (30 T in 60 T, carrier 15 mm): any point on the planet's pitch circle moves on a straight line through the ring's centre, 4 × 15 = 60 mm long — exact, not approximate."
  }
 ],
 "files_license": null,
 "offers": [
  {
   "file": "tusi-couple-straight-line-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/tusi-couple-straight-line-mechanism/tusi-couple-straight-line-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/tusi-couple-straight-line-mechanism/tusi-couple-straight-line-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/tusi-couple-straight-line-mechanism/index.md"
}