{
 "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": "cyclograph-arc-mechanism",
 "name": "Cyclograph: fixed-angle rules sliding on two pins draw a circular arc",
 "kind": "hardware",
 "category": "Mechanisms",
 "group": "Linkages",
 "year": null,
 "question": "How does a cyclograph draw an arc without its centre?",
 "tags": [
  "mechanism",
  "linkages",
  "kinematics",
  "507 mechanical movements"
 ],
 "aliases": [
  "cyclograph",
  "arc drawing instrument",
  "inscribed angle arc tool",
  "arch setting out",
  "ciclógrafo",
  "Zyklograph"
 ],
 "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/cyclograph-arc-mechanism/",
 "sheet_txt": "https://xemstudio.com/objects/cyclograph-arc-mechanism/sheet.txt",
 "sheet": {
  "basis": "Xem Studio design following Brown No. 403 (1868)",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Two rules fastened at a fixed angle φ slide with their edges against two pins at the ends of a chord: the apex always sees the chord under the same angle, so (inscribed-angle theorem) it moves on a circular arc through the two pins — no centre needed, which is how flat arches of large radius are set out.",
   "Chord 100 mm and φ = 120° give R = c / (2 sin φ) = 57.74 mm and a rise of 28.87 mm. The rules' edges are tangent to the Ø3 pins, so the edge apex runs 1.73 mm inside the pin-centre arc. Drawn at the top of the arc, pins touching both edges.",
   "Brown's No. 403 (cyclograph: two rules from the chord's ends to the apex of the versed sine, braced, pencil at the angle).",
   "Parts (each has its own page): cyclograph-rule-150x15x4, cyclograph-brace-165-71, cyclograph-base-plate-180x100-c100, dowel-pins-metric.",
   "Brown's movement No. 403 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size."
  ],
  "table": {
   "columns": [
    "parameter",
    "value"
   ],
   "rows": [
    [
     "chord c",
     "100 mm"
    ],
    [
     "angle φ",
     "120°"
    ],
    [
     "radius",
     "57.74 mm"
    ],
    [
     "rise (versed sine)",
     "28.87 mm"
    ],
    [
     "rules",
     "2 × 150 × 15 × 4"
    ]
   ]
  }
 },
 "sheet_text": "Cyclograph: fixed-angle rules sliding on two pins draw a circular arc — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/cyclograph-arc-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Xem Studio design following Brown No. 403 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Two rules fastened at a fixed angle φ slide with their edges against two pins at the ends of a chord: the apex always sees the chord under the same angle, so (inscribed-angle theorem) it moves on a circular arc through the two pins — no centre needed, which is how flat arches of large radius are set out.\n- Chord 100 mm and φ = 120° give R = c / (2 sin φ) = 57.74 mm and a rise of 28.87 mm. The rules' edges are tangent to the Ø3 pins, so the edge apex runs 1.73 mm inside the pin-centre arc. Drawn at the top of the arc, pins touching both edges.\n- Brown's No. 403 (cyclograph: two rules from the chord's ends to the apex of the versed sine, braced, pencil at the angle).\n- Parts (each has its own page): cyclograph-rule-150x15x4, cyclograph-brace-165-71, cyclograph-base-plate-180x100-c100, dowel-pins-metric.\n- Brown's movement No. 403 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter  value\nchord c  100 mm\nangle φ  120°\nradius  57.74 mm\nrise (versed sine)  28.87 mm\nrules  2 × 150 × 15 × 4\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. 403: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_403.html\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/cyclograph-arc-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=cyclograph-arc-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. 403: figure, his text and an animation",
   "url": "https://507movements.com/mm_403.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": [
  "cyclograph-rule-150x15x4",
  "cyclograph-brace-165-71",
  "cyclograph-base-plate-180x100-c100",
  "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 cyclograph draw an arc without its centre?",
   "a": "Two rules fastened at a fixed angle φ slide with their edges against two pins at the ends of a chord: the apex always sees the chord under the same angle, so (inscribed-angle theorem) it moves on a circular arc through the two pins — no centre needed, which is how flat arches of large radius are set out."
  }
 ],
 "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": "cyclograph-arc-mechanism-assembly",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/cyclograph-arc-mechanism/cyclograph-arc-mechanism-assembly.step",
   "stl": "https://xemstudio.com/files/hardware/cyclograph-arc-mechanism/cyclograph-arc-mechanism-assembly.stl",
   "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)"
  }
 ],
 "markdown": "https://xemstudio.com/objects/cyclograph-arc-mechanism/index.md"
}