{ "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": "sliding-triangle-parallel-ruler-mechanism", "name": "Sliding-triangle parallel ruler", "kind": "hardware", "category": "Mechanisms", "group": "Linkages", "year": null, "question": "How do two sliding triangles draw parallel lines?", "tags": [ "mechanism", "linkages", "kinematics", "507 mechanical movements" ], "aliases": [ "parallel ruler", "sliding triangles", "drafting triangles", "regla paralela de triángulos", "Parallellineal aus zwei Dreiecken" ], "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/sliding-triangle-parallel-ruler-mechanism/", "sheet_txt": "https://xemstudio.com/objects/sliding-triangle-parallel-ruler-mechanism/sheet.txt", "sheet": { "basis": "Xem Studio design following Brown No. 322 (1868)", "overall_mm": { "length": null, "width": null, "height": null }, "notes": [ "Two equal right triangles laid together on their hypotenuses make a rectangle; holding one and sliding the other along the shared hypotenuse moves its outer edge to a parallel position, offset by s·sin of the hypotenuse angle.", "Here 120 × 40 mm triangles slid 25 mm along the hypotenuse: the far edge moves 25 × 40/126.49 = 7.91 mm across (and 23.72 mm along).", "Brown's No. 322, the simplest parallel ruler.", "Parts (each has its own page): parallel-ruler-triangle-120x40.", "Brown's movement No. 322 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size." ], "table": { "columns": [ "parameter", "value" ], "rows": [ [ "triangles", "2 × 120 × 40 × 4 mm" ], [ "slide drawn", "25 mm" ], [ "offset", "7.91 mm" ] ] } }, "sheet_text": "Sliding-triangle parallel ruler — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/sliding-triangle-parallel-ruler-mechanism/ (CC BY 4.0)\nBasis: Xem Studio design following Brown No. 322 (1868)\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Two equal right triangles laid together on their hypotenuses make a rectangle; holding one and sliding the other along the shared hypotenuse moves its outer edge to a parallel position, offset by s·sin of the hypotenuse angle.\n- Here 120 × 40 mm triangles slid 25 mm along the hypotenuse: the far edge moves 25 × 40/126.49 = 7.91 mm across (and 23.72 mm along).\n- Brown's No. 322, the simplest parallel ruler.\n- Parts (each has its own page): parallel-ruler-triangle-120x40.\n- Brown's movement No. 322 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.\n\nparameter value\ntriangles 2 × 120 × 40 × 4 mm\nslide drawn 25 mm\noffset 7.91 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. 322: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_322.html\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/sliding-triangle-parallel-ruler-mechanism/index.json\nAPI: https://xemstudio.com/api/geometry?object=sliding-triangle-parallel-ruler-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. 322: figure, his text and an animation", "url": "https://507movements.com/mm_322.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": [ "parallel-ruler-triangle-120x40" ], "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 two sliding triangles draw parallel lines?", "a": "Two equal right triangles laid together on their hypotenuses make a rectangle; holding one and sliding the other along the shared hypotenuse moves its outer edge to a parallel position, offset by s·sin of the hypotenuse angle." } ], "files_license": null, "offers": [ { "file": "sliding-triangle-parallel-ruler-mechanism-assembly", "formats": [ "step", "stl" ], "price_usd": 0, "license": "CC BY 4.0 (Xem Studio)", "step": "https://xemstudio.com/files/hardware/sliding-triangle-parallel-ruler-mechanism/sliding-triangle-parallel-ruler-mechanism-assembly.step", "stl": "https://xemstudio.com/files/hardware/sliding-triangle-parallel-ruler-mechanism/sliding-triangle-parallel-ruler-mechanism-assembly.stl", "note": "Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)" } ], "markdown": "https://xemstudio.com/objects/sliding-triangle-parallel-ruler-mechanism/index.md" }