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Sliding-triangle parallel ruler

How do two sliding triangles draw parallel lines? · Hardware · basis: Xem Studio design following Brown No. 322 (1868)

Also called: parallel ruler, sliding triangles, drafting triangles, regla paralela de triángulos, Parallellineal aus zwei Dreiecken

Exact dimensions. True size, with no printing tolerance added.

sizes
3 in table

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.

Sliding-triangle parallel ruler size chart

parametervalue
triangles2 × 120 × 40 × 4 mm
slide drawn25 mm
offset7.91 mm

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

Henry T. Brown (1868, public domain)Five Hundred and Seven Mechanical Movements — scan on archive.orgwebPublisher's page; dimensions are facts
507movements.comBrown's movement No. 322: figure, his text and an animationwebPublisher's page; dimensions are facts

Free files

★ Free files 1 parts. Generated by Xem Studio from the standard; threads are plain cylinders at major diameter. CC BY 4.0. index.json

sliding-triangle-parallel-ruler-mechanism-assemblyAssembled mechanism, all parts placed at one pose (STEP keeps each part separate)STEP · STL
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Plain text: sheet.txt · JSON: /api/geometry?object=sliding-triangle-parallel-ruler-mechanism

Sliding-triangle parallel ruler, isometric render of a generated part
Render of sliding-triangle-parallel-ruler-mechanism-assembly from the free STEP; not to scale.

Fits with

Right-triangle ruler 120 × 40 × 4 (half of a sliding parallel ruler), isometric render of a generated part
Right-triangle ruler 120 × 40 × 4 (half of a sliding parallel ruler)120.0×40.0×4.0 mm★ 1 file

Questions

How do two sliding triangles draw parallel lines?

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.