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Elliptic trammel (trammel of Archimedes, ellipsograph)

How does an elliptic trammel draw an ellipse? · Hardware · basis: Xem Studio design following Brown No. 152 (1868)

Also called: elliptic trammel, trammel of archimedes, ellipsograph, ellipse drawing tool, trasmallo de Arquímedes (elipsógrafo), Ellipsenzirkel

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

sizes
4 in table

Notes

  • Two blocks slide in crossed grooves and carry a bar; a point on the bar a distance a from one block and b from the other draws an ellipse with semi-axes a and b.
  • Here the blocks are 40 mm apart on an 80 mm centre-hole link and the pen hole is 40 mm beyond: semi-axes 80 and 40 mm. At 50° the pen is at (51.42, 30.64); x²/80² + y²/40² = 1.
  • Brown's No. 152 (ellipsograph: traverse bar with two studs sliding in grooves of a cross).
  • Parts (each has its own page): trammel-cross-plate-140, slide-block-12x6, centre-hole-link-80, dowel-pins-metric.
  • Brown's movement No. 152 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

Elliptic trammel size chart

parametervalue
semi-axis a80 mm
semi-axis b40 mm
blocks2 × 12 × 6.2 × 5
grooves6.2 × 5 deep, crossed

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. 152: 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

elliptic-trammel-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=elliptic-trammel-mechanism

Elliptic trammel (trammel of Archimedes, ellipsograph), isometric render of a generated part
Render of elliptic-trammel-mechanism-assembly from the free STEP; not to scale.

Fits with

Trammel cross plate 140 × 140 × 8 with crossed 6.2 mm grooves, isometric render of a generated part
Trammel cross plate 140 × 140 × 8 with crossed 6.2 mm grooves140.0×140.0×8.0 mm★ 1 file
Slide block 12 × 6.2 mm for a 6.4 mm slot, isometric render of a generated part
Slide block 12 × 6.2 mm for a 6.4 mm slot2 sizes★ 1 file
Centre-hole link, 80 mm (three Ø3 holes: −40, 0, +40), isometric render of a generated part
Centre-hole link, 80 mm (three Ø3 holes: −40, 0, +40)90.0×10.0×5.0 mm★ 1 file
Dowel pins, 2–6 mm (ISO 2338 / DIN 6325), isometric render of a generated part
Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)5 sizes★ 23 files

Questions

How does an elliptic trammel draw an ellipse?

Two blocks slide in crossed grooves and carry a bar; a point on the bar a distance a from one block and b from the other draws an ellipse with semi-axes a and b.

Which point draws a circle?

The midpoint between the two blocks (a = b) draws a circle of radius half their spacing.