Elliptical gear driving a pinion whose shaft slides in a slotted bar

sizes

4 in table

Notes

• Resize: multiply every length by one factor k and the motion stays identical: angles, ratios, timing and the formulas below do not change, because a mechanism's motion depends only on the ratios of its lengths. Here, scales with k: pinion travel; stays the same: elliptical gear, pinion, pose.
• Resize: Gears scale by the module m (pitch Ø = m·z, centre distance = m·(z₁ + z₂)/2): keep the tooth counts so the ratio stays, and choose a standard module (0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3).
• Resize: fit clearances stay in mm (a slide fit is the same gap at any size); keep every printed wall and pin at least two nozzle widths; mass grows with k³ but part strength only with k², so at k = 2 parts are about 8× heavier and 4× stronger: check pins and thin links when scaling up.
• An elliptical gear turning on its centre drives a round pinion; the pinion's shaft runs in a straight slot pointing at the gear's centre, so it moves in and out as the gear's radius changes and the pitch curves stay touching (Brown: a spring on the pinion's bearing holds it in).
• The pinion's speed varies twice per turn of the gear, roughly between a/r_p and b/r_p times the gear's. Here a 36-tooth, 61.4 × 46.05 mm pitch ellipse and the catalog 18-tooth module 1.5 pinion; the pinion's angle at every gear angle follows from pure rolling of the pitch curves (equal arcs), checked at 72 angles through a turn (largest 2D overlap 0.0036 mm²) and in 3D at seven poses. Drawn with the gear at 25°, the pinion's centre 42.55 mm out.
• Brown's No. 35 (pinion in a slotted bar driven by an elliptical gear). Both are basic-rack involutes, so they mesh at every point of the ellipse.
• Parts (each has its own page): elliptical-gear-m1-5-36t-centre-bore, spur-gears-module-1-5, slotted-guide-bar-150-slot8-elliptical, linear-shafts-h6.
• Brown's movement No. 35 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

Elliptical gear driving a pinion whose shaft slides in a slotted bar size chart

Where the files are

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Free files

★ Free files 1 parts. Xem Studio design: free to use, print and sell things from; not to be republished as files. Xem Studio Design License. index.json

Plain text: sheet.txt · JSON: /api/geometry?object=elliptical-gear-pinion-slotted-bar-mechanism

Fits with

Free

Elliptical gear, module 1.5, 36 teeth, b/a = 0.75, bore at the centre64.18×48.97×12.0 mm★ 1 fileFree

Spur gears, module 1.5: 10 to 80 teeth (20° involute)26 sizes★ 26 filesFree

Slotted guide bar 150 × 30 × 6, Ø8 pivot hole and 8 mm slot for a sliding pinion shaft150.0×30.0×6.0 mm★ 1 fileFree

Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long10 sizes★ 70 files