Elliptical gear driving a pinion whose shaft slides in a slotted bar — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/elliptical-gear-pinion-slotted-bar-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown No. 35 (1868)
Catalog version: 2026-10-20

Sizes: see table below
- 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.

parameter  value
elliptical gear  module 1.5, 36 T, 61.4 × 46.05
pinion  18 T (catalog)
pinion travel  36.53 – 44.2 mm from the centre
pose  gear at 25°

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- 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
- 507movements.com: Brown's movement No. 35: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_035.html

Free files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/elliptical-gear-pinion-slotted-bar-mechanism/index.json
API: https://xemstudio.com/api/geometry?object=elliptical-gear-pinion-slotted-bar-mechanism