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

> How can a pinion stay in mesh with an elliptical gear?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 35 (1868)
- Page: https://xemstudio.com/objects/elliptical-gear-pinion-slotted-bar-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=elliptical-gear-pinion-slotted-bar-mechanism · Plain text: https://xemstudio.com/objects/elliptical-gear-pinion-slotted-bar-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

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

## 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.

## Sizes

| 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° |

## Where the files are

- Henry T. Brown (1868, public domain): [Five Hundred and Seven Mechanical Movements — scan on archive.org](https://archive.org/details/fivehundredseven00browiala) — web — Publisher's page; dimensions are facts
- 507movements.com: [Brown's movement No. 35: figure, his text and an animation](https://507movements.com/mm_035.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/elliptical-gear-pinion-slotted-bar-mechanism/index.json · license: https://xemstudio.com/files/hardware/elliptical-gear-pinion-slotted-bar-mechanism/LICENSE.md

- elliptical-gear-pinion-slotted-bar-mechanism-assembly: [STEP](https://xemstudio.com/files/hardware/elliptical-gear-pinion-slotted-bar-mechanism/elliptical-gear-pinion-slotted-bar-mechanism-assembly.step) · [STL](https://xemstudio.com/files/hardware/elliptical-gear-pinion-slotted-bar-mechanism/elliptical-gear-pinion-slotted-bar-mechanism-assembly.stl) — Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)

## Questions

**How can a pinion stay in mesh with an elliptical gear?**

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).

## Fits with

- [Elliptical gear, module 1.5, 36 teeth, b/a = 0.75, bore at the centre](https://xemstudio.com/objects/elliptical-gear-m1-5-36t-centre-bore/)
- [Spur gears, module 1.5: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1-5/)
- [Slotted guide bar 150 × 30 × 6, Ø8 pivot hole and 8 mm slot for a sliding pinion shaft](https://xemstudio.com/objects/slotted-guide-bar-150-slot8-elliptical/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)