# Bisecting gauge (centre finder with two equal links)

> How does a bisecting gauge find the middle?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 410 (1868)
- Page: https://xemstudio.com/objects/bisecting-gauge-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=bisecting-gauge-mechanism · Plain text: https://xemstudio.com/objects/bisecting-gauge-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

- Two cheeks on a cross-bar (one fixed, one sliding and locked by a thumb-screw) are the pivots of two equal links that meet at a pin carrying the marking point: the point is always on the perpendicular bisector of the cheeks, so set the cheeks against the two sides of a bar and drag the gauge along — it scribes the centre line whatever the width.
- Drawn with the cheeks 70 mm apart and the 50 mm catalog links: marker 35.71 mm from the bar's line. Leaving the sliding cheek free and pressed to the work bisects tapered pieces too, as Brown notes.
- Brown's No. 410 (bisecting gauge).
- Parts (each has its own page): gauge-cross-bar-160x12x6, gauge-cheek-12x40x16-ch12x6, four-bar-links, dowel-pins-metric.
- Brown's movement No. 410 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| cheeks | 2 × 12 × 40 × 16 |
| links | 2 × 50 mm (equal) |
| cheek spacing drawn | 70 mm |
| marker offset | 35.71 mm |

## 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. 410: figure, his text and an animation](https://507movements.com/mm_410.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/bisecting-gauge-mechanism/index.json · license: https://xemstudio.com/files/hardware/bisecting-gauge-mechanism/LICENSE.md

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

## Questions

**How does a bisecting gauge find the middle?**

Two cheeks on a cross-bar (one fixed, one sliding and locked by a thumb-screw) are the pivots of two equal links that meet at a pin carrying the marking point: the point is always on the perpendicular bisector of the cheeks, so set the cheeks against the two sides of a bar and drag the gauge along — it scribes the centre line whatever the width.

## Fits with

- [Gauge cross-bar 160 × 12 × 6](https://xemstudio.com/objects/gauge-cross-bar-160x12x6/)
- [Gauge cheek 12 × 40 × 16 with a 12 × 6 channel for the bar and Ø3 link pivot](https://xemstudio.com/objects/gauge-cheek-12x40x16-ch12x6/)
- [Four-bar links: flat links with 20 to 100 mm hole centres](https://xemstudio.com/objects/four-bar-links/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)