# Watari ago (cogged cross joint)

> What is a watari ago joint?

- Category: Joinery › Japanese joinery
- Kind: Hardware
- Basis: Xem Studio design — geometry computed in the generator from traditional proportions
- Page: https://xemstudio.com/objects/watari-ago-cogged-joint/ · JSON: https://xemstudio.com/api/geometry?object=watari-ago-cogged-joint · Plain text: https://xemstudio.com/objects/watari-ago-cogged-joint/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/)

## Overall (mm)

| length | width | height |
|---|---|---|
| 80.0 | 80.0 | 35.0 |

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

## Notes

- Woodworking joint drawn for 3D printing: the parts lock together by shape, so a print can be joined without glue or screws. Drawn at true size with the parts line to line (zero gap) in their assembled position — add your printer's fit allowance to the mating faces (your AI or slicer can do this).
- Beams crossing at different heights: a shallow notch and a cog lock them while keeping both beams nearly full strength.

## Sizes

| dimension | value |
|---|---|
| stock | 20 × 20 mm square |
| parts | lower beam, upper beam |
| notch | 5 mm deep |
| cog | 6 mm wide |
| assembles | the upper beam drops onto the lower |
| holds | both beams against sliding, without cutting either deeply |

## Where the files are

- Xem Studio: [Joinery design (geometry computed in the generator from traditional proportions)](https://xemstudio.com/) — web — Xem Studio design

## Free STEP/STL (3 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/watari-ago-cogged-joint/index.json · license: https://xemstudio.com/files/hardware/watari-ago-cogged-joint/LICENSE.md

- watari-ago-cogged-joint-lower-beam: [STEP](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-lower-beam.step) · [STL](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-lower-beam.stl) — Lower beam: notched 5 mm, leaving a 6 mm cog
- watari-ago-cogged-joint-upper-beam: [STEP](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-upper-beam.step) · [STL](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-upper-beam.stl) — Upper beam: a 6 mm slot for the cog
- watari-ago-cogged-joint-assembled: [STEP](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-assembled.step) · [STL](https://xemstudio.com/files/hardware/watari-ago-cogged-joint/watari-ago-cogged-joint-assembled.stl) — All parts in their assembled position (each part its own solid)

## Questions

**Why a cog instead of a full lap?**

Each beam loses only 5 mm of depth, so both stay strong.

## Fits with

- [Cross lap joint (cross halving)](https://xemstudio.com/objects/cross-lap-joint/)
- [Bird's mouth joint (rafter seat)](https://xemstudio.com/objects/birds-mouth-joint/)