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Bevel gears for shafts at an oblique angle (60°), 20 : 30

Name: Bevel gears for shafts at an oblique angle (60°), 20 : 30 dimension sheet
Creator: Xem Studio
License: https://creativecommons.org/licenses/by/4.0/

How are gears made for shafts that meet at an angle other than 90°? · Hardware · basis: Xem Studio design following Brown No. 42 (1868)

Also called: angular bevel gears, oblique bevel gears, bevel gears 60 degrees, engranajes cónicos oblicuos, Kegelräder mit schiefem Achswinkel

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

sizes: 5 in table

Notes

Bevel gears work for any shaft angle Σ: each pitch cone angle follows from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ), and δ₁ + δ₂ = Σ. The cones still share an apex where the shafts meet.
Here Σ = 60° with 20 and 30 teeth: δ = 23.41° and 36.59°, cone distance 37.75 mm, ratio 1.5 : 1; spherical-involute teeth, drawn turned 5°.
Brown's No. 42 (gears transmitting rotary motion between shafts set obliquely).
Parts (each has its own page): bevel-gear-m1-5-20t-for-30t-60deg, bevel-gear-m1-5-30t-for-20t-60deg, linear-shafts-h6.
Brown's movement No. 42 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

Bevel gears for shafts at an oblique angle (60°), 20 : 30 size chart

parameter	value
module (large end)	1.5
teeth	20 / 30
shaft angle	60°
pitch cones	23.41° / 36.59°
ratio	1.5 : 1

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

Henry T. Brown (1868, public domain)	Five Hundred and Seven Mechanical Movements — scan on archive.org	web	Publisher's page; dimensions are facts
507movements.com	Brown's movement No. 42: figure, his text and an animation	web	Publisher's page; dimensions are facts

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

oblique-bevel-gears-mechanism-assembly

Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)

STEP · STL

Let your AI pull this. Add https://xemstudio.com/mcp to Claude, ChatGPT, Cursor or any MCP client (free, no account, one minute) and it can look up exact sizes, mating fits and free STEP/STL from every chat.

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Plain text: sheet.txt · JSON: /api/geometry?object=oblique-bevel-gears-mechanism

Bevel gears for shafts at an oblique angle (60°), 20 : 30, isometric render of a generated part — Render of oblique-bevel-gears-mechanism-assembly from the free STEP; not to scale.

Fits with

Free

Bevel pinion, module 1.5, 20 teeth for a 30-tooth wheel at 60° shaft angle, spherical involute, isometric render of a generated part

Bevel pinion, module 1.5, 20 teeth for a 30-tooth wheel at 60° shaft angle, spherical involute32.73×32.73×23.09 mm★ 1 file Free

Bevel wheel, module 1.5, 30 teeth for a 20-tooth pinion at 60° shaft angle, spherical involute, isometric render of a generated part

Bevel wheel, module 1.5, 30 teeth for a 20-tooth pinion at 60° shaft angle, spherical involute47.37×47.22×26.17 mm★ 1 file Free

Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long, isometric render of a generated part

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

Questions

How are gears made for shafts that meet at an angle other than 90°?

Bevel gears work for any shaft angle Σ: each pitch cone angle follows from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ), and δ₁ + δ₂ = Σ. The cones still share an apex where the shafts meet.