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Bevel gears, module 1.5, 20 : 40, shafts at 90°

How do bevel gears turn motion through an angle? · Hardware · basis: Xem Studio design following Brown No. 25 (1868)

Also called: bevel gears, bevel gear pair, mitre gears, right angle gears, conical gears, engranajes cónicos, Kegelradgetriebe

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

sizes
6 in table

Notes

  • Two cone-shaped gears whose pitch cones share an apex roll on each other like friction cones: the shafts meet at the apex at any angle (90° here) and the ratio is the tooth ratio, 40 : 20 = 2 : 1. Equal gears at 90° are mitre gears.
  • Pitch cone angles from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ): 26.57° and 63.43°; cone distance 33.54 mm, face 11.2 mm. The teeth are exact spherical involutes, generated on a sphere about the apex, so the mesh is conjugate at every position; drawn turned 4°.
  • Brown's No. 25 (bevel gears for shafts at an angle; mitre gears when the two are equal).
  • Parts (each has its own page): bevel-gear-m1-5-20t-for-40t-90deg, bevel-gear-m1-5-40t-for-20t-90deg, linear-shafts-h6.
  • Brown's movement No. 25 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

Bevel gears, module 1.5, 20 : 40, shafts at 90° size chart

parametervalue
module (large end)1.5
teeth20 / 40
ratio2 : 1
shaft angle90°
pitch cones26.57° / 63.43°
cone distance33.54 mm

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.orgwebPublisher's page; dimensions are facts
507movements.comBrown's movement No. 25: figure, his text and an animationwebPublisher'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

bevel-gears-mechanism-assemblyAssembled 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=bevel-gears-mechanism

Bevel gears, module 1.5, 20 : 40, shafts at 90°, isometric render of a generated part
Render of bevel-gears-mechanism-assembly from the free STEP; not to scale.

Fits with

Bevel pinion, module 1.5, 20 teeth (for a 40-tooth wheel at 90°), spherical involute, isometric render of a generated part
Bevel pinion, module 1.5, 20 teeth (for a 40-tooth wheel at 90°), spherical involute32.65×32.65×22.02 mm★ 1 file
Bevel wheel, module 1.5, 40 teeth (for a 20-tooth pinion at 90°), spherical involute, isometric render of a generated part
Bevel wheel, module 1.5, 40 teeth (for a 20-tooth pinion at 90°), spherical involute61.28×61.28×32.45 mm★ 1 file
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 do bevel gears turn motion through an angle?

Two cone-shaped gears whose pitch cones share an apex roll on each other like friction cones: the shafts meet at the apex at any angle (90° here) and the ratio is the tooth ratio, 40 : 20 = 2 : 1. Equal gears at 90° are mitre gears.

What is the pitch cone angle of a 20 and 40 tooth bevel pair at 90°?

tan δ = 20/40: 26.57° for the pinion and 63.43° for the wheel.

Why are bevel teeth spherical involutes?

Every point of a bevel gear moves on a sphere about the apex; the tooth shape that rolls conjugately on that sphere is the spherical involute (Tredgold's back-cone method approximates it).