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- TL;DR Summary
- I've found a paper that develops a bunch of equations related to spiral bevel gears. I want to translate those equations into programming code; but I learnt my math a lifetime ago and last used about 1/2 a lifetime ago.

The paper is https://core.ac.uk/display/10365043 (12MB pdf)

My purpose is to construct parametised spiral bevel gears (using OpenSCAD). I know how to produce a correctly formed circular cut (cylindrical) crown gear profile.

My problem is mapping that to a conical surface.

I am looking for someone to help me first understand which of the 85 equations in the paper are the two I think I need, and then help to convert them into code to construct the required affine transform(s).

I see the call for lots of supporting material, but gears are a big subject; and I'd probably end up giving lengthy explanations of wrong things; so I'm hoping it is acceptable to supply further information as required.

The diagrams in the paper are not very clear, so I'll include this which may help in inperpreting some of them.

Thanks.

My purpose is to construct parametised spiral bevel gears (using OpenSCAD). I know how to produce a correctly formed circular cut (cylindrical) crown gear profile.

My problem is mapping that to a conical surface.

I am looking for someone to help me first understand which of the 85 equations in the paper are the two I think I need, and then help to convert them into code to construct the required affine transform(s).

I see the call for lots of supporting material, but gears are a big subject; and I'd probably end up giving lengthy explanations of wrong things; so I'm hoping it is acceptable to supply further information as required.

The diagrams in the paper are not very clear, so I'll include this which may help in inperpreting some of them.

Thanks.