Calculating root of bevel gear with clearance > 0

[pedro-pedrosa]

Calculating root of bevel gear with clearance > 0

[looooo]

I am not sure I understand the question. Is it possible for you to add some drawings explaining what you want to achieve?

[pedro-pedrosa]

so I have a bevel gear with a 45 degree angle

I want to cut away some parts of it as shown in this sketch

I have 3 construction lines that are concentric at the cone apex representing the addendum angle, pitch angle, and root angle. as you can see these constraints are all expressions that take values like pitch angle etc from the gear parameters. figuring out the addendum angle (49.4924 deg) is quite straightforward, figuring out the dedendum (not shown) is also possible but for the root (leftmost construction line) I also have to take the clearance value into account, but I can't figure out the math for it. right now I'm basically using the same math that is being used in this repo but I don't see how it can be correct.

[looooo]

I am not sure but I guess I defined the clearence on the base sphere (radius 1) and afterwards it is projected on to the cross sections which are used for the extrusion (loft). I didn't look into this for years, so difficult to say for me if there is something wrong with the math.

[pedro-pedrosa]

I'd be happy to look into this (measure the actual clearance in a pair of generated meshing gears) and submit a PR, if that's okay?