Hi Bas. I am not sure that I can comment actually. Short answer is, in the end I used the suggestion of @swade above, and modeled my helical gears in FreeCAD, the open-source nurbs modeler.
If you get into it, the problem is around getting the tooth profile right – it is at the normal to the angle of the tooth. So Mitch’s method, i.e. taking a 2D involute gear profile, copying it say 1-inch above, rotating that top one a bit and lofting the result, won’t make a good meshing gear.
I did try to follow the theory of helical gears, but I concluded that for me, to really understand it was a deep project that I could not pursue. The main online resource though is:
SDP/SI 2019, Elements of Metric Gear Technology.
Beyond that, Radzevich 2012, Dudley’s Handbook of Practical Gear Design and Manufacture seems to be floating around the web as a pdf (just saying), and Google Books has large parts of Maitra 1994 Handbook of Gear Design, 2nd ed. I also found a good online method screed by one Ross Korsky, who wrote a helical gear script for Autodesk Fusion – Helical Gear Generator.
But as I say, I was impressed by the FreeCAD ‘Gear Workbench’. This is the work of a fellow named ‘looo’, who has a Github page for the script: https://github.com/looooo/freecad.gears
He has the maths under control, and the gears are theoretically accurate, i.e. should print good 3D gears. He’s also responsive if you ask him anything, either on Github or the FreeCAD forum.
If you want to improve Rhino’s ability in this area, by writing a script, these resources above would be the starting point. You could probably use a lot of looos’ script for the maths side of it.
As to using FreeCAD just to get a one-off job done (make in FC Gear Workbench, export to Step, then into Rhino), I made myself a note on how to make the helical gear (because I am not a regular FreeCAD user, so will forget how I did it). Here’s my ‘note to myself’:
How to make helical gears in FreeCAD:
File>New
View>Workbench>Gear
Select on toolbar ‘create involute Gear’
beta = helix angle
module = 1 / normal diametral pitch
(but note that module defaults to ‘thousandths’ so need to multiply by 1000)
(e.g. Normal Diametral Pitch of 6 is module 0.166667)
Cheers
Ian
PS, if you make your Grasshopper gear also in FC, and export to Rhino, you can compare the FC version with your GH version and see where the geometry diverges. I would trust looo. I’d be interested to hear how it goes for you.