For the last few weeks, I have been studying The Engineer Guy's video and book about Albert Michelson's Harmonic Analyser with the intent to learn whether it could be made into a 3D printable model in OpenSCAD.
A big challenge for me was to learn names for the various gears used in that machine so that I could find ways to model them in OpenSCAD. The first component I began to explore was the Cone Gear Set, as it seems the most complicated.
For the twenty gears that generate the frequencies, it appears I could use a stack of bevel gears. There is plenty of information on bevel gears online and Greg Frost's Parametric Involute Bevel and Spur Gear library seems like a good choice for this.
However, the largest gear in the Cone Gear Set was a very peculiar gear that proved to be much more elusive. It transmits torque from the hand crank to the Cone Gear Set, but it does so at a slight angle (as shown by the red lines in the photo below).
Spur gears operate on parallel shafts. Bevel gears operate on intersecting shafts. And worm gears operate on non-intersecting shafts at a right angle to each other. What type of gear would I need for this particular case, where there are two non-intersecting and non-parallel shafts, that are not exactly perpendicular?
It took me a while to learn this is a helical gear, but a special type of helical gear called "crossed helical gears". If you google "helical gears", you will find plenty of sites that demonstrate them being used as a quieter alternative to spur gears for parallel shafts, or with non-intersecting shafts at 90 degrees to each other, but I only found two documents that speak specifically of using helical gears for transmitting torque across arbitrary angles, these documents are here (fig 7) and here.
Learning the name of this gear was half the battle. The second half was to implement this type of gearing in OpenSCAD. As I mentioned before, I had been using Greg Frost's library for my bevel gears. That library supported helical gears, but the twist parameter did not at all correspond to the so called "helix angle" you need to get them to mate two gears together in the crossed configuration.
It took me some additional sleuthing to find a different gear library, TrinaryLogic's Public Domain Involute Parameterized Gears: Powered Up, which had a compatible definition of "helix angle" suitable for crossed helical gears.
With this new library, I was able to implement Crossed Helical Gears in OpenSCAD and they are a beauty to behold:
I am attaching some OpenSCAD code that demonstrates this particular gearing arrangement. The module it defines is parametrized, so that you can easily configure different gear ratios, as well as choose any angle you desire between the two driving shafts.
While I am sure this kind of information may be obvious to the mechanical engineers out there, I hope this will help others who may need this peculiar type of gearing configuration for a project!