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5 axis drills can machine gears of arbitrary shapes, so I looked to see if there was a car speed box that runs a coned gear rather than 5 different gears, and there weren't any results. I know that automatic gearboxes can use belts... can they use wizard-hat cog?

Are there versions that got tested?

What hitches and force conversions inefficiencies would they come up with?

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  • $\begingroup$ A bit of research should return things like Daf Variomatic... $\endgroup$
    – Solar Mike
    Commented Sep 24, 2023 at 11:16

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I'm an electrical engineer rather than mechanical, but I don't think you can machine what you want.

  • If there are the same number of splines along the cone then their spacing or pitch has to change, getting wider as you move away from the cone's tip. That presents a big problem for anything that is going to engage with it.
  • If you try to keep the pitch constant then the number of "teeth" must decrease as one approaches the cone's tip. This means that spines must "peter out" but that in turn means that the pitch will vary and that's contrary to what we're trying to do in this case.

There are other approaches. The NuVinci continuously variable bicycle hub is one. There's a link in that page to variators which you might find interesting. They're all smooth. Not a spline in sight.

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  • $\begingroup$ Oh genius I was lacking that thinking, just that gears have to parallel. There are volumetric weird gears like the triple-gear google.com/search?q=triple+gear however that is parallel too. I think that I have to question the mathematics forum. bugman123.com/Gears $\endgroup$
    – bandybabboon
    Commented Sep 25, 2023 at 3:27
  • $\begingroup$ I think you've hit it. To use gears, you need teeth, and you need the number of teeth to change moving along the cone. Gear teeth cannot be continuously variable, which is why cone drives use belts or wheels, not gears. Gear teeth on a cone that change with the diameter really isn't continuous, it's a bunch of gears stacked together. Good job, sparky. $\endgroup$
    – Tiger Guy
    Commented Sep 25, 2023 at 19:34

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