[Chris is me]

Originally Posted by asid61

I looked into using just 32 pitch, 20* pressure angle gears for the initial reduction stage once.
The problem is that your design actually won't get any smaller or lighter. This is because the CIM shaft is 8mm. A 20p or 32p gear that has an 8mm bore will have a diameter of around 0.6" regardless of its pitch. Then the mating gear will need to have a pitch diameter of between 2-4", regardless of pitch again, because the speed ratio is determined by the pitch diameters, not pitch.

In short, this isn't true.

In this case, two factors determine the minimum diameter (and by extension pitch diameter) of a gear. You are right in that the first factor is the shaft size - obviously the pitch diameter can't be smaller than 8mm. The second factor determining the minimum diameter of the gear is the tooth size. In theory, the smallest possible gear would have an outer diameter equal to the bore plus 2x the tooth height. Since a 32 DP gear tooth is much smaller than a 20T gear tooth (that's the point!), the pinion can be smaller as well.

In the real world, there needs to be some material between the bore and the root of the gear teeth for a gear to hold up, but not a lot. Let's say 1mm of material is needed between the bore and the teeth making the minimum root diameter 10mm, or .393 inches.

This root diameter is just shy of the root diameter of a 15 tooth pinion. A 15 tooth 32DP gear has an outer diameter of ~.531 inches and a pitch diameter of ~.469 inches. Compare these to the smallest practical 20 DP pinion*, 12 tooth, which has an outer diameter of .7 inches and a pitch diameter of .6 inches, and you can see that the 32DP pinion can be much smaller.

This allows for a reduction in a smaller space, even accounting for the greater number of teeth on the 32DP gear. Say you want a 4:1 reduction. That would be a 15:60 pair in the 32DP example and a 12:48 in the 20DP example. The 32DP gearset center distance would be ~1.172 inches, while the 20DP gearset center distance would be ~1.5 inches.

If you want to experience this for yourself, just make a CAD model of a basic, single-stage gearbox and see what happens.

This is a great way to demonstrate that a 32DP initial reduction saves space. Just use the AndyMark 15T and 60T models (they're just pitch circles, by the way) and compare them to either AndyMark or VexPro models for 12T and 48T gears. On 2791's 2014 robot, we used the 32DP gearset to save space in several large reduction gearboxes. Our winch would not have been able to nicely package itself at the back of our shooter, with the winch rope popping out around the middle of the gearbox, if we did not use the 32DP gearset.

Also, some tips on lightening gears: If you can, I would pocket the gears at their current thickness before thinning them. You can take a lot of material out of a gear by turning the gear on a lathe and thinning the material between the bore and the root, or by drilling a hole circle into the gear. Done right, strength shouldn't be compromised at all (teeth still fail first) and you'll save a dramatic amount of weight.

* An 11 tooth pinion that doesn't use the 12T pitch circle is possible, but it gets a bit weaker than I'm comfortable with, especially when the 11T with 12T pitch circle gear is both COTS and much stronger.