I was looking at harmonic drives on AliExpress (to see how my £4 hypothetical solution measured up) and I've just realised that I've actually modelled a 13:1 reduction, not 14:1 as intended. I'd need efficiencies of >77% to obtain 10x torque. I've also remembered that the actual torque of Nema motors usually peak at 75% their rated torque (e.g. you only get 0.9Nm from a 1.2Nm Nema23). so even if I did get the 10x torque, I might only have 1.425Nm to work with.
Assuming I use a 148mm arm, and also assuming that it center of mass when fully extended (see below) is 200mm, I only have 727gf. Oh, I don't have to assume where the center of mass is, at least by just going off the 3 motors.
It's 173mm away, which equates to 840gf. Remember, that doesn't include a lot of other components that could push it out further.
Each motor is 175g on its own and the harmonic gearbox is likely 25g or more, so I'm already down like 600gf ish.
I've also looked into the pile of papers that exist for harmonic drive reducers, and I found this interesting part of one:
The teeth actually look rather cylindrical, no? I can also see that the actual mesh angle is rather steep actually, further implying that I should try to keep that angle under 30 degrees. If I changed the design for a 14:1, I'd get a 35 degree angle. I could always change the flexspline pins for 1mm pins and get a mighty steep 10 degree angle though.
Lastly, I remembered that the difference between the major and minor axis of the elipse required will be different at the wave generator compared to right at the pins. Think of doing an offset on a rectangle (see below). The inside rectangle is much narrower than the outside one. The same thing happens for the wave generator, and it was 0.6mm short. That doesn't sound like much, but it's like 0.3mm each side, which is 20% the diameter of a pin.