Looking at the current file, the Tile sticks out of the wall by 140mm. I think it's possible to reduce this to under 100mm. To do this, I need to design an even smaller harmonic drive, yet with high durability, low load displacement (high torsional rigidity) and high torque efficiency. I'm going to take some ideas seen in the below videos, as well as the findings I've found in the past.
For starters, I'm making all contacts metal-on-metal, looking at the pro gearbox in [Video 1]. The contacts between gears is the main part that requires the lowest tolerances, lowest friction and highest durability. "How are you going to fabricate that?", you may ask? Well, you know how the cyclodial drive in [Video 3] was made with steel dowel pins? While working on #Tetrinsic [gd0041], I found some ultra precise stainless steel tubes that come in 8mm or 10mm lengths that I plan to use as the teeth. This type of gear is called a "Lantern Pinion".
The gearbox needs to fit in a 40 x 40 x 25mm volume. 25mm is the height that the shaft of the Nema14 motors I have extends past the mounting face. Ideally, the height of the gearbox would be 20mm. As seen in [Video 1] and [Video 2], I'll be moving away from deep-groove ball bearings and instead be using loose ball bearings for the wave generator.
I'm wondering why spur gears are used instead of helical gears, looking at [Video 5]. Perhaps it's because the teeth hop from one position to the next? It could just be that it's harder to traditionally manufacture the metal harmonic gears. Another hypothesis could be that the straight tooth profile reduces displacement when a load is exerted.
I'm also wondering why a 3-contact-point wave generator is seldom used. I can only imagine it's because one would need more teeth to get the same reduction, as well as increasing the amount of contact points, hence friction.
Turns out ScienceDirect has a stack of papers related to the optimisation of "strain wave gear" and "harmonic drive", so perhaps the answers are somewhere in there... or not as I just skimmed though some and they're all essentially just optimizations.