Calculate the amount of load on each gearbox output (torque), then make some assumptions regarding how much contact area you have, which gives you the pressure at the contact areas. It's a simple lookup in material data tables to see how much bending or deformation you will have. Then probably double the pressure due to inaccuracies and check again.
Surface finish is huge. Accuracy is huge. Amount of eccentricity is important. There is sliding in this geartrain. There will be higher pressures than you think. Cycloidals don't backspin well so you'd need to freewheel the gearbox to allow the vehicle to coast. Plastic anything will not last more than 2 seconds. There is no substitute for harder steel. Cycloidals are incredibly tough but not a magic bullet.
Gearboxes are for shrinking the size of the electric engine. Given enough space, they're not necessarily needed. A car for instance, has lots of room for battery and controller and copper. Power is power, there is no cheating science.
Torque (lb.in) = 63,025 x Power (HP) / Speed (RPM)
Power (HP) = Torque (lb.in) x Speed (RPM) / 63,025
Torque (N.m) = 9.5488 x Power (kW) / Speed (RPM)
Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488
[courtesy
http://wentec.com/unipower/calculators/power_torque.asp]
These equations are equivalent everywhere in the universe, minus the singularity. On the motor shaft. On the gearbox output. On the wheels. Gearboxes only convert speed to torque, they don't create anything, allow less current for more torque or make up for a mismatched electric system. The do give the vehicle designer options. Power is power.
I bet 3d printed cycloidals won't be great, even printed metal. Ideally the positional tolerances for the ring gear and cycloid are under 0.001" each, 0.005" is marginal and anything more 0.01" will bang itself to death. Several tolerances stack up in the case of cycloidals, more so than an involute planetary, so keeping everything tight without binding is important.
-dave
