gear ring inner helical

I've been toying around with something similar to @rodrigo_rivas_costa 's Bevel Gears script, but for spur + helix + tapered + inner [ring] gears. Think helical spur gears like you'd get from the usual script, but with a taper towards the outer edge. Analytical solutions like Rodrigo's are beyond my math skills, but I've…

I am trying to create something like this http://tim.cexx.org/?p=1282 It is a gear driven 3D printed peristaltic pump using helical gears. How do I design the profile of the ring gears. In the Planetary Gear Set Simple how was the profile of the ring gears teeth arrived at (sketch 3)? The tooth from this sketch is then…