I have done some calculations about them. But the manual I used was so vague about everything that I can't honestly say why and how for certain. My current understanding is that first you select gear ratio, then you get somewhat good nominal distance for the axels, and then you adjust teeth shape to accommodate all that.
The only real constraint is that the teeth must roll into one another as you concluded.
There's a good animation on wikipedia:
https://en.wikipedia.org/wiki/Involute_gear
Involute gears are the only shape that satisfy those constraints.
http://www.ikona.ca/technologies_tooth.shtml
And the patents are about to expire...
EDIT: An application of the Ikona gear tooth form, implementing a CVT with no clutch plate or other frictional components:
One bug though: you can't back out from the site, the history is flooded with geargenerator.com addresses. Had to close the tab (Firefox 40.0.3 on Windows).
I'm seeing this a lot in apps these days. In many places I think it is intentional: where the entire state of the current view can be encoded in the URL it effectively gives you a "free" undo feature and can be quite useful (like when I'm playing with potential new running routes in Google maps).
Tested video gives a good overview... youtu.be/0R3mMUsHFvU
Need to see more reviews showing negative aspects. There's always negatives.
Edit: found a negative: shipping price. To Australia it's US$1380 for the model with air filter. That's crazy. Almost 2 grand Australian dollars for shipping.
Also, is there a way to export to a format that can be loaded into SolveSpace?
Cutting it (on a pre-Glowforge laser): https://goo.gl/photos/pxJKDipWPtj6RXvZ7
http://hessmer.org/gears/InvoluteSpurGearBuilder.html
It allows you to specify additional parameters like backlash, clearance, and profile shift. It also allows you to output in DXF which tends to be more of a standard in the engineering world.
I've been battling with making my own gears in Modo for a while (the inbuilt primitive scales the teeth size as well as number of teeth)
However this allows me to create ratios AND test them at the same time. This is invaluable.
When I get time I shall be using this for my laser cuttings.
