Hi Mr. Fisher,
... these little facets are the result of building up the teeth profile by cutting the cable into reel while rotating it by a certain degree. Selecting smaller rotation steps will result in more, but smaller ripples. As per my intuitive estimation height of ripple is a function ~wireRadius*cablePitch*sin(angleRotationStep), so an increasing number of cut-rotation steps will quickly decrease the wavelets' height, but also increase the number of facets. I think it would be reasonable to select the step's quantity equal to the number of teeth on the wheel. It would be nothing wrong to double/quadruple/... it, however successive operations on the model (milling, 3D printing, etc.) might suffer performance issue. Anyway, probably in the application in hand, wrinkles will be smoothed out in no time.
The analytical/mathematical formula describing tooth surface/profile could be probably calculated ( with some efforts though), but for now, the described approximation should suffice.
It would be also worth to consider forces vs materials vs design calculations beforehand.
I personally debt that the single tooth strength can withstand operation you briefly described.
Why not try simulating the design in SIMULATION environment of F360,
as it is, by all means, the interesting example of:
"Simulation of a springy long body interacting conformally with a squishy, curvy and continually rotating one"
Consider checking universities around, they might be interested to endow such Ph.D. dissertation? 🙂
If not, movie studios might be interested!
Regarding:
"I assume this roller gear is equally effective (smooth operation and "gripping strength") turning in either direction...correct?"
Yes, personally it would be my choice. Yes, it is bidirectional/symmetric by design with forces nicely distributed and offering limitless design variations. Such design concept functions in many technical corners of technology.
With Regards
MichaelT
Now seriously, about the simulation!
It would be a valuable educational lesson if somebody with some time in hand takes on the challenge!
MichaelT