While I appreciate the beauty this piece, I can't help but think of the irony of such a complicated piece to explain something which mechanics and engineers, who actually use gears, understand completely intuitively.
Why is it ironic? The target audience clearly is not mechanics and engineers who actually use gears.
I had the same feeling, hoping to receive an epiphany, perhaps on the bevel of the gear teeth, but nope. Then I thought, ok, surely there's an insight to be gained regarding helical gears, but it was never discussed.
I'm not sure this is intuitive for many mechanics. I can remember studying for the ASVABs in high school (it has, or at least it did, have a whole section on spatial orientation and gears and pulleys), and it was pretty common for people to be flummoxed by the questions about picking which direction a gear in a set would turn when another was rotated. And this was with a set of people that tended to tinker on cars and snowmobiles all the time for fun.