On Sun, Jul 12, 2015 at 2:30 AM, Bill Gosper <billgosper@gmail.com> wrote:
On Sat, Jul 11, 2015 at 11:59 PM, Julian Ziegler Hunts < julianj.zh@gmail.com> wrote:
Rokicki's right; Smith's misreading the proof (more specifically, I think he's noticing that two angles are the same, but thinking that those two angles change when the mechanism is rotating, which they don't—they're related to the relative positions of the gears).
The hard parts in animating gears are (i) the fact that gears don't actually move as if they're non-slipping adjacent circles and (ii) deciding what the teeth should look like, paying attention to the fact that, because (i) is most easily solved by ignoring it, you have to put effort into making it look realistic (no intersections, no gaps).
I mostly ignored these problems in creating the attached gif, which shows a complete cycle. It's not very smooth, but it gets the point across and it's already 1.6MB.
Julian
gosper.org/blockysomsky2.gif Superb. Thank you! Considering the spectrum of possible working configurations, it looks like the revolution (not rotation) period of the sun gear goes to infinity as its radius of gyration goes to zero.
Obviously wrong. It's just the orbital periods of the planets. Derp. --Bill
Another pathway to van Deventer's 11 million to 1 reducer? --Bill