<This note is from van Deventer. I approved the non-member post, but then it was apprehended by the Math-Fun Magical Mystery Spam Filter. I had to remove the cute diagram. It's four gears of different sizes, surrounding a fifth sun gear that also rotates and has a moving center, all inside a sixth concave-circular gear. --rich> Hi Bill (Gosper), Thank you for sharing this with me. I am including Bill (Somsky) and Warren Smith at the cc, as they may be interested in this too. Oskar -------- Original Message -------- Subject: Re: [math-fun] math-fun Somsky gear controversy Date: 2015-07-12 02:30 From: Bill Gosper <billgosper@gmail.com> To: Julian Ziegler Hunts <julianj.zh@gmail.com> Cc: math-fun@mailman.xmission.com Reply-To: math-fun <math-fun@mailman.xmission.com> 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

[diagram removed --rich] 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. Another pathway to van Deventer's 11 million to 1 reducer? --Bill