Mutual admiration society ... WFL On 7/14/15, Tom Rokicki <rokicki@gmail.com> wrote:
Gee, Fred, I was just about to say I like your graph cycle argument!
On Mon, Jul 13, 2015 at 5:45 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
In this context, I like Tom Rokicki's "continuous belt" (in another thread): it is only necessary to consider paths along which gear motion direction is everywhere a continuous function of position. Weights along such a path have all the same sign.
WFL
On 7/13/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The graph appropriate to consideration of meshing in an epicyclic gear system has vertices representing contact points, and directed edges weighted with (signed real) distances along corresponding arcs of gears.
The constraint ensuring exact meshing is that all closed paths should have total length equal to an integer, measured in units of gear teeth; it suffices to consider a finite basis comprising the faces of the (planar) graph.
Somsky's diagram referred to earlier shows an example where the lengths of both nontrivial faces are zero, once appropriate signs -- omitted there -- are taken into account.
Fred Lunnon
On 7/13/15, Warren D Smith <warren.wds@gmail.com> wrote:
I got tired of posting wrong theorem+proofs that get refuted by return mail, so I wrote it more carefully, put it in a file and stuck it on the web via dropbox. You can read the theorem & proof here:
https://dl.dropboxusercontent.com/u/3507527/GearTopologies.txt
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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