Yeah... Now that do the computations a bit more closely, it looks like the 7 doesn't fit exactly w/ the 5,8,11. Dang... Awfully close though. It slipped thru the 'fuzz limit' I had set to allow for inexact calculations. You called it Fred. - WRSomsky On 2015-07-30 20:34, William R Somsky wrote:
Enforcing bilateral symmetry, you can definitely get 2x5, 2x8 and 2x11 to work. The question is then if the 7's will fit properly (the 9's would follow). I know they're close, but don't know in my calculations if the discrepancies are real, or artifacts of finite precision. Do you have an analytic answer, or a numeric computation?
I don't really understand your 2pi comment though. What I'm saying is that the displacement of the sun gear from the center of the annulus is 6.479... times the "radius of a 1-tooth gear". I use this as my unit of length. (I'm not talking about a tooth pitch of 1)
- WRSomsky
On 2015-07-30 18:55, Fred Lunnon wrote:
I find that none of 8, 9, 11-tooth planets fits exactly on the same side of the axis with 7, 5 . (Of course 9, 11 fit happily on the other side.)
The discrepancy is however only ~1/10000 at ring-sun offset 6.479405920550 using our customary units.
Unfortunately, Tom Rockiki's simulator is not yet sufficiently advanced to do more than confirm that 7, 5 co-exist (to working accuracy, at any rate).
Contradicting the assertion below, these numbers should be divided by 2pi for unit teeth.
WFL
On 7/30/15, William R Somsky <wrsomsky@gmail.com> wrote:
I've not confirmed the mesh analytically as yet, but I believe this is an exact "Somsky-Gear" system of 10 planets, all non-overlapping:
Annulus: 73 teeth, Sun: 57, Planets: 2x5, 2x7, 2x8, 2x9, 2x11 Sun Displacement: 6.47941... (in units where a gear of radius n has n teeth)
Static png: https://drive.google.com/open?id=0B2889vNnzpsTMjEwNDlDSnZjRWc Animated gif: https://drive.google.com/open?id=0B2889vNnzpsTNTBFUGhqVXNGTjQ
-- WRSomsky <wrsomsky@gmail.com>
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