Are these approximate x and y numbers roots of polynomials? If not, thought to be algebraic anyway? If the latter, and available to high precision, I could run them through RootApproximant. --rwg On Mon, Aug 3, 2015 at 12:02 PM, William R Somsky <wrsomsky@gmail.com> wrote:
WHOOPS! Sorry, went to plot it, and found I'd done the wrong set.
The proper match to 26-9-7-5 is 26-9-5,10:
26 9 5 10 13.702903 0.072038 26 9 5 10 11.174443 0.338222 26 9 5 10 9.588008 0.585295 26 9 5 10 8.527280 0.807389 26 9 5 10 7.805237 0.997014 26 9 5 10 7.330664 0.144455 26 9 5 10 7.064324 0.236996
And 25-10-6-4 is 25-10-4,9:
25 10 4 9 13.702903 0.572038 25 10 4 9 11.174443 0.838222 25 10 4 9 9.588008 0.085295 25 10 4 9 8.527280 0.307389 25 10 4 9 7.805237 0.497014 25 10 4 9 7.330664 0.644455 25 10 4 9 7.064324 0.736996
Also 24-11-3,8:
24 11 3 8 11.174443 0.338222 24 11 3 8 9.588008 0.585295 24 11 3 8 8.527280 0.807389 24 11 3 8 7.805237 0.997014 24 11 3 8 7.330664 0.144455 24 11 3 8 7.064324 0.236996
So, using the 7.805 displacement you get the attached diagram, (also available as https://drive.google.com/open?id=0B2889vNnzpsTWVJzTTZ6TUNod0U) which has concentric gears.
WRSomsky
On 08/03/15 11:23, William R Somsky wrote:
In my tabulations, the set you call 26-9-7-5 is 26-9-5,12 (ring-sun-list-planets) where the planets are in increasing size and all from one side of the centerline. (7 & 12 form a complementary "somsky-set", if you want to call it that, but the 7 is on the opposite side of the 5)
For 26-9-5,12 you get the solutions (ring, sun, planet, planet, offset, sun-phase):
26 9 5 12 16.048313 0.500000 26 9 5 12 13.388239 1.000000 26 9 5 12 11.624141 0.500000 26 9 5 12 10.372542 0.000000 26 9 5 12 9.448488 0.500000 26 9 5 12 8.750000 1.000000 26 9 5 12 8.215897 0.500000 26 9 5 12 7.807356 1.000000 26 9 5 12 7.498839 0.500000 26 9 5 12 7.273254 1.000000 26 9 5 12 7.119219 0.500000 26 9 5 12 7.029480 1.000000 26 9 5 12 7.000000 0.500000
For 25-10-4,11 you get:
25 10 4 11 13.388239 0.500000 25 10 4 11 11.624141 1.000000 25 10 4 11 10.372542 0.500000 25 10 4 11 9.448488 1.000000 25 10 4 11 8.750000 0.500000 25 10 4 11 8.215897 0.000000 25 10 4 11 7.807356 0.500000 25 10 4 11 7.498839 0.000000 25 10 4 11 7.273254 0.500000 25 10 4 11 7.119219 0.000000 25 10 4 11 7.029480 0.500000 25 10 4 11 7.000000 0.000000
If you use the same offset, you get concentric matches.
"But you said that they can always be concentric, barring overlap? What about the 16.04?" you ask. Well, in the 25-10-4,11 case, an offset of 16.04 causes the sun and ring to overlap, and my program (and Tom's I certainly believe) doesn't even consider those cases.
If you used Tom's program, I expect it might be using the greatest possible offset, which would be 16.04 for one case, and 13.38 for the other. (Also, there may be scaling problems, as I don't know if Tom scales his image to the size of the ring gear -- mine normally does -- otherwise a set w/ a ring of 7 would look tiny, while a ring of 57 would go off the image area.)
Bill