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 On 08/03/15 10:59, William R Somsky wrote:
No, ignoring overlap, they would all be, or CAN all be, coaxial...
The one thing you need to be careful with though, is that, in general, there are several different sun-ring offsets that work for a given set of gears. If you pick one offset for one set of gears and a different one for the shifted set, they won't be coaxial. But if you pick the same offset, they are.
On 08/03/15 01:46, M. Oskar van Deventer wrote:
Dear Bill, Tom, all,
Thanks to Tom's fantastic tool and your explanation, I now understand that any set of Somsky Gears can be offset to produce an new set. I tested this with a random set from Tom's program (26-9-7-5) and I could see that its offset (25-10-6-4) is a Somsky set too. However, those two Somsky sets are not coaxial. I used some crude editing to overlay the two, see the attached figure. It is clear to see that the two are not coaxial.
Tom has already provided me with a set of Somsky Gears, which can be coaxially offset into another set of Somsky Gears. However, not all sets of Somsky Gears can be coaxially offset like this. So what is the additional requirement that enables this? Is there a quick way how I can determine whether a Somsky set can be coaxially offset?
Best regards,
Oskar
-----Original Message----- From: wrsomsky@gmail.com Sent: Friday, July 31, 2015 6:44 AM
From some thinking I've done, the answer is yes. Ignoring overlap, any set of Somsky Gears can be offset to produce an new set. You can prove it by noting that for a given ring-sun-planet, the strap-length changes by pi (one half a tooth) if you increase the ring and planet radii by one, and decrease the sun radius by one (or vice versa).
On 2015-07-21 13:12, M. Oskar van Deventer wrote:
Gentlemen,
Whiles I am still unsure whether there is agreement about Tom Rokicki's analysis that all Somsky Gears can be offset, nor can I follow that various mathematical reasonings, so I did an experiment with regular 120-degrees planetary gears. The attached sketch shows that a 26-8-10 fits as well as the 27-9-9 that it was offset from. Of course this does not prove anything, but at least it is consistent with Tom's analysis.
Oskar