Let me take a look and see if I still have my program which would tabulate the 4-gear exact matches for small tooth-count gears (I think I did up to an annulus of 50 teeth). Scanning that should see if there are any that match your criterion. On 07/13/15 12:00, M. Oskar van Deventer wrote:
Gentlemen, While you are still discussing new theorems about the Somsky Gears (which I am unable to parse as non-mathematician), I would like to take the liberty and pose a new challenge: Offset Somsky Gears. What Bill Somksy has proven, is that there are plenty of exact solutions for planetary gears where the sun is offset from the annulus gear, with exactly meshing gears. Bill sent me the below 34-18-10-8-6 example mid 2012. G34-18-10-8-6 So how about offsetting the generating circle of each gear as shown in the image below? In this example, I offset Bill’s 34-18-10-8-6 geometry into a 35-17-11-9-7 geometry. So the circles fit in this geometry. However, when drawing the corresponding gears, you will discover that they won’t mesh. So offsetting these Somsky Gears does not yield more Somsky Gears. Offset Somsky Gears - view 1 For regular planetary gears, the classic threefold symmetrical (120-degrees) concentric geometry has many solutions with different gearing ratios that all mesh. Now, the challenge is to find asymmetric concentric planetary-gear geometry and/or a Somsky geometry that meshes, AND where the above-described offset yields another exactly meshing configuration. I hope that the challenge is a bit clear. Probably, a professional mathematician can provide a proper definition of the challenge. Enjoy! Oskar