However, if the radii b and b' are unequal then Somsky's proof indicates the two gears with centers B and B' will rotate at constant angular velocity hence necessarily eventually collide.
TR: I just don't see this at all; why must they rotate at constant angular velocity? For any flat 2D system of gears not slipping, the speed of movement of the contact points on each gear is fixed across all gears, WDS: Only if all axes have fixed location are the rim speeds constant! And if you look at the Deventer video https://www.youtube.com/watch?v=M_BUn4TDns8 about 2:37-3:10 you can see with own eyes that the sun gear is about to hit the outer rim when he pulls it over... in the pictorial proof by Somsky he calls the angle Omega... -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)