On Thu, Jul 9, 2015 at 12:14 PM, Warren D Smith <warren.wds@gmail.com> wrote:
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.
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, and the angular velocity of each gear is inversely proportional to the gear radius (big gears rotate more slowly). This should be the same for this system, and thus, I see the gears continuing to rotate forever without collision. Put another way, if I put an axle through each gear and lock it to the plane, the gears will rotate (clearly the axle through the outer gear has to be imagined). But you state it so confidently so I must be missing something important. Can you clue me in? Thanks! -- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --