I'm trying to design a system of two arms connected by a couple of gears. The attached picture shows the setup better than I can describe it. Note, the arms are of equal length and the gears are of equal size. What I'm trying to understand is how to calculate the optimal number of teeth per gear. I want them strong enough to support the intended load (say, 150 lbs puling in the direction of the blue arrow - and I do realize that the arm length matters) and to minimize machining costs, but small enough to ensure smooth operation. I'm not sure what material I'll use, but brass, aluminium, and stainless steel are all on the table. Can anyone point me in the right direction? I'm not looking so much for the absolute answer, but where go to start learning about how to do this sort of analysis and design. Thanks in advance.