The torque from the motor at F is 1200 lb-in. The allowable shearing stress is 10.5 ksi. The radii of the gears are rD = 8 in, and rG = 3 in. The torque at F due to the motor is the torque on gear G:
At the point of contact between the gears, the force of G on D is the same as the force of D on G, so
Now I use the stress equation to determine the diameters:
