...
The images above depict the finished mechanism with a coordinate axis so that the origin is at the center of the train tracks, the tracks rotate around the z-axis, and the handle rotates around the y-axis. When the handle rotates around the positive y-axis, the tracks rotate around the negative z-axis. Similarly, the tracks rotate around the positive z-axis when the handle rotates around the negative y-axis. So, the signs of the input and output angular velocities are always opposites. This makes sense because the device uses external gears.
Assuming power is conserved, the (absolute value) ratio of force on the train to force on the handle (Fout/Fin) is equal to the (absolute value) ratio of velocity on the handle to the velocity of the train (Vin/Vout). The radius of the handle is r1 and distance of the train from the center of the tracks is r2.
r1 = 3.3 cm
r2 = 7 cm
The absolute value of Vin/Vout equals the absolute value of mT (torque ratio) times the ratio of the radii (r1/r2).
Vin/Vout = mT * r1/r2 = .94
Fout/Fin = .94.