Gearboxes can be engineered to allow gear ratio changes to enable output shaft speed while keeping the input speed and torque at the same value.   The primary advantage for using a gearbox for changing speed is to enable the full power to be transmitted at the different speeds.  Electric motors and other prime movers are rated for a maximum torque at the optimum speed.  If the speed is reduced using electronic controls the resulting developed torque is not proportionally increased.Gearboxes also allow the input shaft and the output shaft to be in different directions.
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