a61098417 said:
There are many solutions. There is no one correct design.
Where an additional bearing is provided, it must be positioned and aligned correctly, or it will not carry the required forces without increasing stresses in the shaft. Will you have a flexible coupling between the gearbox and the pulley shaft?
The problem with supporting the output shaft on both sides of the belt pulley is that you are restricted to a mounting that enables you to change the belts quickly, without special tools.
What does the belt drive? A compression strut, floating in spherical self-aligning bearings, between two shafts, can counter the belt tension, while making it possible to change the belt quickly.
Specify the power to be transmitted.
Specify the RPM of the output shaft.
Compute the torque in the shaft.
Specify the pulley diameter and the tension in the belt.
The minimum possible shaft diameter to consider must satisfy that torque requirement.
Now analyse the bending due to belt tension with one or two support pulleys.