The question asks about the primary function of a double-acting cylinder in pneumatic systems, specifically in the context of workshop equipment.

A double-acting cylinder is a type of pneumatic actuator that differs from a single-acting cylinder. Below is an explanation of the options given:

1. It uses spring force to return the piston after extension: This describes a single-acting cylinder, not a double-acting cylinder. A single-acting cylinder uses air pressure in one direction and a spring for the return.

2. It provides controlled force in both directions for movement: This is the correct option. A double-acting cylinder uses air pressure for movement in both directions, which allows it to provide controlled force during both the extension and retraction strokes.

3. It creates a vacuum inside the cylinder for retraction: This is irrelevant to double-acting cylinders. Pneumatic systems generally work with compressed air, not vacuum creation for retraction.

4. It only delivers force in one direction with air pressure: This too describes a single-acting cylinder where air pressure is only applied in one direction.

In conclusion, the primary function of a double-acting cylinder in pneumatic systems is to provide controlled force in both directions for movement. This design enables efficiency and precision in various applications, such as in workshop equipment where varying levels of force may be required to move a load in both directions.