I have a servo that is fixed and that can move a heavy load approximately one inch. I need the fixed servo to move a light load approximately 4 inches. How can I do this with a set of pulleys? Is it even possible. I don't have access to any sort of gears or timing belts either, just pulleys.
Yes it's simply a pulley in reverse - pull on the pulley block and the free end of the rope moves.
Pulling on the rope (red arrow) with a small force for a large distance, moves the load (blue arrow) with 4x the force but only 1/4x the distance.