Movable pulleys are useful to raising objects below one's head. Education.com lists a third compound, the multiple pulley, which is comprised of both fixed and movable pulley systems. These pulleys are easiest to lift objects, as the mechanical advantage increases in tandem with the inclusion of more ropes, as cited by TeachEngineering.
Massless pulleys act in very much the same way as the massless lever discussed previously. Consider the system shown below. The pulley has two radii, r 1 and r 2. If the pulley moves through an angle θ the distance x 1 is given by r 1 ·θ, and the distance x 2 is given by r 2 ·θ.
The drive element of a pulley system can be a rope, cable, belt, or chain. Hero of Alexandria identified the pulley as one of six simple machines used to lift weights. Pulleys are assembled to form a block and tackle in order to provide mechanical advantage to apply large forces.