Mode of Operation
A differential pulley can lift very large masses a short distance. It consists of two fixed pulleys of unequal radii that are attached to each other and rotate together, a single pulley bearing the load, and an endless rope looped around the pulleys. To avoid slippage, the rope is usually replaced by a chain, and the connected pulleys by sprockets.
The two sections of chain carrying the single pulley exert opposing and unequal torques on the connected pulleys, such that only the difference of these torques has to be compensated manually by pulling the loose part of the chain. This leads to a mechanical advantage: the force needed to lift a load is only a fraction of the load's weight. At the same time, the distance the load is lifted is smaller than the length of chain pulled by the same factor. This factor (the mechanical advantage MA) depends on the relative difference of the radii r and R of the connected pulleys:
The effect on the forces and distances (see figure) is quantitatively:
The difference in radii can be made very small, making the mechanical advantage of this pulley system very large. In the extreme case of zero difference in radii, MA becomes infinite, thus no force (besides friction) is needed to move the chain, but moving the chain will no longer lift the load.
At the other extreme, when r is zero, the system becomes a simple gun tackle with a mechanical advantage of 2.
The same principle is used in a differential windlass, where the connected pulleys are replaced by winches.
Read more about this topic: Differential Pulley
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