Pulley

For the band see Pulley (band); for the village see Pulley, Shropshire

A pulley is a wheel with a groove along its edge, for holding a rope or cable. Pulleys are usually used in sets designed to reduce the amount of force needed to lift a load. However, the same amount of work is necessary for the load to reach the same height as it would without the pulleys. The magnitude of the force is reduced, but it must act through a longer distance. The effort needed to pull a load up is roughly the weight of the load divided by the number of wheels. The more wheels there are, the less efficient a system is, because of more friction between the rope and the wheels. Pulleys are one of the six simple machines.

It is not recorded when or by whom the pulley was first developed, but most likely came from Eurasia. The basic building block of a pulley, the wheel, was unknown to cultures in the western hemisphere, sub-Saharan Africa and Australia until relatively recent encounters with Eurasians. It is believed however that Archimedes developed the first documented block and tackle pulley system, as recorded by Plutarch.

Types of pulleys

Polea-simple-movil.jpg

Fixed A fixed or class 1 pulley has a fixed axle. That is, the axle is "fixed" or anchored in place. A fixed pulley is used to redirect the force in a rope (called a belt when it goes in a full circle). A fixed pulley has a mechanical advantage of 1.
Movable A movable or class 2 pulley has a free axle. That is, the axle is "free" to move in space. A movable pulley is used to transform forces. A movable pulley has a mechanical advantage of 2. That is, if one end of the rope is anchored, pulling on the other end of the rope will apply a doubled force to the object attached to the pulley.
Compound A compound pulley is a combination fixed and movable pulley system.
- Block and tackle - A block and tackle is a compound pulley where several pulleys are mounted on each axle, further increasing the mechanical advantage. Plutarch reported that Archimedes moved an entire warship, laden with men, using compound pulleys and his own strength.

Theory of operation

The simplest theory of operation for a pulley system assumes that the pulleys and lines are weightless, and that there is no energy loss due to friction. It is also assumed that the lines do not stretch. With this assumption, it follows that, in equilibrium, the total force on the pulley must be zero. This means that the force on the axle of the pulley is shared equally by the two lines looping through the pulley. The situation is schematically illustrated in diagram 1. For the case where the lines are not parallel, the tensions in each line are still equal, but now the vector sum of all forces is zero. A second basic equation for the pulley follows from the conservation of energy: The product of the weight lifted times the distance it is moved is equal to the product of the lifting force (the tension in the lifting line) times the distance the lifting line is moved. The weight lifted divided by the lifting force is defined as the advantage of the pulley system. It is important to notice that the amount of work done in an ideal pulley is aways the same. The work is given by the effort times the distance moved. The pulley simply allows trading effort for distance.

Pulley1a.png In diagram 2, a single movable pulley allows a unit weight to be lifted with only half the force needed to lift the weight without assistance. The total force needed is divided between the lifting force (red arrow) and the "ceiling" which is some immovable object (such as the earth). In this simple system, the lifting force is directed in the same direction as the movement of the weight. The advantage of this system is 2. Although the force needed to lift the unit weight is only half of the unit weight, we will need to draw a length of rope that is twice the distance that the weight is lifted, so that the total amount of work done (Force x distance) remains the same.

Pulley2a.png

The addition of a fixed pulley to the single pulley system can yield an increase of advantage. In diagram 3, the addition of a fixed pulley yields a lifting advantage of 3. The tension in each line is 1/3 the unit weight, and the force on the axles of each pulley is 2/3 of a unit weight. As in the case of diagram 2a, another pulley may be added to reverse the direction of the lifting force, but with no increase in advantage. This situation is shown in diagram 3a.

Polispasto4.jpg This process can be continued indefinitely with each additional pulley yielding a unit increase in advantage. The above pulley systems are known collectively as block and tackle pulley systems. In diagram 4a, a block and tackle system with advantage 4 is shown. A practical implementation in which the connection to the ceiling is combined and the fixed and movable pulleys are encased in single housings is shown in figure 4b.

Other pulley systems are possible, and some can deliver an increased advantage with fewer pulleys than the block and tackle system. The advantage of the block and tackle system is that each pulley and line is subjected to equal tensions and forces. Efficient design dictates that each line and pulley be capable of handling its load, and no more. Other pulley designs will require different strengths of line and pulleys depending on their position in the system, but a block and tackle system can use the same line size throughout, and can mount the fixed and movable pulleys on a common axle.

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Types of pulleys

Theory of operation

See also