A pulley is a

wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...

on an

axle An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, bearing ...

shaft Shaft may refer to: Rotating machine elements * Shaft (mechanical engineering), a rotating machine element used to transmit power * Line shaft, a power transmission system * Drive shaft, a shaft for transferring torque * Axle, a shaft around whi ...

enabling a taut cable or

belt Belt may refer to: Apparel * Belt (clothing), a leather or fabric band worn around the waist * Championship belt, a type of trophy used primarily in combat sports * Colored belts, such as a black belt or red belt, worn by martial arts practition ...

passing over the wheel to move and change direction, or transfer power between itself and a shaft. A sheave or pulley wheel is a pulley using an axle supported by a frame or shell (block) to guide a cable or exert force. A pulley may have a

groove Groove or Grooves may refer to: Music * Groove (music) * Groove (drumming) * The Groove (band), an Australian rock/pop band of the 1960s * The Groove (Sirius XM), a US radio station * Groove 101.7FM, a former Perth, Australia, radio station * ...

or grooves between

flange A flange is a protruded ridge, lip or rim (wheel), rim, either external or internal, that serves to increase shear strength, strength (as the flange of an iron beam (structure), beam such as an I-beam or a T-beam); for easy attachment/transfer of ...

s around its

circumference In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to ...

to locate the cable or belt. The drive element of a pulley system can be a

rope A rope is a group of yarns, plies, fibres, or strands that are twisted or braided together into a larger and stronger form. Ropes have tensile strength and so can be used for dragging and lifting. Rope is thicker and stronger than similarly ...

cable Cable may refer to: Mechanical * Nautical cable, an assembly of three or more ropes woven against the weave of the ropes, rendering it virtually waterproof * Wire rope, a type of rope that consists of several strands of metal wire laid into a hel ...

, belt, or

chain A chain is a serial assembly of connected pieces, called links, typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression but linear, rigid, and load-bearing in tension. A c ...

. The earliest evidence of pulleys dates back to Ancient Egypt in the

Twelfth Dynasty The Twelfth Dynasty of ancient Egypt (Dynasty XII) is considered to be the apex of the Middle Kingdom by Egyptologists. It often is combined with the Eleventh, Thirteenth, and Fourteenth dynasties under the group title, Middle Kingdom. Some s ...

(1991–1802 BC) and

Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the F ...

in the early 2nd millennium BC. In

Roman Egypt , conventional_long_name = Roman Egypt , common_name = Egypt , subdivision = Province , nation = the Roman Empire , era = Late antiquity , capital = Alexandria , title_leader = Praefectus Augustalis , image_map = Roman E ...

Hero of Alexandria Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greece, Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egy ...

(c. 10–70 AD) identified the pulley as one of six

simple machines A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...

used to lift weights. Pulleys are assembled to form a

block and tackle A block and tackle or only tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift heavy loads. The pulleys are assembled to form blocks and then blocks are paired so that one is fixed and one ...

in order to provide

mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for t ...

to apply large forces. Pulleys are also assembled as part of

and

chain drive Chain drive is a way of transmitting mechanical power from one place to another. It is often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles. It is also used in a wide variety of machines besides vehicles. ...

s in order to transmit power from one rotating shaft to another.

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...

's ''

Parallel Lives Plutarch's ''Lives of the Noble Greeks and Romans'', commonly called ''Parallel Lives'' or ''Plutarch's Lives'', is a series of 48 biographies of famous men, arranged in pairs to illuminate their common moral virtues or failings, probably writt ...

'' recounts a scene where

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

proved the effectiveness of compound pulleys and the block-and-tackle system by using one to pull a fully laden ship towards him as if it was gliding through water.

Block and tackle

A block is a set of pulleys (wheels) assembled so that each pulley rotates independently from every other pulley. Two blocks with a rope attached to one of the blocks and threaded through the two sets of pulleys form a

. A

is assembled so one block is attached to the fixed mounting point and the other is attached to the moving load. The

ideal mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for t ...

of the block and tackle is equal to the number of sections of the rope that support the moving block. In the diagram on the right, the ideal mechanical advantage of each of the block and tackle assemblies shown is as follows: * Gun tackle: 2 * Luff tackle: 3 * Double tackle: 4 * Gyn tackle: 5 * Threefold purchase: 6

Rope and pulley systems

A rope and pulley system—that is, a

—is characterised by the use of a single continuous rope to transmit a tension force around one or more pulleys to lift or move a load—the rope may be a light line or a strong cable. This system is included in the list of

simple machine A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...

s identified by Renaissance scientists. If the rope and pulley system does not dissipate or store energy, then its

is the number of parts of the rope that act on the load. This can be shown as follows. Consider the set of pulleys that form the moving block and the parts of the rope that support this block. If there are ''p'' of these parts of the rope supporting the load ''W,'' then a force balance on the moving block shows that the tension in each of the parts of the rope must be ''W/p.'' This means the input force on the rope is ''T''=''W/p.'' Thus, the block and tackle reduces the input force by the factor ''p.'' Image:Polispasto2B.jpg, A gun tackle has a single pulley in both the fixed and moving blocks with two rope parts supporting the load ''W.'' Image:Pulley1a.svg, Separation of the pulleys in the gun tackle show the force balance that results in a rope tension of ''W/2.'' Image:Polispasto4.jpg, A double tackle has two pulleys in both the fixed and moving blocks with four rope parts supporting the load ''W.'' Image:Pulley3a.svg, Separation of the pulleys in the double tackle show the force balance that results in a rope tension of ''W/4.''

Method 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. In equilibrium, the forces on the moving block must sum to zero. In addition the tension in the rope must be the same for each of its parts. This means that the two parts of the rope supporting the moving block must each support half the load. Image:Polea-simple-fija.jpg, Fixed pulley Image:Pulley0.svg, Diagram 1: The load ''F'' on the moving pulley is balanced by the tension in two parts of the rope supporting the pulley. Image:Polea-simple-movil2.jpg, Movable pulley Image:Pulley1.svg, Diagram 2: A movable pulley lifting the load ''W'' is supported by two rope parts with tension ''W/2.'' These are different types of pulley systems: * Fixed: A ''fixed'' pulley has an axle mounted in bearings attached to a supporting structure. A fixed pulley changes the direction of the force on a rope or belt that moves along its circumference. Mechanical advantage is gained by combining a fixed pulley with a movable pulley or another fixed pulley of a different diameter. * Movable: A ''movable'' pulley has an axle in a movable block. A single movable pulley is supported by two parts of the same rope and has a mechanical advantage of two. * Compound: A combination of fixed and movable pulleys forms a

. A ''block and tackle'' can have several pulleys mounted on the fixed and moving axles, further increasing the mechanical advantage. Image:Pulley2.svg, Diagram 3: The gun tackle "rove to advantage" has the rope attached to the moving pulley. The tension in the rope is ''W/3'' yielding an advantage of three. Image:Pulley2a.svg, Diagram 3a: The Luff tackle adds a fixed pulley "rove to disadvantage." The tension in the rope remains ''W/3'' yielding an advantage of three. The mechanical advantage of the gun tackle can be increased by interchanging the fixed and moving blocks so the rope is attached to the moving block and the rope is pulled in the direction of the lifted load. In this case the

is said to be "rove to advantage." Diagram 3 shows that now three rope parts support the load ''W'' which means the tension in the rope is ''W/3''. Thus, the mechanical advantage is three. By adding a pulley to the fixed block of a gun tackle the direction of the pulling force is reversed though the mechanical advantage remains the same, Diagram 3a. This is an example of the Luff tackle.

Free body diagrams

The

of a pulley system can be analysed using

free body diagram A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it. In physics and engineering, a free body diagram (FBD; also called a force ...

s which balance the tension force in the rope with the

force of gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...

on the load. In an ideal system, the massless and frictionless pulleys do not dissipate energy and allow for a change of direction of a rope that does not stretch or wear. In this case, a force balance on a free body that includes the load, ''W'', and ''n'' supporting sections of a rope with tension ''T'', yields: :

n T -W = 0.

The ratio of the load to the input tension force is the mechanical advantage ''MA'' of the pulley system, :

MA = \frac = n.

Thus, the mechanical advantage of the system is equal to the number of sections of rope supporting the load.

Belt and pulley systems

A belt and pulley system is characterized by two or more pulleys in common to a

. This allows for

mechanical power : ''For the physics concept, see .'' Mechanical power is a medical term which is a measure of the amount of energy imparted to a patient by a mechanical ventilator. While in many cases mechanical ventilation is a life-saving or life-preserving int ...

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

, and

speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...

to be transmitted across axles. If the pulleys are of differing diameters, a mechanical advantage is realized. A belt drive is analogous to that of a

; however, a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket,

spur gear Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Viewing the gear at 90 degrees from the shaft length (side on) the tooth faces are straight and aligned parallel to ...

, or timing belt) so that the mechanical advantage is approximately given by the ratio of the pitch diameter of the sheaves only, not fixed exactly by the ratio of teeth as with gears and sprockets. In the case of a drum-style pulley, without a groove or flanges, the pulley often is slightly convex to keep the

flat belt A belt is a loop of flexible material used to link two or more rotating Drive shaft, shafts mechanically, most often parallel. Belts may be used as a source of motion, to Transmission (mechanics), transmit power efficiently or to track relative m ...

centered. It is sometimes referred to as a crowned pulley. Though once widely used on factory

line shaft A line shaft is a power-driven rotating shaft for power transmission that was used extensively from the Industrial Revolution until the early 20th century. Prior to the widespread use of electric motors small enough to be connected directly to e ...

s, this type of pulley is still found driving the rotating brush in upright

vacuum cleaner A vacuum cleaner, also known simply as a vacuum or a hoover, is a device that causes suction in order to remove dirt from floors, upholstery, draperies, and other surfaces. It is generally electrically driven. The dirt is collected by either a ...

s, in

belt sander A belt sander or strip sander is a sander used in shaping and finishing wood and other materials. It consists of an electric motor that turns a pair of drums on which a continuous loop of sandpaper is mounted. Belt sanders may be handheld and mo ...

s and

bandsaw A bandsaw (also written band saw) is a power saw with a long, sharp blade consisting of a continuous band of toothed metal stretched between two or more wheels to cut material. They are used principally in woodworking, metalworking, and lumb ...

s. Agricultural

tractors A tractor is an engineering vehicle specifically designed to deliver a high tractive effort (or torque) at slow speeds, for the purposes of hauling a trailer or machinery such as that used in agriculture, mining or construction. Most common ...

built up to the early 1950s generally had a belt pulley for a flat belt (which is what '' Belt Pulley'' magazine was named after). It has been replaced by other mechanisms with more flexibility in methods of use, such as

power take-off A power take-off or power takeoff (PTO) is one of several methods for taking power from a power source, such as a running engine, and transmitting it to an application such as an attached implement or separate machine. Most commonly, it is a sp ...

and

hydraulics Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

. Just as the diameters of

gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic pr ...

s (and, correspondingly, their number of teeth) determine a

gear ratio A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission ...

and thus the speed increases or reductions and the

that they can deliver, the diameters of pulleys determine those same factors. Cone pulleys and step pulleys (which operate on the same principle, although the names tend to be applied to flat belt versions and

V-belt A belt is a loop of flexible material used to link two or more rotating shafts mechanically, most often parallel. Belts may be used as a source of motion, to transmit power efficiently or to track relative movement. Belts are looped over pulley ...

versions, respectively) are a way to provide multiple drive ratios in a belt-and-pulley system that can be shifted as needed, just as a

transmission Transmission may refer to: Medicine, science and technology * Power transmission ** Electric power transmission ** Propulsion transmission, technology allowing controlled application of power *** Automatic transmission *** Manual transmission *** ...

provides this function with a

gear train A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission ...

that can be shifted. V-belt step pulleys are the most common way that

drill presses A drill is a tool used for making round holes or driving fasteners. It is fitted with a bit, either a drill or driverchuck. Hand-operated types are dramatically decreasing in popularity and cordless battery-powered ones proliferating due to i ...

deliver a range of spindle speeds. With belts and pulleys, friction is one of the most important forces. Some uses for belts and pulleys involve peculiar angles (leading to bad belt tracking and possibly slipping the belt off the pulley) or low belt-tension environments, causing unnecessary slippage of the belt and hence extra wear to the belt. To solve this, pulleys are sometimes lagged. Lagging is the term used to describe the application of a coating, cover or wearing surface with various textured patterns which is sometimes applied to pulley shells. Lagging is often applied in order to extend the life of the shell by providing a replaceable wearing surface or to improve the friction between the belt and the pulley. Notably drive pulleys are often rubber lagged (coated with a rubber friction layer) for exactly this reason.

References

External links

{{Authority control Mechanics Simple machines Mechanical power transmission Egyptian inventions