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A pulley is a wheel 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, beari ...
or
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 ...
that is designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. In the case of a pulley supported by a frame or shell that does not transfer power to a shaft, but is used to guide the cable or exert a force, the supporting shell is called a block, and the pulley may be called a sheave. A pulley may have a groove 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 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 similarl ...
, cable,
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 practiti ...
, 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. ...
. The earliest evidence of pulleys dates back to Ancient Egypt in the Twelfth Dynasty (1991-1802 BCE) 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 ...
in the early 2nd millennium BCE. 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 Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. H ...
(c. 10-70 CE) 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 ref ...
used to lift weights. Pulleys are assembled to form a block and tackle in order to provide mechanical advantage to apply large forces. Pulleys are also assembled as part of
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 practiti ...
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 hi ...
'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 scientis ...
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 block and tackle. A block and tackle is assembled so one block is attached to fixed mounting point and the other is attached to the moving load. The ideal mechanical advantage 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 block and tackle—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 r ...
s identified by Renaissance scientists. If the rope and pulley system does not dissipate or store energy, then its mechanical advantage 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 block and tackle. 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 block and tackle 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 mechanical advantage of a pulley system can be analysed using free body diagrams which balance the tension force in the rope with the force of gravity 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,Tiner, J. H. ''Exploring the World of Physics: From Simple Machines to Nuclear Energy''. Master Books (May 1, 2006) p. 68. :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
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 practiti ...
. This allows for mechanical power,
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 quant ...
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
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. ...
; however, a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, 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 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 pulleys ...
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 t ...
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 m ...
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 lu ...
s. Agricultural tractors built up to the early 1950s generally had a belt pulley for a flat belt (which is what ''
Belt Pulley ''Belt Pulley'' was a U.S.-based magazine dedicated to antique farm tractors of all brands and makes. It published successfully for over 2 decades and was one of the best known titles in the category. It was a family business run first by the Auma ...
'' 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 s ...
and hydraulics. 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 ...
s (and, correspondingly, their number of teeth) determine a gear ratio and thus the speed increases or reductions and the mechanical advantage 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 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 that can be shifted. V-belt step pulleys are the most common way that drill presses 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.


See also


References


External links

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