Pulley
Pulleys on a ship. In this context, pulleys are usually known as blocks.
Classification	Simple machine
Industry	Construction, transportation
Powered	No
Wheels	1
Axles	1

A pulley is a wheel on an axle that is designed to support movement of a cable or belt along its circumference.^[1] Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power.

A pulley is also called a sheave or drum and may have a groove between two flanges around its circumference. The drive element of a pulley system can be a rope, cable, belt, or chain that runs over the pulley inside the groove.

Hero of Alexandria identified the pulley as one of six simple machines used to lift weights.^[2] 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 and chain drives in order to transmit power from one rotating shaft to another.^[3][4]

Block and tackle[link]

Various ways of rigging a tackle.^[5]

A set of pulleys assembled so they rotate independently on the same axle form a block. Two blocks with a rope attached to one of the blocks and threaded through the two sets of pulleys form a block and tackle.^[6][7]

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 mechanical advantage of the block and tackle is equal to the number of parts of the rope that support the moving block.

In the diagram on the right the mechanical advantage of each of the block and tackle assemblies^[5] shown is as follows:

• Gun Tackle: 2
• Luff Tackle: 3
• Double Tackle: 4
• Gyn Tackle: 5
• Threefold purchase: 6

Rope and pulley systems[link]

Pulley in oil derrick

A hoist using the compound pulley system yielding an advantage of 4. The single fixed pulley is installed on the hoist (device). The two movable pulleys (joined together) are attached to the hook. One end of the rope is attached to the crane frame, another to the winch.

A rope and pulley system, that is a block and tackle, is characterized 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 machines identified by Renaissance scientists.^[8][9]

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.

• 

  A gun tackle has a single pulley in both the fixed and moving blocks with two rope parts supporting the load W.

• 

  Separation of the pulleys in the gun tackle show the force balance that results in a rope tension of W/2.

• 

  A double tackle has two pulleys in both the fixed and moving blocks with four rope parts supporting the load W.

• 

  Separation of the pulleys in the double tackle show the force balance that results in a rope tension of W/4.

How it works[link]

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 one-half the load.

• 

  Fixed pulley

• 

  Diagram 1: The load F on the moving pulley is balanced by the tension in two parts of the rope supporting the pulley.

• 

  Movable pulley

• 

  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 a 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.

• 

  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.

• 

  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."^[10] 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.

Belt and pulley systems[link]

Flat belt on a belt pulley

Belt and pulley system

Cone pulley driven from above by a line shaft

Cone pulley driven from below by an electric motor

A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed 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, 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 centered. It is sometimes referred to as a crowned pulley. Though once widely used in factory line shafts, this type of pulley is still found driving the rotating brush in upright vacuum cleaners. Agricultural tractors built up to the early 1950s generally had a belt pulley. It had limited use as the tractor and equipment being powered needed to be stationary. It has thus been replaced by other mechanisms, such as power take-off and hydraulics.

See also[link]

• Block and tackle
• Differential pulley
• Hoist
• Portsmouth Block Mills
• Reel
• V-belt

References[link]

Look up pulley in Wiktionary, the free dictionary.

Wikimedia Commons has media related to: Pulleys

Table of simple mechanisms, from Chambers' Cyclopedia, 1728.^[1] Simple machines provide a "vocabulary" for understanding more complex machines.

A simple machine is a mechanical device that changes the direction or magnitude of a force.^[2] In general, they can be defined as the simplest mechanisms that provide mechanical advantage (also called leverage).^[3]

Usually the term refers to the six classical simple machines which were defined by Renaissance scientists:^[4]

• Lever
• Wheel and axle
• Pulley
• Inclined plane
• Wedge
• Screw

A simple machine is an elementary device that has a specific movement (often called a mechanism), which can be combined with other devices and movements to form a machine. Thus simple machines are considered to be the "building blocks" of more complicated machines. This analytical view of machines as decomposable into simple machines first arose in the Renaissance as a neoclassical amplification of ancient Greek texts on technology,^[5] and is still a central part of engineering in today's age of applied science. For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle.^[6][7] Between the simple machines and complex assemblies, several intermediate classes can be defined, which may be termed "compound machines"^[8][3][9] or "machine elements".^[10] The mechanical advantage of a compound machine is simply the product of the mechanical advantages of the simple machines of which it is composed.

Various authors have compiled lists of simple machines and machine elements, sometimes lumping them together under a single term such as "simple machines",^[1] "basic machines",^[6] "compound machines",^[8] or "machine elements"; the use of the term "simple machines" in this broader sense is a departure from the neoclassical sense of the six essential simple machines, which is why many authors prefer to avoid its use, preferring the other terms (such as "machine element"). In all cases, the theme of an analytical and synthetic connection from simple to compound to complex is at work. A page from a 1728 text by Ephraim Chambers^[1] (in the figure to the right) shows more machine elements. By the late 1800s, Franz Reuleaux^[11] identified hundreds of machine elements (calling them "simple machines"). Models of these devices can be found at Cornell University's KMODDL website.^[12]

History[link]

The idea of a "simple machine" originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the "Archimedean" simple machines: lever, pulley, and screw.^[3][13] He discovered the principle of mechanical advantage in the lever.^[14] Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage.^[5] Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw,^[13] and describes their fabrication and uses.^[15] However the Greeks' understanding was limited to the statics of simple machines; the balance of forces, and did not include dynamics; the tradeoff between force and distance, or the concept of work.

During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how much useful work they could perform, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche ("On Mechanics").^[16][17] He was the first to understand that simple machines do not create energy, only transform it.^[16]

The classic rules of sliding friction in machines were discovered by Leonardo Da Vinci (1452–1519), but remained unpublished in his notebooks. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785).^[18]

Mechanical advantage[link]

A simple machine has an applied force that works against a load force. If there are no friction losses, the work done on the load is equal to the work done by the applied force. This allows an increase in the output force at the cost of a proportional decrease in the distance moved by the load. The ratio of the output force to the input force is the mechanical advantage of the machine.

If the simple machine does not dissipate or absorb energy, then its mechanical advantage can be calculated from the machine's geometry. For example, the mechanical advantage of a lever is equal to the ratio of its lever arms. A simple machine with no friction or elasticity is often called an ideal machine.^[19][20]

The mechanical advantage of an ideal simple machine is easily obtained from the requirement the rate of energy in, or power in, equals the rate of energy out, or power out, that is

Failed to parse (Missing texvc executable; please see math/README to configure.): P_{in} = P_{out}.\!

Because power is the product of a force and the velocity of its point of application, the applied force times the velocity the input point moves, v_in, must be equal to the load force times the velocity the load moves, v_out, given by

Failed to parse (Missing texvc executable; please see math/README to configure.): F_{in}v_{in} = F_{out}v_{out}.\,

So the ratio of output to input force, the mechanical advantage, of a frictionless machine is equal to the "velocity ratio"; the ratio of input velocity to output velocity:

Failed to parse (Missing texvc executable; please see math/README to configure.): MA = \frac{F_{out}}{F_{in}} = \frac{v_{in}}{v_{out}} \,

      (Ideal Mechanical Advantage)

In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned.

Compound machine[link]

A compound machine is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example a bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series.

The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{MA}_{compound} = \frac {F_{\mathrm{out} n}} {F_{\mathrm{in} 1}}. \,

Because the output force of each machine is the input of the next, Failed to parse (Missing texvc executable; please see math/README to configure.): F_{out 1}=F_{in 2} \,

and Failed to parse (Missing texvc executable; please see math/README to configure.):  F_{out k} =F_{in k+1} \,

, this mechanical advantage is also given by,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{MA}_{compound} = \frac {F_{out 1}} {F_{in 1}} \frac {F_{out 2}} {F_{in 2}} \ldots\frac {F_{out n}} {F_{in n}}. \,

Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{MA}_{compound} = \mathrm{MA}_1 \mathrm{MA}_2 \ldots\mathrm{MA}_n \,

Energy losses and efficiency[link]

Machines lose energy through friction, deformation and wear, which is dissipated as heat. This means the power out of the machine is less than power in. The ratio of power out to power in is the efficiency η of the machine, and is a measure of the energy losses,

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta = \frac{P_{out}}{P_{in}}. \,

The velocity ratio of a machine is fixed by its dimensions, so it is the mechanical advantage that is reduced by the losses, that is

Failed to parse (Missing texvc executable; please see math/README to configure.): MA = \frac{F_{out}}{F_{in}} = \eta \frac{v_{in}}{v_{out}}.

So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency η. So a machine that includes losses such as friction, deformation and wear, will not be able to move as large a load as a corresponding ideal machine using the same input force.

The efficiency of a compound machine is the product of the efficiencies of the series of simple machines that form it,

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta_{compound} = \eta_1 \eta_2 \ldots \eta_n.\,

Kinematic chains[link]

Illustration of a four-bar linkage from Kinematics of Machinery, 1876

Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.

Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a six-bar linkage or in series to form a robot.^[19]

Classification of machines[link]

The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.

However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley and wheel and axle are in essence the same device, a body rotating about a hinge, and that an inclined plane, wedge and screw are similarly a block sliding on a flat surface.^[21]

This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the rotary joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.^[19]

See also[link]

• Machine (mechanical)
• Mechanism (engineering)
• Linkage (mechanical)
• Four-bar linkage
• Six-bar linkage
• Gear train
• Mechanical advantage
• Power (physics)

References[link]