Lever | |
---|---|

Classification | Simple machine |

Components | fulcrum or pivot, load and effort |

Examples | see-saw, bottle opener, etc. |

A **lever** ( /ˈliːvər/ or US: /ˈlɛvər/ ) is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or * fulcrum *. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types. Also, leverage is mechanical advantage gained in a system. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide **leverage**. The ratio of the output force to the input force is the mechanical advantage of the lever. As such, the lever is a mechanical advantage device, trading off force against movement.The formula for mechanical advantage of a lever is

The word "lever" entered English about 1300 from Old French, in which the word was *levier*. This sprang from the stem of the verb *lever*, meaning "to raise". The verb, in turn, goes back to the Latin *levare*,^{ [1] } itself from the adjective *levis*, meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European stem *legwh-*, meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light".^{ [2] }

The earliest evidence of the lever mechanism dates back to the ancient Near East circa 5000 BC, when it was first used in a simple balance scale.^{ [3] } In ancient Egypt circa 4400 BC, a foot pedal was used for the earliest horizontal frame loom.^{ [4] } In Mesopotamia (modern Iraq) circa 3000 BC, the shadouf, a crane-like device that uses a lever mechanism, was invented.^{ [3] } In ancient Egypt technology, workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers.^{ [5] }

The earliest remaining writings regarding levers date from the 3rd century BC and were provided by Archimedes. He stated, "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world".

A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the *law of the lever.*^{[ citation needed ]}

The mechanical advantage of a lever can be determined by considering the balance of moments or torque, *T*, about the fulcrum. If the distance traveled is greater, then the output force is lessened.

where F_{1} is the input force to the lever and F_{2} is the output force. The distances *a* and *b* are the perpendicular distances between the forces and the fulcrum.

Since the moments of torque must be balanced, . So, .

The mechanical advantage of the lever is the ratio of output force to input force.

This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to the pull of gravity) of both *a* and *b* change (diminish) as the lever changes to any position away from the horizontal.

Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force *the effort* and the output force *the load* or *the resistance.* This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort:^{ [6] }

**Class I**— Fulcrum between the effort and resistance: The effort is applied on one side of the fulcrum and the resistance (or load) on the other side, for example, a seesaw, a crowbar or a pair of scissors, a common balance , a claw hammer. Mechanical advantage may be greater than, less than, or equal to 1.**Class II**— Resistance (or load) between the effort and fulcrum: The effort is applied on one side of the resistance and the fulcrum is located on the other side, e.g. in a wheelbarrow, a nutcracker, a bottle opener or the brake pedal of a car, the load arm is smaller than the effort arm, and the mechanical advantage is always greater than one. It is also called force multiplier lever.**Class III**— Effort between the fulcrum and resistance: The resistance (or load) is on one side of the effort and the fulcrum is located on the other side, for example, a pair of tweezers, a hammer, a pair of tongs, fishing rod, common balance^{ [7] }or the mandible of our skull. The effort arm is smaller than the load arm. Mechanical advantage is always less than 1. It is also called speed multiplier lever.

These cases are described by the mnemonic *fre 123* where the *f* fulcrum is between *r* and *e* for the 1st class lever, the *r* resistance is between *f* and *e* for the 2nd class lever, and the *e* effort is between *f* and *r* for the 3rd class lever.

A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys.

The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot.

As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity.^{ [8] }

If *a* and *b* are distances from the fulcrum to points *A* and *B* and the force *F _{A}* applied to

This is the *law of the lever*, which was proven by Archimedes using geometric reasoning.^{ [9] } It shows that if the distance *a* from the fulcrum to where the input force is applied (point *A*) is greater than the distance *b* from fulcrum to where the output force is applied (point *B*), then the lever amplifies the input force. On the other hand, if the distance *a* from the fulcrum to the input force is less than the distance *b* from the fulcrum to the output force, then the lever reduces the input force.

The use of velocity in the static analysis of a lever is an application of the principle of virtual work.

A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force **F**_{A} at a point *A* located by the coordinate vector **r**_{A} on the bar. The lever then exerts an output force **F**_{B} at the point *B* located by **r**_{B}. The rotation of the lever about the fulcrum *P* is defined by the rotation angle *θ* in radians.

Let the coordinate vector of the point *P* that defines the fulcrum be **r**_{P}, and introduce the lengths

which are the distances from the fulcrum to the input point *A* and to the output point *B*, respectively.

Now introduce the unit vectors **e**_{A} and **e**_{B} from the fulcrum to the point *A* and *B*, so

The velocity of the points *A* and *B* are obtained as

where **e**_{A}^{⊥} and **e**_{B}^{⊥} are unit vectors perpendicular to **e**_{A} and **e**_{B}, respectively.

The angle *θ* is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by

where *F*_{A} and *F*_{B} are components of the forces that are perpendicular to the radial segments *PA* and *PB*. The principle of virtual work states that at equilibrium the generalized force is zero, that is

Thus, the ratio of the output force *F*_{B} to the input force *F*_{A} is obtained as

which is the mechanical advantage of the lever.

This equation shows that if the distance *a* from the fulcrum to the point *A* where the input force is applied is greater than the distance *b* from fulcrum to the point *B* where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point *A* is less than from the fulcrum to the output point *B*, then the lever reduces the magnitude of the input force.

- Applied mechanics – Practical application of mechanics
- Linkage (mechanical) – Assembly of bodies connected to manage forces and movement
- Mechanism (engineering)
- On the Equilibrium of Planes
- Simple machine – Mechanical device that changes the direction or magnitude of a force

In physics, **angular momentum** is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant.

A **centripetal force** is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits.

**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 this is the *law of the lever.* Machine components designed to manage forces and movement in this way are called mechanisms. An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal mechanism does not include a power source, is frictionless, and is constructed from rigid bodies that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal.

In physics, **power** is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called *activity*. Power is a scalar quantity.

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 to multiply force. Usually the term refers to the six classical simple machines that were defined by Renaissance scientists:

In physics and mechanics, **torque** is the rotational equivalent of linear force. It is also referred to as the **moment**, **moment of force**, **rotational force** or **turning effect**, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically or **τ**, the lowercase Greek letter *tau*. When being referred to as moment of force, it is commonly denoted by M.

An **inclined plane**, also known as a **ramp**, is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Inclined planes are widely used to move heavy loads over vertical obstacles; examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade.

**Magnetoresistance** is the tendency of a material to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov–de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems, giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed.

**Kinematics** is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.

**Ray transfer matrix analysis** is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element is described by a 2×2 *ray transfer matrix* which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.

In physics, a **moment** is an expression involving the product of a distance and physical quantity, and in this way it accounts for how the physical quantity is located or arranged.

In analytical mechanics, the term **generalized coordinates** refers to the parameters that describe the configuration of the system relative to some reference configuration. These parameters must uniquely define the configuration of the system relative to the reference configuration. This is done assuming that this can be done with a single chart. The **generalized velocities** are the time derivatives of the generalized coordinates of the system.

In mechanics, **virtual work** arises in the application of the *principle of least action* to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action. *The work of a force on a particle along a virtual displacement is known as the virtual work*.

The **wheel and axle** is a machine consisting of a wheel attached to a smaller axle so that these two parts rotate together in which a force is transferred from one to the other. The wheel and axle can be viewed as a version of the lever, with a drive force applied tangentially to the perimeter of the wheel and a load force applied to the axle, respectively, that are balanced around the hinge which is the fulcrum.

A **gear train** is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage.

In classical mechanics, the **shell theorem** gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy.

In classical mechanics, the **Kepler problem** is a special case of the two-body problem, in which the two bodies interact by a central force *F* that varies in strength as the inverse square of the distance *r* between them. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over time given their masses, positions, and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements.

In astronomy, **position angle** is the convention for measuring angles on the sky. The International Astronomical Union defines it as the angle measured relative to the north celestial pole (NCP), turning positive into the direction of the right ascension. In the standard (non-flipped) images, this is a counterclockwise measure relative to the axis into the direction of positive declination.

A **screw** is a mechanism that converts rotational motion to linear motion, and a torque to a linear force. It is one of the six classical simple machines. The most common form consists of a cylindrical shaft with helical grooves or ridges called *threads* around the outside. The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut can rotate around a stationary screw shaft. Geometrically, a screw can be viewed as a narrow inclined plane wrapped around a cylinder.

A **mechanical amplifier**, or a mechanical amplifying element, is a linkage mechanism that amplifies the magnitude of mechanical quantities such as force, displacement, velocity, acceleration and torque in linear and rotational systems. In some applications, mechanical amplification induced by nature or unintentional oversights in man-made designs can be disastrous. When employed appropriately, it can help to magnify small mechanical signals for practical applications.

- ↑ Chisholm, Hugh, ed. (1911).
*Encyclopædia Britannica*.**16**(11th ed.). Cambridge University Press. p. 510. . - ↑ Etymology of the word "lever" in the Online Etymological
- 1 2 Paipetis, S. A.; Ceccarelli, Marco (2010).
*The Genius of Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy, June 8-10, 2010*. Springer Science & Business Media. p. 416. ISBN 9789048190911. - ↑ Bruno, Leonard C.; Olendorf, Donna (1997).
*Science and technology firsts*. Gale Research. p. 2. ISBN 9780787602567.4400 B.C. Earliest evidence of the use of a horizontal loom is its depiction on a pottery dish found in Egypt and dated to this time. These first true frame looms are equipped with foot pedals to lift the warp threads, leaving the weaver's hands free to pass and beat the weft thread.

- ↑ Clarke, Somers; Engelbach, Reginald (1990).
*Ancient Egyptian Construction and Architecture*. Courier Corporation. pp. 86–90. ISBN 9780486264851. - ↑ Davidovits, Paul (2008). "Chapter 1".
*Physics in Biology and Medicine, Third edition*. Academic Press. p. 10. ISBN 978-0-12-369411-9. - ↑ "What is the working principle of common balance? From Physics Units and Measurement Class 11 CBSE".
- ↑ Uicker, John; Pennock, Gordon; Shigley, Joseph (2010).
*Theory of Machines and Mechanisms*(4th ed.). Oxford University Press, USA. ISBN 978-0-19-537123-9. - ↑ Usher, A. P. (1929).
*A History of Mechanical Inventions*. Harvard University Press (reprinted by Dover Publications 1988). p. 94. ISBN 978-0-486-14359-0. OCLC 514178 . Retrieved 7 April 2013.

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Look up in Wiktionary, the free dictionary. lever |

- Lever at Diracdelta science and engineering encyclopedia
*A Simple Lever*by Stephen Wolfram, Wolfram Demonstrations Project.- Levers: Simple Machines at EnchantedLearning.com

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