The compound

lever A lever 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 div ...

is a

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 ...

operating on the premise that 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. Almost all scales use some sort of compound lever to work. Other examples include

nail clippers A nail clipper (also called nail clippers, a nail trimmer, a nail cutter or nipper type) is a hand tool used to trim fingernails, toenails and hangnails. Design Nail clippers are usually made of stainless steel but can also be made of plastic a ...

and

piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

keys.

Mechanical advantage

arm uses the

fulcrum A fulcrum is the support about which a lever pivots. Fulcrum may also refer to: Companies and organizations * Fulcrum (Anglican think tank), a Church of England think tank * Fulcrum Press, a British publisher of poetry * Fulcrum Wheels, a bicy ...

to lift the load using and intensifying an applied

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

. In practice, conditions may prevent the use of a single lever to accomplish the desired result, e.g., a restricted space, the inconvenient location of the point of delivery of the resultant force, or the prohibitive length of the lever arm needed. In these conditions, combinations of simple levers, called compound levers, are used. Compound levers can be constructed from first, second and/or third-order levers. In all types of compound lever, the rule is that force multiplied by the force arm equals the weight multiplied by the weight arm. The output from one lever becomes the input for the next lever in the system, and so the advantage is magnified. The figure on the left illustrates a compound lever formed from two first-class levers, along with a short derivation of how to compute the mechanical advantage. With the dimensions shown, the mechanical advantage, W/F can be calculated as meaning that an applied force of 1 pound (or 1 kg) could lift a weight of 7.5 lb (or 7.5 kg). Alternatively, if the position of the fulcrum on lever AA' were moved so that and then the mechanical advantage W/F is calculated as meaning that an applied force will lift an equivalent weight and there is no mechanical advantage. This is not usually the goal of a compound lever system, though in rare situations the geometry may suit a specific purpose. Nail clipper compound lever

The distances used in calculation of mechanical advantage are measured perpendicular to the force. In the example of a

nail clipper A nail clipper (also called nail clippers, a nail trimmer, a nail cutter or nipper type) is a hand tool used to trim fingernails, toenails and hangnails. Design Nail clippers are usually made of stainless steel but can also be made of plastic an ...

on the right (a compound lever made of a class 2 and a class 3 lever), because the effort is applied vertically (that is, not

perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...

to the lever), distances to the respective fulcrums are measured horizontally, instead of along the lever. In this example, W/F is Note that (7 + 1) cm = 8 cm is the distance from the point of application of the effort to the fulcrum of the first lever, perpendicular to the applied effort.

Examples

A few examples of the compound lever are the scale, train brakes, and a common type of

. Another example is the elbow-joint press, which is used in printing, molding or

handloading Handloading, or reloading, is the practice of making firearm cartridges by assembling the individual components (case, primer, propellant, and projectile), rather than purchasing mass-assembled, factory-loaded ammunition. The term ''hand ...

bullets, minting coins and medals, and in hole punching. Compound balances are used to weigh heavy items. These all use multiple levers to magnify force to accomplish a specific purpose. The train brake translates the force of pushing back the stick to the levers and they rub against the wheels, using friction to slow and eventually stop the train. These are everyday applications of this mechanism. Broadwood grand square action

A piano key is a compound lever of the first-class, since the fulcrum is between the weight to be moved and the power. The purpose of this lever is to translate a small movement (depression of the key) into a larger and fast movement of the hammer on the strings. The quality of the resulting tone depends on whether the final speed is brought about by gradual or sudden movement of the key. Illu auditory ossicles-en

The ''

malleus The malleus, or hammer, is a hammer-shaped small bone or ossicle of the middle ear. It connects with the incus, and is attached to the inner surface of the eardrum. The word is Latin for 'hammer' or 'mallet'. It transmits the sound vibrations fro ...

'', ''

incus The ''incus'' (plural incudes) or anvil is a bone in the middle ear. The anvil-shaped small bone is one of three ossicles in the middle ear. The ''incus'' receives vibrations from the ''malleus'', to which it is connected laterally, and transmit ...

'' and ''

stapes The ''stapes'' or stirrup is a bone in the middle ear of humans and other animals which is involved in the conduction of sound vibrations to the inner ear. This bone is connected to the oval window by its annular ligament, which allows the foot ...

'' are small bones (ossicles) in the

middle ear The middle ear is the portion of the ear medial to the eardrum, and distal to the oval window of the cochlea (of the inner ear). The mammalian middle ear contains three ossicles, which transfer the vibrations of the eardrum into waves in the ...

, connected as compound levers, that transfer sound waves from the

eardrum In the anatomy of humans and various other tetrapods, the eardrum, also called the tympanic membrane or myringa, is a thin, cone-shaped membrane that separates the external ear The outer ear, external ear, or auris externa is the extern ...

to the

oval window The oval window (or ''fenestra vestibuli'' or ''fenestra ovalis'') is a membrane-covered opening from the middle ear to the cochlea of the inner ear. Vibrations that contact the tympanic membrane travel through the three ossicles and into the in ...

of the

cochlea The cochlea is the part of the inner ear involved in hearing. It is a spiral-shaped cavity in the bony labyrinth, in humans making 2.75 turns around its axis, the modiolus. A core component of the cochlea is the Organ of Corti, the sensory org ...

History

The earliest remaining writings regarding levers date from the 3rd century BC and were provided by

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 ...

. "''Give me a place to stand, and I shall move the earth with a lever''" is a remark attributed to Archimedes, who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria). One of the earliest examples of a compound lever is from

Han dynasty The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...

(202 BC - 220 AD) crossbow trigger mechanisms which featured a triple compound lever. Such a mechanism was placed within the crossbow stock itself. The idea of the compound lever is attributed to the

Birmingham Birmingham ( ) is a city and metropolitan borough in the metropolitan county of West Midlands in England. It is the second-largest city in the United Kingdom with a population of 1.145 million in the city proper, 2.92 million in the West ...

inventor John Wyatt in 1743, when he designed a

weighing machine A scale or balance is a device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, and weight balances. The traditional scale consists of two plates or bowls suspended at equal distances from a ...

that used four compound levers to transfer a load from a weighing platform to a central lever from which the weight could be measured.

References

{{Reflist Mechanical engineering Simple machines