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 refers to the six classical simple machines that were defined by Renaissance scientists:
Lever Wheel and axle Pulley Inclined plane Wedge Screw A simple machine uses a single applied force to do work against a single load force. Ignoring friction losses, the work done on the load is equal to the work done by the applied force. A machine can therefore increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the applied force is called the mechanical advantage. Simple machines can be regarded as elementary "building blocks" of which more complicated machines (sometimes called "compound machines") are composed. For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle. The mechanical advantage of a compound machine can be determined as the product of the mechanical advantages contained in the simple machines of which it is composed. Although they continue to be of great importance in engineering and applied science, modern mechanics has moved beyond the view of the simple machines as the ultimate building blocks of which all machines are composed, which conception arose in the Renaissance as a neoclassical amplification of ancient Greek texts. The proliferation and sophistication of modern machine linkages, intensified during the Industrial Revolution, is inadequately described by these six simple categories. Various post-Renaissance authors have compiled expanded lists of "simple machines", often using terms like basic machines, compound machines, or machine elements to distinguish them from the classical simple machines above. By the late 1800s, Franz Reuleaux had identified hundreds of machine elements, calling them simple machines. Modern machine theory analyzes machines as kinematic chains composed of elementary linkages called kinematic pairs.
History 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. He discovered the principle of mechanical advantage in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," (Greek: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω) expresses his realization that there was no limit to the degree of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to calculate their (ideal) mechanical advantage. For example, Heron of Alexandria (c. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion": lever, windlass, pulley, wedge, and screw, and describes their fabrication and uses. 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 far they could lift a load, in addition to the force they could apply, 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 Mecaniche (On Mechanics), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it. The classic rules of sliding friction in machines were discovered by Leonardo da Vinci (1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an ethereal fluid. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785).
Ideal simple machine If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions. Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force F in {\displaystyle F_{\text{in}}} is applied to the device at one point, and it does work moving a load F out {\displaystyle F_{\text{out}}} at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage
M A = F out F in {\displaystyle \mathrm {MA} ={F_{\text{out}} \over F_{\text{in}}}}
that can be calculated from the machine's geometry and friction. Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. A simple machine with no friction or elasticity is called an ideal machine. Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time P out {\displaystyle P_{\text{out}}} is equal to the power input P in {\displaystyle P_{\text{in}}}
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