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A worker operating a milling machine in the early 20th century

A machine is a thermodynamic system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.

Renaissance natural philosophers identified six simple machines which were the elementary devices that put a load into motion, and calculated the ratio of output force to input force, known today as mechanical advantage.[1]

Modern machines are complex systems that consist of structural elements, mechanisms and control components and include interfaces for convenient use. Examples include: a wide range of vehicles, such as trains, automobiles, boats and airplanes; appliances in the home and office, including computers, building air handling and water handling systems; as well as farm machinery, machine tools and factory automation systems and robots.

Etymology

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The English word machine comes through Middle French from Latin machina,[2] which in turn derives from the Greek (Doric μαχανά makhana, Ionic μηχανή mekhane 'contrivance, machine, engine',[3] a derivation from μῆχος mekhos 'means, expedient, remedy'[4]).[5] The word mechanical (Greek: μηχανικός) comes from the same Greek roots. A wider meaning of 'fabric, structure' is found in classical Latin, but not in Greek usage. This meaning is found in late medieval French, and is adopted from the French into English in the mid-16th century.

In the 17th century, the word machine could also mean a scheme or plot, a meaning now expressed by the derived machination. The modern meaning develops out of specialized application of the term to stage engines used in theater and to military siege engines, both in the late 16th and early 17th centuries. The OED traces the formal, modern meaning to John Harris' Lexicon Technicum (1704), which has:

Machine, or Engine, in Mechanicks, is whatsoever hath Force sufficient either to raise or stop the Motion of a Body. Simple Machines are commonly reckoned to be Six in Number, viz. the Ballance, Leaver, Pulley, Wheel, Wedge, and Screw. Compound Machines, or Engines, are innumerable.

The word engine used as a (near-) synonym both by Harris and in later language derives ultimately (via Old French) from Latin ingenium 'ingenuity, an invention'.

History

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A flint hand axe was found in Winchester.

The hand axe, made by chipping flint to form a wedge, in the hands of a human transforms force and movement of the tool into a transverse splitting forces and movement of the workpiece. The hand axe is the first example of a wedge, the oldest of the six classic simple machines, from which most machines are based. The second oldest simple machine was the inclined plane (ramp),[6] which has been used since prehistoric times to move heavy objects.[7][8]

The other four simple machines were invented in the ancient Near East.[9] The wheel, along with the wheel and axle mechanism, was invented in Mesopotamia (modern Iraq) during the 5th millennium BC.[10] The lever mechanism first appeared around 5,000 years ago in the Near East, where it was used in a simple balance scale,[11] and to move large objects in ancient Egyptian technology.[12] The lever was also used in the shadoof water-lifting device, the first crane machine, which appeared in Mesopotamia c. 3000 BC,[11] and then in ancient Egyptian technology c. 2000 BC.[13] The earliest evidence of pulleys date back to Mesopotamia in the early 2nd millennium BC,[14] and ancient Egypt during the Twelfth Dynasty (1991–1802 BC).[15] The screw, the last of the simple machines to be invented,[16] first appeared in Mesopotamia during the Neo-Assyrian period (911–609) BC.[14] The Egyptian pyramids were built using three of the six simple machines, the inclined plane, the wedge, and the lever.[17]

Three of the simple machines were studied and described by Greek philosopher Archimedes around the 3rd century BC: the lever, pulley and screw.[18][19] Archimedes discovered the principle of mechanical advantage in the lever.[20] Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage.[1] Hero 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,[19] and describes their fabrication and uses.[21] However, the Greeks' understanding was limited to statics (the balance of forces) and did not include dynamics (the tradeoff between force and distance) or the concept of work.[citation needed]

This ore crushing machine is powered by a water wheel.

The earliest practical wind-powered machines, the windmill and wind pump, first appeared in the Muslim world during the Islamic Golden Age, in what are now Iran, Afghanistan, and Pakistan, by the 9th century AD.[22][23][24][25] The earliest practical steam-powered machine was a steam jack driven by a steam turbine, described in 1551 by Taqi ad-Din Muhammad ibn Ma'ruf in Ottoman Egypt.[26][27]

The cotton gin was invented in India by the 6th century AD,[28] and the spinning wheel was invented in the Islamic world by the early 11th century,[29] both of which were fundamental to the growth of the cotton industry. The spinning wheel was also a precursor to the spinning jenny.[30]

The earliest programmable machines were developed in the Muslim world. A music sequencer, a programmable musical instrument, was the earliest type of programmable machine. The first music sequencer was an automated flute player invented by the Banu Musa brothers, described in their Book of Ingenious Devices, in the 9th century.[31][32] In 1206, Al-Jazari invented programmable automata/robots. He described four automaton musicians, including drummers operated by a programmable drum machine, where they could be made to play different rhythms and different drum patterns.[33]

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").[34][35] He was the first to understand that simple machines do not create energy, they merely transform it.[34]

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).[36]

James Watt patented his parallel motion linkage in 1782, which made the double acting steam engine practical.[37] The Boulton and Watt steam engine and later designs powered steam locomotives, steam ships, and factories.

Bonsack's machine
James Albert Bonsack's cigarette rolling machine was invented in 1880 and patented in 1881.

The Industrial Revolution was a period from 1750 to 1850 where changes in agriculture, manufacturing, mining, transportation, and technology had a profound effect on the social, economic and cultural conditions of the times. It began in the United Kingdom, then subsequently spread throughout Western Europe, North America, Japan, and eventually the rest of the world.

Starting in the later part of the 18th century, there began a transition in parts of Great Britain's previously manual labour and draft-animal-based economy towards machine-based manufacturing. It started with the mechanisation of the textile industries, the development of iron-making techniques and the increased use of refined coal.[38]

Simple machines

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Main article: Simple machine
Chambers' Cyclopædia (1728) has a table of simple mechanisms.[39] Simple machines provide a "vocabulary" for understanding more complex machines.

The idea that a machine can be decomposed into simple movable elements led Archimedes to define the lever, pulley and screw as simple machines. By the time of the Renaissance this list increased to include the wheel and axle, wedge and inclined plane. The modern approach to characterizing machines focusses on the components that allow movement, known as joints.

Wedge (hand axe): Perhaps the first example of a device designed to manage power is the hand axe, also called biface and Olorgesailie. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint.

Lever: The lever is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If a is the distance from the pivot to the point where the input force is applied and b is the distance to the point where the output force is applied, then a/b is the mechanical advantage of the lever. The fulcrum of a lever is modeled as a hinged or revolute joint.

Wheel: The wheel is an important early machine, such as the chariot. A wheel uses the law of the lever to reduce the force needed to overcome friction when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.

Illustration of a Four-bar linkage from Kinematics of Machinery, 1876
The Kinematics of Machinery (1876) has an illustration of a four-bar linkage.

The classification of simple machines to provide a strategy for the design of new machines was developed by Franz Reuleaux, who collected and studied over 800 elementary machines.[40] He recognized that the classical simple machines can be separated into the lever, pulley and wheel and axle that are formed by a body rotating about a hinge, and the inclined plane, wedge and screw that are similarly a block sliding on a flat surface.[41]

Simple machines are elementary examples of kinematic chains or linkages 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.

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 called a mechanism.[42]

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.[42]

Mechanical systems

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Boulton & Watt Steam Engine
The Boulton & Watt Steam Engine, 1784

A mechanical system manages power to accomplish a task that involves forces and movement. Modern machines are systems consisting of (i) a power source and actuators that generate forces and movement, (ii) a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement, (iii) a controller with sensors that compare the output to a performance goal and then directs the actuator input, and (iv) an interface to an operator consisting of levers, switches, and displays. This can be seen in Watt's steam engine in which the power is provided by steam expanding to drive the piston. The walking beam, coupler and crank transform the linear movement of the piston into rotation of the output pulley. Finally, the pulley rotation drives the flyball governor which controls the valve for the steam input to the piston cylinder.

The adjective "mechanical" refers to skill in the practical application of an art or science, as well as relating to or caused by movement, physical forces, properties or agents such as is dealt with by mechanics.[43] Similarly Merriam-Webster Dictionary[44] defines "mechanical" as relating to machinery or tools.

Power flow through a machine provides a way to understand the performance of devices ranging from levers and gear trains to automobiles and robotic systems. The German mechanician Franz Reuleaux[45] wrote, "a machine is a combination of resistant bodies so arranged that by their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion." Notice that forces and motion combine to define power.

More recently, Uicker et al.[42] stated that a machine is "a device for applying power or changing its direction."McCarthy and Soh[46] describe a machine as a system that "generally consists of a power source and a mechanism for the controlled use of this power."

Power sources

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Diesel engine, friction clutch and gear transmission of an automobile
Early Ganz Electric Generator in Zwevegem, West Flanders, Belgium

Human and animal effort were the original power sources for early machines.[citation needed]

Waterwheel: Waterwheels appeared around the world around 300 BC to use flowing water to generate rotary motion, which was applied to milling grain, and powering lumber, machining and textile operations. Modern water turbines use water flowing through a dam to drive an electric generator.

Windmill: Early windmills captured wind power to generate rotary motion for milling operations. Modern wind turbines also drives a generator. This electricity in turn is used to drive motors forming the actuators of mechanical systems.

Engine: The word engine derives from "ingenuity" and originally referred to contrivances that may or may not be physical devices.[47] A steam engine uses heat to boil water contained in a pressure vessel; the expanding steam drives a piston or a turbine. This principle can be seen in the aeolipile of Hero of Alexandria. This is called an external combustion engine.

An automobile engine is called an internal combustion engine because it burns fuel (an exothermic chemical reaction) inside a cylinder and uses the expanding gases to drive a piston. A jet engine uses a turbine to compress air which is burned with fuel so that it expands through a nozzle to provide thrust to an aircraft, and so is also an "internal combustion engine."[48]

Power plant: The heat from coal and natural gas combustion in a boiler generates steam that drives a steam turbine to rotate an electric generator. A nuclear power plant uses heat from a nuclear reactor to generate steam and electric power. This power is distributed through a network of transmission lines for industrial and individual use.

Motors: Electric motors use either AC or DC electric current to generate rotational movement. Electric servomotors are the actuators for mechanical systems ranging from robotic systems to modern aircraft.

Fluid Power: Hydraulic and pneumatic systems use electrically driven pumps to drive water or air respectively into cylinders to power linear movement.

Electrochemical: Chemicals and materials can also be sources of power.[49] They may chemically deplete or need re-charging, as is the case with batteries,[50] or they may produce power without changing their state, which is the case for solar cells and thermoelectric generators.[51][52] All of these, however, still require their energy to come from elsewhere. With batteries, it is the already existing chemical potential energy inside.[50] In solar cells and thermoelectrics, the energy source is light and heat respectively.[51][52]

Mechanisms

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The mechanism of a mechanical system is assembled from components called machine elements. These elements provide structure for the system and control its movement.

The structural components are, generally, the frame members, bearings, splines, springs, seals, fasteners and covers. The shape, texture and color of covers provide a styling and operational interface between the mechanical system and its users.

The assemblies that control movement are also called "mechanisms."[45][42] Mechanisms are generally classified as gears and gear trains, which includes belt drives and chain drives, cam and follower mechanisms, and linkages, though there are other special mechanisms such as clamping linkages, indexing mechanisms, escapements and friction devices such as brakes and clutches.

The number of degrees of freedom of a mechanism, or its mobility, depends on the number of links and joints and the types of joints used to construct the mechanism. The general mobility of a mechanism is the difference between the unconstrained freedom of the links and the number of constraints imposed by the joints. It is described by the Chebychev–Grübler–Kutzbach criterion.

Gears and gear trains

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The Antikythera mechanism (main fragment)

The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:

Cam and follower mechanisms

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A cam and follower is formed by the direct contact of two specially shaped links. The driving link is called the cam (also see cam shaft) and the link that is driven through the direct contact of their surfaces is called the follower. The shape of the contacting surfaces of the cam and follower determines the movement of the mechanism.

Linkages

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Schematic of the actuator and four-bar linkage that position an aircraft landing gear

A linkage is a collection of links connected by joints. Generally, the links are the structural elements and the joints allow movement. Perhaps the single most useful example is the planar four-bar linkage. However, there are many more special linkages:

  • Watt's linkage is a four-bar linkage that generates an approximate straight line. It was critical to the operation of his design for the steam engine. This linkage also appears in vehicle suspensions to prevent side-to-side movement of the body relative to the wheels. Also see the article Parallel motion.
  • The success of Watt's linkage lead to the design of similar approximate straight-line linkages, such as Hoeken's linkage and Chebyshev's linkage.
  • The Peaucellier linkage generates a true straight-line output from a rotary input.
  • The Sarrus linkage is a spatial linkage that generates straight-line movement from a rotary input.
  • The Klann linkage and the Jansen linkage are recent inventions that provide interesting walking movements. They are respectively a six-bar and an eight-bar linkage.

Planar mechanism

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A planar mechanism is a mechanical system that is constrained so the trajectories of points in all the bodies of the system lie on planes parallel to a ground plane. The rotational axes of hinged joints that connect the bodies in the system are perpendicular to this ground plane.

Spherical mechanism

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A spherical mechanism is a mechanical system in which the bodies move in a way that the trajectories of points in the system lie on concentric spheres. The rotational axes of hinged joints that connect the bodies in the system pass through the center of these circle.

Spatial mechanism

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A spatial mechanism is a mechanical system that has at least one body that moves in a way that its point trajectories are general space curves. The rotational axes of hinged joints that connect the bodies in the system form lines in space that do not intersect and have distinct common normals.

Flexure mechanisms

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A flexure mechanism consists of a series of rigid bodies connected by compliant elements (also known as flexure joints) that is designed to produce a geometrically well-defined motion upon application of a force.

Machine elements

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The elementary mechanical components of a machine are termed machine elements. These elements consist of three basic types (i) structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants, (ii) mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and (iii) control components such as buttons, switches, indicators, sensors, actuators and computer controllers.[53] While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide a styling and operational interface between the mechanical components of a machine and its users.

Structural components

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A number of machine elements provide important structural functions such as the frame, bearings, splines, spring and seals.

  • The recognition that the frame of a mechanism is an important machine element changed the name three-bar linkage into four-bar linkage. Frames are generally assembled from truss or beam elements.
  • Bearings are components designed to manage the interface between moving elements and are the source of friction in machines. In general, bearings are designed for pure rotation or straight line movement.
  • Splines and keys are two ways to reliably mount an axle to a wheel, pulley or gear so that torque can be transferred through the connection.
  • Springs provides forces that can either hold components of a machine in place or acts as a suspension to support part of a machine.
  • Seals are used between mating parts of a machine to ensure fluids, such as water, hot gases, or lubricant do not leak between the mating surfaces.
  • Fasteners such as screws, bolts, spring clips, and rivets are critical to the assembly of components of a machine. Fasteners are generally considered to be removable. In contrast, joining methods, such as welding, soldering, crimping and the application of adhesives, usually require cutting the parts to disassemble the components

Controllers

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Controllers combine sensors, logic, and actuators to maintain the performance of components of a machine. Perhaps the best known is the flyball governor for a steam engine. Examples of these devices range from a thermostat that as temperature rises opens a valve to cooling water to speed controllers such as the cruise control system in an automobile. The programmable logic controller replaced relays and specialized control mechanisms with a programmable computer. Servomotors that accurately position a shaft in response to an electrical command are the actuators that make robotic systems possible.

Computing machines

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Arithmometr computing machine
The arithmometre was designed by Charles Xavier Thomas, c. 1820, for the four rules of arithmetic. It was manufactured 1866–1870 AD and exhibited in the Tekniska museet, Stockholm, Sweden.

Charles Babbage designed machines to tabulate logarithms and other functions in 1837. His Difference engine can be considered an advanced mechanical calculator and his Analytical Engine a forerunner of the modern computer, though none of the larger designs were completed in Babbage's lifetime.

The Arithmometer and the Comptometer are mechanical computers that are precursors to modern digital computers. Models used to study modern computers are termed State machine and Turing machine.

Molecular machines

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A ribosome is a biological machine that utilizes protein dynamics.

The biological molecule myosin reacts to ATP and ADP to alternately engage with an actin filament and change its shape in a way that exerts a force, and then disengage to reset its shape, or conformation. This acts as the molecular drive that causes muscle contraction. Similarly the biological molecule kinesin has two sections that alternately engage and disengage with microtubules causing the molecule to move along the microtubule and transport vesicles within the cell, and dynein, which moves cargo inside cells towards the nucleus and produces the axonemal beating of motile cilia and flagella. "In effect, the motile cilium is a nanomachine composed of perhaps over 600 proteins in molecular complexes, many of which also function independently as nanomachines. Flexible linkers allow the mobile protein domains connected by them to recruit their binding partners and induce long-range allostery via protein domain dynamics. "[54] Other biological machines are responsible for energy production, for example ATP synthase which harnesses energy from proton gradients across membranes to drive a turbine-like motion used to synthesise ATP, the energy currency of a cell.[55] Still other machines are responsible for gene expression, including DNA polymerases for replicating DNA,[citation needed] RNA polymerases for producing mRNA,[citation needed] the spliceosome for removing introns, and the ribosome for synthesising proteins. These machines and their nanoscale dynamics are far more complex than any molecular machines that have yet been artificially constructed.[56] These molecules are increasingly considered to be nanomachines.[citation needed]

Researchers have used DNA to construct nano-dimensioned four-bar linkages.[57][58]

Impact

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Mechanization and automation

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Main articles: Mechanization and Automation
This water-powered mine hoist was used for raising ore. This woodblock is from De re metallica by Georg Bauer (Latinized name Georgius Agricola, c. 1555), an early mining textbook that contains numerous drawings and descriptions of mining equipment.

Mechanization (or mechanisation in BE) is providing human operators with machinery that assists them with the muscular requirements of work or displaces muscular work. In some fields, mechanization includes the use of hand tools. In modern usage, such as in engineering or economics, mechanization implies machinery more complex than hand tools and would not include simple devices such as an un-geared horse or donkey mill. Devices that cause speed changes or changes to or from reciprocating to rotary motion, using means such as gears, pulleys or sheaves and belts, shafts, cams and cranks, usually are considered machines. After electrification, when most small machinery was no longer hand powered, mechanization was synonymous with motorized machines.[59]

Automation is the use of control systems and information technologies to reduce the need for human work in the production of goods and services. In the scope of industrialization, automation is a step beyond mechanization. Whereas mechanization provides human operators with machinery to assist them with the muscular requirements of work, automation greatly decreases the need for human sensory and mental requirements as well. Automation plays an increasingly important role in the world economy and in daily experience.

Automata

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Main article: Automaton

An automaton (plural: automata or automatons) is a self-operating machine. The word is sometimes used to describe a robot, more specifically an autonomous robot. A Toy Automaton was patented in 1863.[60]

Mechanics

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Usher[61] reports that Hero of Alexandria's treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics and dynamics of these systems.

Dynamics of machines

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The dynamic analysis of machines begins with a rigid-body model to determine reactions at the bearings, at which point the elasticity effects are included. The rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.[62][63]

The dynamics of a rigid body system is defined by its equations of motion, which are derived using either Newtons laws of motion or Lagrangian mechanics. The solution of these equations of motion defines how the configuration of the system of rigid bodies changes as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.

Kinematics of machines

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The dynamic analysis of a machine requires the determination of the movement, or kinematics, of its component parts, known as kinematic analysis. The assumption that the system is an assembly of rigid components allows rotational and translational movement to be modeled mathematically as Euclidean, or rigid, transformations. This allows the position, velocity and acceleration of all points in a component to be determined from these properties for a reference point, and the angular position, angular velocity and angular acceleration of the component.

Machine design

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Machine design refers to the procedures and techniques used to address the three phases of a machine's lifecycle:

  1. invention, which involves the identification of a need, development of requirements, concept generation, prototype development, manufacturing, and verification testing;
  2. performance engineering involves enhancing manufacturing efficiency, reducing service and maintenance demands, adding features and improving effectiveness, and validation testing;
  3. recycle is the decommissioning and disposal phase and includes recovery and reuse of materials and components.

See also

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Main articles: Outline of machines and Outline of industrial machinery

References

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Further reading

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Machine

View on Grokipedia
from Grokipedia
A machine is a device composed of rigid or resistant bodies connected to move with definite relative motions, thereby transmitting force and performing mechanical work. Machines operate on fundamental physical principles, altering the direction, magnitude, or speed of applied forces to accomplish tasks that would otherwise require greater human effort, while conserving in ideal cases where input work equals output work. The simplest forms, known as simple machines, include the , , , , , and , which serve as the foundational elements for constructing more intricate . The origins of machines trace back to ancient civilizations, where basic tools like ramps (inclined planes) facilitated monumental constructions as early as prehistoric times. By the 3rd century BCE, the Greek mathematician formalized the study of simple machines, deriving mathematical principles for levers, pulleys, and screws to explain their mechanical advantages. These early insights laid the groundwork for later developments, including the Hellenistic engineer Hero of Alexandria's descriptions of automata and geared mechanisms in the 1st century CE, which demonstrated automated force transmission. In modern engineering, machines range from everyday tools to complex systems like engines and robots, designed to optimize efficiency through —the ratio of output force to input force—while accounting for real-world factors such as and material limits. Complex machines, built by combining simple ones, power industries from to transportation, embodying principles of (motion without force) and dynamics (motion with force). Advances in and computation continue to enhance machine performance, enabling precision and scalability in applications worldwide.

Etymology and Terminology

Etymology

The term "machine" traces its roots to the word mēkhanḗ (μηχανή), denoting a contrivance, device, or artifice designed to achieve a practical end. This term, often linked to mechanical ingenuity in philosophical and technical contexts, derives from the variant mā khanā (μαχανά), emphasizing an expedient or means of contrivance, and appears in classical literature exploring natural and artificial mechanisms. For instance, works attributed to , such as the Mechanical Problems within the Aristotelian corpus, utilize mēkhanḗ to discuss levers, pulleys, and other s that extend human capability through clever arrangement. The Greek concept was transmitted to Latin as machina, retaining connotations of engineered tools or engines for construction, warfare, or spectacle. A pivotal early use occurs in Marcus Pollio's (c. 15 BCE), where Book 10 extensively applies machina to describe water-lifting devices, hoisting apparatus, and particularly siege engines like ballistae and battering rams, framing them as essential architectural and military contrivances. ' treatise thus bridges classical Greek theory with Roman practice, solidifying machina as a term for purposeful mechanical assemblies. During the , the word reemerged prominently through Latin texts and machine, entering English around the 1540s to signify any structured device, evolving by the to highlight artificial mechanisms with moving parts for transmitting power. This shift underscored a growing distinction between natural processes and human-engineered artifacts, influencing modern technical lexicon while preserving the ancient emphasis on contrivance. The etymological lineage from mēkhanḗ also informs brief connections to foundational elements like levers, viewed as archetypal devices in early mechanical thought.

Modern Definitions

In contemporary , a machine is defined as an assembly, fitted with or intended to be fitted with a drive system other than directly applied human or animal effort, consisting of linked parts or components, at least one of which moves, and which are joined together for a specific application. This definition, established in the (ISO) 12100:2010 standard on machinery safety, emphasizes the transmission or modification of energy to perform intended tasks, often involving relative motion among parts to apply forces or control motion and energy. Philosophically, the concept of a machine traces to , who portrayed machines as deterministic automata governed solely by mechanical principles, lacking consciousness, reason, or agency, as exemplified in his view of animals as soulless mechanisms operating through physical arrangements alone. extended this mechanistic worldview by distinguishing artificial machines—finite, human-constructed devices following strict causal laws without perception—from natural machines, such as living organisms, which he saw as infinitely divisible systems infused with primitive perceptions (monads) yet still operating deterministically absent true agency in their material aspects. Both thinkers framed machines as systems where outcomes arise predictably from structural configurations and inputs, devoid of independent volition. Legally, in the context of , the United States Patent and Trademark Office (USPTO) defines a as a concrete thing consisting of parts or of certain devices and combinations of devices, where the elements integrate to achieve a specific purpose beyond mere aggregation. This interpretation, outlined in the Manual of Patent Examining Procedure (MPEP) § 2106.03, underscores interrelated components functioning cooperatively, distinguishing patentable from abstract ideas or simple assemblages. Key distinctions clarify the term's scope: unlike tools, which are typically handheld implements relying on direct without independent power sources or complex assemblies (e.g., a versus a powered ), machines incorporate external sources and to amplify or automate work. Similarly, a mechanism refers to a subsystem or constrained arrangement of parts producing specific motions within a larger machine, such as a , whereas a machine constitutes the complete apparatus designed to perform useful work through integrated mechanisms.

Historical Development

Ancient and Medieval Machines

The development of machines in ancient civilizations began with simple yet ingenious devices that leveraged basic mechanical principles to address practical needs such as , , and . In around 2000 BC, the shaduf emerged as a pivotal lever-based tool for , consisting of a long pole balanced on a fulcrum with a on one end and a on the other, allowing a single operator to lift water from the River or canals to higher fields during the dry season. This device significantly enhanced agricultural productivity in the Valley by enabling more efficient water distribution beyond natural flood levels, marking an early application of leverage in human-engineered systems. In the , Greek engineer invented the around 250 BC, a helical device housed in a that rotated to lift water continuously from lower to higher elevations, revolutionizing and drainage in arid regions. The operated on the principle of a continuous wrapped around a central shaft, powered manually or by animal traction, and was particularly effective for raising water in mines and agricultural settings. Concurrently, in during the 2nd century AD, inventor created the first seismoscope in 132 AD, a bronze urn equipped with eight dragon heads positioned around its perimeter, each holding a ball above an open-mouthed toad; seismic vibrations would dislodge a ball from the corresponding dragon into the toad below, indicating the earthquake's direction up to 400 miles away. This mechanism, likely involving a central to detect subtle ground movements, represented an early feat in detecting and recording natural phenomena through mechanical response. Roman engineering advanced these concepts in and during the , incorporating siphons into aqueduct systems to transport water across valleys and uneven terrain, as seen in structures like the Aqua Appia (312 BC) and later aqueducts that delivered up to 1,000,000 cubic meters of water daily to via lead pipes under . Complementing this, the polyspastos crane, described by around 25 BC, featured a wooden tower with multiple blocks—up to three sheaves per block—allowing teams of workers to hoist loads of 3,000 kg or more for monumental building projects, such as temples and aqueducts, through coordinated operation. By the 3rd century AD in , mechanical engineer Ma Jun refined the , a wheeled with an internal differential gear mechanism that ensured a mounted figurine consistently pointed south regardless of the chariot's turns, aiding military without magnetic reliance. This , driven by the differential rotation of the wheels, maintained directional stability through a series of interconnected wooden gears and linkages. During the Medieval , polymath (1136–1206) documented over 100 mechanical innovations in his 1206 treatise The Book of Knowledge of Ingenious Mechanical Devices, including early and automata that integrated cams, gears, and water power for automated functions. Al-Jazari's , featured in pumps and mills, converted rotary motion to linear reciprocation via a , enabling efficient water-lifting devices like the double-acting that operated continuously without manual intervention. His automata, such as humanoid robots serving drinks or musical instruments with programmable sequences, employed float valves, pegged cylinders, and hydraulic timing to simulate human actions, showcasing advanced control systems in entertainment and practical engineering. These inventions built on Hellenistic and earlier Asian traditions, often incorporating simple machines like levers and pulleys to amplify human or natural forces in diverse cultural contexts from to amusement.

Industrial Revolution

The Industrial Revolution, spanning the late 18th and early 19th centuries, marked a pivotal era in the history of machines, as innovations in mechanical design and power sources enabled the shift from agrarian economies to industrialized production, particularly in Britain. Textile manufacturing emerged as a cornerstone, driven by machines that automated spinning and weaving processes, vastly increasing output and laying the groundwork for . These developments transformed machines from isolated tools into integrated systems that powered factories, fundamentally altering labor, trade, and societal structures across . A landmark invention was the , developed by in 1764, which allowed a single operator to spin multiple threads simultaneously on a multi-spindle machine, revolutionizing processing by boosting productivity without requiring proportional increases in labor. This hand-operated device, initially used in domestic settings, facilitated the of the in , England, where it addressed bottlenecks in production for weavers. Hargreaves' , though simple in design, exemplified the early application of mechanical principles to scale human effort, setting a for subsequent factory-based machines. Complementing this, patented the in 1769, a water-powered spinning machine that produced stronger, finer thread suitable for warp yarns, enabling continuous mechanized production. Arkwright's design integrated rollers and spindles to draw out and twist fibers mechanically, which was first implemented at his mill in , , marking the advent of the factory system where workers operated centralized machinery under one roof. This system centralized production, reduced reliance on skilled artisans, and accelerated the growth of the industry, with Arkwright's mills employing hundreds and influencing similar setups across Britain and . James Watt's improvements to the , patented in , further amplified these machines by providing a reliable, non-water-dependent power source that could drive multiple units simultaneously. Watt's separate condenser and rotary motion adaptations increased efficiency by up to 75% over earlier Newcomen engines, allowing to power factories in urban areas far from rivers and expanding industrial capacity. Partnering with , Watt's engines were deployed in mills by the , fueling Britain's dominance in global exports and spreading to and , which supported machine production itself. The proliferation of these machines spurred profound societal impacts, including rapid as rural workers migrated to industrial cities like and Birmingham, where populations swelled by over 50% between 1801 and 1851. Economic shifts favored capital owners, with Britain's GDP growth averaging 2% annually from 1760 to 1820, but at the cost of exploitative labor practices, including widespread child labor in mills where children as young as six worked 12-14 hour shifts under hazardous conditions. These changes exacerbated class divisions in Britain and influenced , where similar mechanization in and prompted protective tariffs and labor reforms by the mid-19th century. Resistance to machine-driven displacement manifested in the rebellions from 1811 to 1816, when skilled textile workers in , , and destroyed automated looms and knitting frames to protest wage cuts and unemployment caused by labor-saving devices. Named after the mythical "," these organized protests involved thousands and led to military crackdowns, with over 12,000 troops deployed; the movement highlighted tensions between technological progress and artisan livelihoods, ultimately suppressed by harsh penalties including executions.

20th and 21st Century Advances

The 20th century marked a pivotal shift in machine design through , enabling unprecedented efficiency and in . Henry Ford's introduction of the moving in 1913 at the revolutionized automobile production by integrating electric motors to power conveyor belts and tools, reducing the time to assemble a Model T from over 12 hours to approximately 93 minutes and enabling on a scale previously unimaginable. This electrification extended beyond assembly lines; by the , electric motors became standard in industrial machinery, powering everything from lathes to pumps and facilitating the growth of the electrical machinery sector, which saw U.S. production rise from 1.5 million horsepower in 1900 to over 30 million by 1930. The mid-20th century ushered in the digital era, transforming machines from purely mechanical systems to programmable entities. Computer (CNC) machines, first developed in the by researchers at MIT's Servomechanisms under a U.S. contract, used to automate tool paths on milling machines, with the first functional prototype demonstrated in for component fabrication. This innovation spread rapidly, evolving into microprocessor-based systems by the that allowed for complex, three-dimensional with micron-level precision. Paralleling CNC advancements, industrial emerged with the installation of , the world's first industrial , at ' Trenton, New Jersey plant in 1961; designed by and , it performed die-casting tasks, lifting hot metal parts and increasing production speed by up to 50% while reducing worker exposure to hazards. In the late 20th and early 21st centuries, machines increasingly incorporated and , further blurring lines between and computing. , commonly known as , was patented in 1986 by Charles Hull as , a process using UV light to cure layers of resin into solid objects, enabling that shortened design cycles from weeks to hours. By the 2010s, widespread adoption of fused deposition modeling and metal expanded applications to and medical devices, with the global market growing from $2.2 billion in 2013 to over $13 billion by 2020. AI-driven machines gained prominence in the , exemplified by autonomous vehicles that integrate for real-time decision-making; systems like Tesla's Full Self-Driving capability, rolled out progressively from 2019, use neural networks to process sensor data for navigation, operating at SAE Level 2 autonomy (requiring active driver supervision) as of November 2025. These developments were accelerated by events such as the series (2004–2005) and Urban Challenge (2007), which spurred advancements in self-driving technology by awarding prizes for vehicles navigating complex terrains without human intervention, leading to foundational algorithms now used in commercial systems. By 2025, advancements in AI have enabled more adaptive robotic systems in , improving efficiency in sectors like automotive assembly. Modern machines often rely on sophisticated controllers for such integrations, drawing from principles to ensure seamless operation.

Fundamental Concepts

Simple Machines

Simple machines are the basic mechanical devices that alter the magnitude or direction of a force, serving as the foundational building blocks for more complex machinery by providing without adding energy. The six classical simple machines—, , , , , and —were systematically and classified during the by on principles, enabling the analysis of force multiplication in mechanical systems. The , one of the earliest recognized simple machines, consists of a rigid bar pivoting on a fulcrum to lift or move loads; a common example is the , where a small applied at a distance from the fulcrum can balance a larger load closer to it. The (MA) of a is given by the ratio of the effort arm length to the load arm length, expressed as MA=LeLlMA = \frac{L_e}{L_l}, where LeL_e is the distance from the fulcrum to the effort and LlL_l is the distance to the load. The operates on a similar , with a larger attached to a smaller to amplify ; for instance, a on a allows a driver to turn the with reduced effort. The system uses a with a grooved rim and to redirect , often multiplying it in block-and-tackle arrangements; its equals the number of supporting ropes, as each shares the load. The reduces the force needed to lift objects by spreading the effort over a longer distance, as seen in ramps used in to move heavy materials to elevated positions without steep inclines. The transforms into separation force, functioning like a movable ; examples include axes for splitting wood or doorstops to secure openings. Finally, the applies rotational motion to generate linear force through a helical incline wrapped around a , commonly used in clamps or bottle caps to hold or advance components securely. These devices trace their conceptual origins to Greek philosophers, with Heron of Alexandria in the AD describing five fundamental powers (, , , , and ) in his work Mechanica, which influenced later classifications that incorporated the .

Power Sources

Power sources provide the energy necessary to operate machines, converting various forms of energy into mechanical work to enable motion and perform tasks. These sources have evolved from biological and natural forces to advanced engineered systems, influencing the design, efficiency, and application of machines across industries. Early machines relied on human and animal muscle power, where the kinetic energy from biological exertion directly drove simple mechanisms like mills or plows. Human labor, capable of producing around 0.1 horsepower continuously, powered hand tools and early agricultural devices, while animal power, such as from horses or oxen, scaled up to 1-2 horsepower for tasks like grinding grain or pulling carts. These sources dominated pre-industrial eras due to their availability but were limited by fatigue and inconsistent output. Mechanical power sources store and release without continuous input, using components like springs or flywheels to provide intermittent bursts of motion. Springs, compressed or tensioned to store , drive clocks and toys through elastic deformation, while flywheels maintain rotational to smooth power delivery in engines or machinery. These are ideal for short-duration applications where steady input is unavailable, offering high reliability in compact forms. Thermal power sources convert heat into mechanical work via engines, a cornerstone of industrial machinery. Steam engines, heated by burning to expand against pistons, powered factories from the onward, while internal combustion engines ignite -air mixtures to drive pistons. The efficiency of heat engines is fundamentally limited by the Carnot efficiency, given by the formula η=1−TcTh,\eta = 1 - \frac{T_c}{T_h}, where TcT_c and ThT_h are the absolute temperatures of the cold and hot reservoirs, respectively; this theoretical maximum underscores why practical thermal engines achieve 20-40% efficiency. Electrical power sources supply energy through electromagnetic means, enabling precise control in modern machines. Electric motors convert into rotational motion via electromagnetic fields, powering everything from household appliances to industrial robots, while batteries store for portable applications. Rechargeable batteries, particularly lithium-ion types, deliver high —up to 250 Wh/kg—making them essential for mobile devices and vehicles. Fluid power sources utilize pressurized liquids or gases to transmit , offering advantages in heavy-duty tasks. Hydraulic systems employ incompressible fluids like to multiply via pistons, as in excavators where pressures reach 3000 psi, while pneumatic systems use compressible air for lighter, faster actuation in tools like drills. These provide smooth, controllable power but require pumps or compressors as intermediaries. Historically, power sources shifted from medieval water wheels, which harnessed gravitational potential energy from flowing water to generate up to 60 horsepower for milling and , to renewable electrical sources like solar panels emerging in the 1970s. Photovoltaic cells convert sunlight directly into electricity, with early silicon-based panels achieving 10-15% efficiency; by 2025, advancements in perovskite cells have pushed tandem efficiencies beyond 34%. Representative examples illustrate this progression: the , patented by in the 1890s, uses compression ignition of heavy fuel oils to achieve 30-50% in vehicles and generators, far surpassing steam engines. In contrast, modern lithium-ion batteries in electric vehicles store 50-100 kWh per pack, enabling ranges over 300 miles with 90% round-trip efficiency, reducing reliance on fossil fuels.

Components and Mechanisms

Machine Elements

Machine elements refer to the fundamental structural and functional components that form the backbone of mechanical systems, providing support, alignment, and connectivity while ensuring operational under load. These elements are essential for maintaining the stability and of machines, distinct from mechanisms that transmit motion. Structural components such as and housings serve as the primary supportive framework in machines, offering rigidity, alignment, and protection for internal parts. , often constructed from robust materials to withstand static and dynamic loads, act as the foundational that distributes forces evenly across the assembly. Housings enclose sensitive components, shielding them from environmental factors like and while facilitating . Bearings are critical machine elements designed to support loads while permitting relative motion between rotating or sliding parts, primarily to minimize and . Ball bearings employ spherical rolling elements constrained between inner and outer races, enabling low-friction rotation suitable for high-speed applications with moderate loads. Roller bearings, utilizing cylindrical or tapered rollers, provide higher load-bearing capacity and are preferred for radial and loads in heavier machinery. These anti-friction designs significantly reduce energy loss compared to plain bearings by replacing sliding contact with rolling motion. Fasteners enable the secure assembly of machine elements, allowing for disassembly when needed or permanent joining as required. Bolts and screws, typically threaded rods with heads, clamp components together by applying preload through nuts or tapped holes, resisting shear and tension forces in joints. Welds create permanent bonds by fusing metals at high temperatures, ideal for high-strength structural connections in frames. Adhesives, including structural epoxies, bond dissimilar materials like metals and composites, distributing loads evenly and reducing weight in assemblies. Materials selection for machine elements balances strength, weight, , and cost to meet demands. Metals like , particularly alloys such as AISI 1040, are widely used for their high tensile strength and in load-bearing frames and fasteners. Composites, including carbon fiber-reinforced polymers, offer superior strength-to-weight ratios and resistance, making them prevalent in applications for lightweight housings and structural components. Standards from organizations like ANSI and ASME ensure , safety, and reliability in design and . ANSI B18.2.1 specifies dimensions and tolerances for bolts and screws, facilitating precise assembly. ASME standards cover load-bearing capacities for bearings and fasteners, including guidelines for tolerances in structural components to prevent failure under specified conditions. These standards promote consistent quality across industries by defining material properties, geometric limits, and testing protocols.

Gears and Gear Trains

are fundamental mechanical components used to transmit and motion between rotating shafts, enabling changes in speed, direction, and in machines. They consist of toothed wheels that together, converting efficiently while minimizing slippage. This transmission is essential in systems requiring precise control over mechanical power, such as engines and machinery. have been integral to since ancient times, but their modern design emphasizes durability, efficiency, and . Common types of gears include , which have straight teeth parallel to the axis of rotation and are used for parallel shaft applications due to their simplicity and cost-effectiveness. Helical gears feature angled teeth that create a smoother, quieter operation by gradual engagement, making them suitable for high-speed applications, though they generate axial thrust that requires additional bearings. Bevel gears transmit motion between intersecting shafts, typically at right angles, and are essential in differential systems. Worm gears, consisting of a screw-like worm and a wheel, provide high gear ratios in a compact form and are self-locking, preventing back-driving in applications like elevators. The gear ratio determines the relationship between input and output speeds and s, defined as the ratio of the number of teeth on the driven gear to the driving gear, where output speed equals input speed divided by the gear ratio, and is inversely proportional. This allows machines to achieve desired mechanical advantages, such as increasing at the expense of speed. In gear trains, multiple are arranged to compound these ratios. A simple gear train involves two meshed for basic speed or direction changes, while a compound gear train uses multiple gear pairs on intermediate shafts to achieve high overall ratios, common in reductions exceeding 10:1, enhancing in multi-stage transmissions. Gear design must account for strength to withstand bending and wear, with the Lewis formula providing a key method for calculating the bending stress in gear teeth: the bending stress σ is given by σ=WtPdFY\sigma = \frac{W_t P_d}{F Y}, where WtW_t is the tangential load, PdP_d is the diametral pitch, FF is the face width, and YY is the Lewis form factor dependent on tooth geometry. This empirical equation, derived from beam theory applied to gear teeth, ensures gears can handle operational loads without failure, often with safety factors incorporated for dynamic conditions. Applications of gears and gear trains are widespread; in automotive transmissions, helical and bevel gears enable smooth shifting and differential action for vehicle control, while in clockworks, compound trains with spur and escape wheels provide precise timekeeping through regulated ratios. Shafts, as basic machine elements, support these gears by providing rotational axes.

Linkages and Cams

Linkages and cams are essential mechanisms in machines for converting one type of motion into another, such as transforming rotary motion into linear or oscillatory paths, enabling precise control in various mechanical systems. Linkages typically consist of rigid bars connected by joints to achieve desired trajectories, while cams use a rotating or translating profile to impart intermittent or variable motion to a follower. These components are widely applied in engines, automation, and consumer devices, often integrated with other elements like gears for power transmission in combined systems.

Linkages

A is a fundamental planar mechanism comprising four rigid links connected in a closed loop by revolute joints, used to convert input rotation into output oscillation or rotation. The behavior of the linkage—whether it can achieve full rotation or only rocking motion—depends on Grashof's criterion, which states that for a four-bar linkage with link lengths s (shortest), l (longest), and p, q (the other two), the condition s + l ≤ p + q must hold for at least one link to fully rotate relative to the others. If the shortest link is the input (crank) and the criterion is satisfied, the mechanism operates as a crank-rocker, where the crank rotates fully and the rocker oscillates, a configuration common in machinery requiring continuous input with limited output swing. The , a variant with one sliding joint instead of all revolute, converts rotary motion to reciprocating and is central to internal engines, where the 's rotation drives the 's back-and-forth movement via a . In this setup, force on the generates on the , enabling the engine's power cycle. Watt's linkage, invented by in 1784, is a type of approximate designed to guide a piston rod in nearly within the double-acting . It consists of two equal-length arms connected to a central point that traces a path closely approximating a straight line over a significant portion of its travel, improving efficiency by reducing side loads on the cylinder. This innovation, detailed in Watt's patent, addressed the limitations of earlier beam engines by enabling more direct . In applications like transmissions, four-bar linkages connect the pedals directly to the rear wheel, converting pedaling rotation into wheel without a , as demonstrated in designs where the linkage ensures smooth torque transfer.

Cams

Cams are profiled elements that impart prescribed motion to a follower through direct contact, typically converting constant rotary input into variable output displacement. Common types include the disk cam, which rotates in a plane to drive a follower radially or tangentially, and the cylindrical cam, where the follower moves parallel to the cam's axis along a helical or grooved surface. Disk cams are suited for high-speed applications due to their compact form, while cylindrical cams provide axial motion for linear guides. Follower profiles vary to optimize contact and reduce wear: flat-faced followers use a planar surface for broad contact and simplicity, ideal for low-speed operations, whereas roller followers incorporate a rolling element to minimize and allow higher speeds by converting sliding to rolling motion. Roller followers are particularly effective in precision machinery, as the roller's center defines the trace point for profile design. For smooth operation, cam displacement is often designed using cycloidal motion, which provides constant followed by constant deceleration, avoiding infinite jerk at reversal points. The displacement ss of the follower as a function of cam angle θ\theta over rise angle β\beta and total rise hh is given by: s=hβ(θ−β2πsin⁡(2πθβ))s = \frac{h}{ \beta } \left( \theta - \frac{ \beta }{ 2\pi } \sin \left( \frac{2\pi \theta }{ \beta } \right) \right) This ensures gradual buildup, with maximum vmax⁡=hβv_{\max} = \frac{h}{\beta} and amax⁡=2πhβ2a_{\max} = \frac{2\pi h}{\beta^2}, making it suitable for mechanisms requiring minimal . In sewing machines, cams control the needle's lateral swing and motion to produce decorative stitches, where interchangeable cam profiles dictate patterns like zigzags or scallops for automated . This application leverages the cam's ability to generate precise, repeatable intermittent actions.

Advanced Mechanisms

Spatial mechanisms extend beyond planar configurations to enable motion in three-dimensional space, allowing for complex trajectories with up to (DOF). These mechanisms are essential in and , where serial or parallel arrangements facilitate tasks requiring translation and rotation in multiple axes. A prominent example is the , a parallel mechanism consisting of a top platform connected to a base via six extensible legs, which provides high stiffness and load-bearing capacity for applications like flight simulators and positioning. The achieves full six-DOF motion—three translations and three rotations—through the coordinated extension of its actuated legs, offering advantages in dynamic response over serial manipulators due to distributed load paths. Originally proposed for simulating vehicle motion, it has been adapted for robotic and systems, where its parallel architecture minimizes singularities in the workspace compared to sequential joint chains. Spherical mechanisms specialize in pure rotational motion about a fixed point, ideal for orienting devices without translational offset. These are commonly implemented in gimbals, which use nested orthogonal rings or linkages to allow unrestricted rotation in and , as seen in antenna pointing systems for maintaining alignment with ground stations. In , spherical parallel manipulators, such as those with three rotational DOF, enable compact wrist designs for end-effectors, providing a wide orientation range with reduced . For instance, antenna pointing mechanisms often employ two-axis gimbals driven by stepper motors to achieve precise tracking within ±69° and unlimited . Flexure mechanisms, also known as compliant mechanisms, achieve motion through elastic deformation of flexible elements rather than traditional rigid joints, eliminating backlash, , and assembly needs. These designs distribute compliance across the , often using slender beams or hinges that deflect under load while maintaining precision, particularly in micro-electro-mechanical systems () for sensors and actuators. In applications, flexure-based grippers or mirrors operate without joints, relying on material properties like to guide motion, enabling sub-micron accuracies in optical switches and biomedical devices. A key design approach involves small-length flexural pivots, where the hinge's is optimized to approximate ideal rotational while accommodating large deflections without fatigue. The analysis of serial spatial mechanisms, such as robotic arms, commonly employs the Denavit-Hartenberg (DH) parameters to model systematically. This convention assigns four parameters to each : link length aia_i, link twist αi\alpha_i, joint angle θi\theta_i, and link offset did_i, which define the homogeneous between consecutive frames. The forward is then computed by multiplying these 4x4 matrices along the chain, yielding the end-effector's pose relative to the base. Introduced for lower-pair mechanisms, DH parameters simplify the description of spatial chains by standardizing frame assignments at , facilitating both manual and computational analysis in robot design. The general DH transformation matrix from frame i−1i-1 to ii is given by: i−1Ti=[cos⁡θi−sin⁡θicos⁡αisin⁡θisin⁡αiaicos⁡θisin⁡θicos⁡θicos⁡αi−cos⁡θisin⁡αiaisin⁡θi0sin⁡αicos⁡αidi0001]{}^{i-1}T_i = \begin{bmatrix} \cos\theta_i & -\sin\theta_i \cos\alpha_i & \sin\theta_i \sin\alpha_i & a_i \cos\theta_i \\ \sin\theta_i & \cos\theta_i \cos\alpha_i & -\cos\theta_i \sin\alpha_i & a_i \sin\theta_i \\ 0 & \sin\alpha_i & \cos\alpha_i & d_i \\ 0 & 0 & 0 & 1 \end{bmatrix}
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