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Machine

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.^[1] 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 energy in ideal cases where input work equals output work.^[2] The simplest forms, known as simple machines, include the lever, wheel and axle, pulley, inclined plane, wedge, and screw, which serve as the foundational elements for constructing more intricate devices.^[3] The origins of machines trace back to ancient civilizations, where basic tools like ramps (inclined planes) facilitated monumental constructions as early as prehistoric times.^[4] By the 3rd century BCE, the Greek mathematician Archimedes formalized the study of simple machines, deriving mathematical principles for levers, pulleys, and screws to explain their mechanical advantages.^[5] 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.^[6] In modern engineering, machines range from everyday tools to complex systems like engines and robots, designed to optimize efficiency through mechanical advantage—the ratio of output force to input force—while accounting for real-world factors such as friction and material limits.^[7] Complex machines, built by combining simple ones, power industries from manufacturing to transportation, embodying principles of kinematics (motion without force) and dynamics (motion with force).^[8] Advances in materials science and computation continue to enhance machine performance, enabling precision and scalability in applications worldwide.^[9]

Etymology and Terminology

Etymology

The term "machine" traces its roots to the ancient Greek word mēkhanḗ (μηχανή), denoting a contrivance, device, or artifice designed to achieve a practical end.^[10] This term, often linked to mechanical ingenuity in philosophical and technical contexts, derives from the Doric Greek variant mā khanā (μαχανά), emphasizing an expedient or means of contrivance, and appears in classical literature exploring natural and artificial mechanisms.^[10] For instance, works attributed to Aristotle, such as the Mechanical Problems within the Aristotelian corpus, utilize mēkhanḗ to discuss levers, pulleys, and other devices 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.^[10] A pivotal early use occurs in Marcus Vitruvius Pollio's De Architectura (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. Vitruvius' treatise thus bridges classical Greek theory with Roman engineering practice, solidifying machina as a term for purposeful mechanical assemblies. During the Renaissance, the word reemerged prominently through Latin texts and Middle French machine, entering English around the 1540s to signify any structured device, evolving by the 17th century to highlight artificial mechanisms with moving parts for transmitting power.^[10] This shift underscored a growing distinction between natural processes and human-engineered artifacts, influencing modern technical lexicon while preserving the ancient emphasis on contrivance.^[10] The etymological lineage from mēkhanḗ also informs brief connections to foundational elements like levers, viewed as archetypal devices in early mechanical thought.^[10]

Modern Definitions

In contemporary engineering, 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.^[11] This definition, established in the International Organization for Standardization (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.^[12] Philosophically, the concept of a machine traces to René Descartes, 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.^[13] Gottfried Wilhelm Leibniz 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.^[14] Both thinkers framed machines as systems where outcomes arise predictably from structural configurations and inputs, devoid of independent volition. Legally, in the context of United States patent law, the United States Patent and Trademark Office (USPTO) defines a machine 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.^[15] This interpretation, outlined in the Manual of Patent Examining Procedure (MPEP) § 2106.03, underscores interrelated components functioning cooperatively, distinguishing patentable machines from abstract ideas or simple assemblages. Key distinctions clarify the term's scope: unlike tools, which are typically handheld implements relying on direct human force without independent power sources or complex assemblies (e.g., a hammer versus a powered drill), machines incorporate external energy sources and moving parts to amplify or automate work.^[16] Similarly, a mechanism refers to a subsystem or constrained arrangement of parts producing specific motions within a larger machine, such as a gear train, whereas a machine constitutes the complete apparatus designed to perform useful work through integrated mechanisms.^[17]

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 irrigation, construction, and navigation. In ancient Egypt around 2000 BC, the shaduf emerged as a pivotal lever-based tool for irrigation, consisting of a long pole balanced on a fulcrum with a bucket on one end and a counterweight on the other, allowing a single operator to lift water from the Nile River or canals to higher fields during the dry season.^[18] This device significantly enhanced agricultural productivity in the Nile Valley by enabling more efficient water distribution beyond natural flood levels, marking an early application of leverage in human-engineered systems.^[18] In the Hellenistic period, Greek engineer Archimedes invented the screw around 250 BC, a helical device housed in a cylinder that rotated to lift water continuously from lower to higher elevations, revolutionizing irrigation and drainage in arid regions.^[19] The Archimedes screw operated on the principle of a continuous inclined plane wrapped around a central shaft, powered manually or by animal traction, and was particularly effective for raising water in mines and agricultural settings.^[19] Concurrently, in China during the 2nd century AD, inventor Zhang Heng 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.^[20] This mechanism, likely involving a central pendulum to detect subtle ground movements, represented an early feat in detecting and recording natural phenomena through mechanical response.^[20] Roman engineering advanced these concepts in infrastructure and construction during the 1st century BC, 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 Rome via lead pipes under pressure.^[21] Complementing this, the polyspastos crane, described by Vitruvius around 25 BC, featured a wooden tower with multiple pulley 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 treadwheel operation.^[22] By the 3rd century AD in China, mechanical engineer Ma Jun refined the south-pointing chariot, a wheeled vehicle with an internal differential gear mechanism that ensured a mounted figurine consistently pointed south regardless of the chariot's turns, aiding military navigation without magnetic reliance.^[4] This gear train, driven by the differential rotation of the wheels, maintained directional stability through a series of interconnected wooden gears and linkages.^[4] During the Medieval Islamic Golden Age, polymath Ismail al-Jazari (1136–1206) documented over 100 mechanical innovations in his 1206 treatise The Book of Knowledge of Ingenious Mechanical Devices, including early crankshafts and automata that integrated cams, gears, and water power for automated functions.^[23] Al-Jazari's crankshaft, featured in pumps and mills, converted rotary motion to linear reciprocation via a connecting rod, enabling efficient water-lifting devices like the double-acting piston pump that operated continuously without manual intervention.^[23] 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.^[23] 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 agriculture to amusement.^[23]

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 mass production. These developments transformed machines from isolated tools into integrated systems that powered factories, fundamentally altering labor, trade, and societal structures across Europe.^[24] A landmark invention was the spinning jenny, developed by James Hargreaves in 1764, which allowed a single operator to spin multiple threads simultaneously on a multi-spindle machine, revolutionizing cotton processing by boosting productivity without requiring proportional increases in labor. This hand-operated device, initially used in domestic settings, facilitated the mechanization of the textile industry in Lancashire, England, where it addressed bottlenecks in yarn production for weavers. Hargreaves' innovation, though simple in design, exemplified the early application of mechanical principles to scale human effort, setting a precedent for subsequent factory-based machines.^[25]^[26] Complementing this, Richard Arkwright patented the water frame in 1769, a water-powered spinning machine that produced stronger, finer cotton 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 Cromford, Derbyshire, 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 cotton industry, with Arkwright's mills employing hundreds and influencing similar setups across Britain and Europe.^[27]^[28] James Watt's improvements to the steam engine, patented in 1769, further amplified these textile 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 steam to power factories in urban areas far from rivers and expanding industrial capacity. Partnering with Matthew Boulton, Watt's engines were deployed in textile mills by the 1780s, fueling Britain's dominance in global cotton exports and spreading to ironworks and mining, which supported machine production itself.^[29]^[30] The proliferation of these machines spurred profound societal impacts, including rapid urbanization as rural workers migrated to industrial cities like Manchester 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 continental Europe, where similar mechanization in France and Belgium prompted protective tariffs and labor reforms by the mid-19th century.^[24]^[31]^[32] Resistance to machine-driven displacement manifested in the Luddite rebellions from 1811 to 1816, when skilled textile workers in Nottinghamshire, Yorkshire, and Lancashire destroyed automated looms and knitting frames to protest wage cuts and unemployment caused by labor-saving devices. Named after the mythical "Ned Ludd," 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.^[33]

20th and 21st Century Advances

The 20th century marked a pivotal shift in machine design through electrification, enabling unprecedented efficiency and automation in manufacturing. Henry Ford's introduction of the moving assembly line in 1913 at the Highland Park Ford Plant 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 mass production on a scale previously unimaginable. This electrification extended beyond assembly lines; by the 1920s, 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 Numerical Control (CNC) machines, first developed in the 1950s by researchers at MIT's Servomechanisms Laboratory under a U.S. Air Force contract, used punched tape to automate tool paths on milling machines, with the first functional prototype demonstrated in 1952 for aircraft component fabrication. This innovation spread rapidly, evolving into microprocessor-based systems by the 1970s that allowed for complex, three-dimensional machining with micron-level precision. Paralleling CNC advancements, industrial robotics emerged with the installation of Unimate, the world's first industrial robot, at General Motors' Trenton, New Jersey plant in 1961; designed by George Devol and Joseph Engelberger, 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 artificial intelligence and additive manufacturing, further blurring lines between mechanical engineering and computing. Additive manufacturing, commonly known as 3D printing, was patented in 1986 by Charles Hull as stereolithography, a process using UV light to cure layers of photopolymer resin into solid objects, enabling rapid prototyping that shortened design cycles from weeks to hours. By the 2010s, widespread adoption of fused deposition modeling and metal 3D printing expanded applications to aerospace 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 2020s, exemplified by autonomous vehicles that integrate machine learning 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.^[34] These developments were accelerated by events such as the DARPA Grand Challenge 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 manufacturing, improving efficiency in sectors like automotive assembly. Modern machines often rely on sophisticated controllers for such integrations, drawing from automation 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 mechanical advantage without adding energy. The six classical simple machines—lever, wheel and axle, pulley, inclined plane, wedge, and screw—were systematically identified and classified during the Renaissance by scientists drawing on ancient Greek principles, enabling the analysis of force multiplication in mechanical systems.^[4] The lever, 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 seesaw, where a small force applied at a distance from the fulcrum can balance a larger load closer to it. The mechanical advantage (MA) of a lever is given by the ratio of the effort arm length to the load arm length, expressed as MA = \frac{L_e}{L_l}, where L_e is the distance from the fulcrum to the effort force and L_l is the distance to the load.^[7] The wheel and axle operates on a similar principle, with a larger wheel attached to a smaller axle to amplify torque; for instance, a steering wheel on a vehicle allows a driver to turn the axle with reduced effort. The pulley system uses a wheel with a grooved rim and rope to redirect force, often multiplying it in block-and-tackle arrangements; its mechanical advantage equals the number of supporting ropes, as each shares the load.^[35] The inclined plane reduces the force needed to lift objects by spreading the effort over a longer distance, as seen in ramps used in architecture to move heavy materials to elevated positions without steep inclines. The wedge transforms linear motion into separation force, functioning like a movable inclined plane; examples include axes for splitting wood or doorstops to secure openings. Finally, the screw applies rotational motion to generate linear force through a helical incline wrapped around a cylinder, 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 1st century AD describing five fundamental powers (lever, wheel and axle, pulley, wedge, and screw) in his work Mechanica, which influenced later classifications that incorporated the inclined plane.^[36]

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.^[37] 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.^[38] Mechanical power sources store and release energy without continuous input, using components like springs or flywheels to provide intermittent bursts of motion. Springs, compressed or tensioned to store potential energy, drive clocks and toys through elastic deformation, while flywheels maintain rotational kinetic energy 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.^[39] Thermal power sources convert heat into mechanical work via engines, a cornerstone of industrial machinery. Steam engines, heated by burning fuel to expand water vapor against pistons, powered factories from the 18th century onward, while internal combustion engines ignite fuel-air mixtures to drive pistons. The efficiency of heat engines is fundamentally limited by the Carnot efficiency, given by the formula \eta = 1 - \frac{T_c}{T_h}, where T_c and T_h are the absolute temperatures of the cold and hot reservoirs, respectively; this theoretical maximum underscores why practical thermal engines achieve 20-40% efficiency.^[40] Electrical power sources supply energy through electromagnetic means, enabling precise control in modern machines. Electric motors convert electrical energy into rotational motion via electromagnetic fields, powering everything from household appliances to industrial robots, while batteries store chemical energy for portable applications. Rechargeable batteries, particularly lithium-ion types, deliver high energy density—up to 250 Wh/kg—making them essential for mobile devices and vehicles.^[41] Fluid power sources utilize pressurized liquids or gases to transmit force, offering advantages in heavy-duty tasks. Hydraulic systems employ incompressible fluids like oil to multiply force 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.^[39] 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 forging, 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%.^[42]^[43]^[44]^[45] Representative examples illustrate this progression: the Diesel engine, patented by Rudolf Diesel in the 1890s, uses compression ignition of heavy fuel oils to achieve 30-50% thermal efficiency 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.^[46]^[47]

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 integrity under load. These elements are essential for maintaining the stability and efficiency of machines, distinct from mechanisms that transmit motion.^[48] Structural components such as frames and housings serve as the primary supportive framework in machines, offering rigidity, alignment, and protection for internal parts. Frames, often constructed from robust materials to withstand static and dynamic loads, act as the foundational skeleton that distributes forces evenly across the assembly. Housings enclose sensitive components, shielding them from environmental factors like dust and vibration while facilitating heat dissipation.^[48]^[49] Bearings are critical machine elements designed to support loads while permitting relative motion between rotating or sliding parts, primarily to minimize friction and wear. 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 thrust loads in heavier machinery. These anti-friction designs significantly reduce energy loss compared to plain bearings by replacing sliding contact with rolling motion.^[50]^[48] 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.^[48]^[51] Materials selection for machine elements balances strength, weight, durability, and cost to meet performance demands. Metals like steel, particularly alloys such as AISI 1040, are widely used for their high tensile strength and toughness in load-bearing frames and fasteners. Composites, including carbon fiber-reinforced polymers, offer superior strength-to-weight ratios and corrosion resistance, making them prevalent in aerospace applications for lightweight housings and structural components.^[52] Standards from organizations like ANSI and ASME ensure interoperability, safety, and reliability in machine element design and manufacturing. 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.^[51]^[48]

Gears and Gear Trains

Gears are fundamental mechanical components used to transmit torque and motion between rotating shafts, enabling changes in speed, direction, and torque in machines. They consist of toothed wheels that mesh together, converting rotational energy efficiently while minimizing slippage. This transmission is essential in systems requiring precise control over mechanical power, such as engines and machinery. Gears have been integral to mechanical engineering since ancient times, but their modern design emphasizes durability, efficiency, and noise reduction. Common types of gears include spur gears, 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 torques, 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 torque is inversely proportional. This allows machines to achieve desired mechanical advantages, such as increasing torque at the expense of speed. In gear trains, multiple gears are arranged to compound these ratios. A simple gear train involves two meshed gears 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 efficiency 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 \sigma = \frac{W_t P_d}{F Y}, where W_t is the tangential load, P_d is the diametral pitch, F is the face width, and Y is the Lewis form factor dependent on tooth geometry.^[53] 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.^[54] 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.^[55] These components are widely applied in engines, automation, and consumer devices, often integrated with other elements like gears for power transmission in combined systems.^[54]

Linkages

A four-bar linkage 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.^[54] 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.^[56] 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.^[57] The slider-crank linkage, a variant with one sliding joint instead of all revolute, converts rotary motion to reciprocating linear motion and is central to internal combustion engines, where the crankshaft's rotation drives the piston's back-and-forth movement via a connecting rod.^[58] In this setup, combustion force on the piston generates torque on the crankshaft, enabling the engine's power cycle.^[59] Watt's linkage, invented by James Watt in 1784, is a type of approximate straight-line mechanism designed to guide a piston rod in nearly linear motion within the double-acting steam engine. 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.^[60] This innovation, detailed in Watt's patent, addressed the limitations of earlier beam engines by enabling more direct power transmission. In applications like chainless bicycle transmissions, four-bar linkages connect the pedals directly to the rear wheel, converting pedaling rotation into wheel propulsion without a chain, as demonstrated in designs where the linkage ensures smooth torque transfer.^[61]

Cams

Cams are profiled elements that impart prescribed motion to a follower through direct contact, typically converting constant rotary input into variable output displacement.^[55] 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.^[62] Disk cams are suited for high-speed applications due to their compact form, while cylindrical cams provide axial motion for linear guides.^[55] 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 friction and allow higher speeds by converting sliding to rolling motion.^[55] Roller followers are particularly effective in precision machinery, as the roller's center defines the trace point for profile design.^[63] For smooth operation, cam displacement is often designed using cycloidal motion, which provides constant acceleration followed by constant deceleration, avoiding infinite jerk at reversal points.^[64] The displacement s of the follower as a function of cam angle \theta over rise angle \beta and total rise h is given by:

s = \frac{h}{ \beta } \left( \theta - \frac{ \beta }{ 2\pi } \sin \left( \frac{2\pi \theta }{ \beta } \right) \right)

This equation ensures gradual velocity buildup, with maximum velocity v_{\max} = \frac{h}{\beta} and acceleration a_{\max} = \frac{2\pi h}{\beta^2}, making it suitable for mechanisms requiring minimal vibration.^[64] In sewing machines, cams control the needle's lateral swing and feed dog motion to produce decorative stitches, where interchangeable cam profiles dictate patterns like zigzags or scallops for automated embroidery.^[65] This application leverages the cam's ability to generate precise, repeatable intermittent actions.^[66]

Advanced Mechanisms

Spatial mechanisms extend beyond planar configurations to enable motion in three-dimensional space, allowing for complex trajectories with up to six degrees of freedom (DOF). These mechanisms are essential in robotics and precision engineering, where serial or parallel arrangements facilitate tasks requiring translation and rotation in multiple axes. A prominent example is the Stewart platform, 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 telescope positioning.^[67] The Stewart platform 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 surgery and vibration isolation systems, where its parallel architecture minimizes singularities in the workspace compared to sequential joint chains.^[67] 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 azimuth and elevation, as seen in satellite antenna pointing systems for maintaining alignment with ground stations. In robotics, spherical parallel manipulators, such as those with three rotational DOF, enable compact wrist designs for end-effectors, providing a wide orientation range with reduced inertia. For instance, antenna pointing mechanisms often employ two-axis gimbals driven by stepper motors to achieve precise tracking within ±69° elevation and unlimited azimuth.^[68] Flexure mechanisms, also known as compliant mechanisms, achieve motion through elastic deformation of flexible elements rather than traditional rigid joints, eliminating backlash, wear, and assembly needs. These designs distribute compliance across the structure, often using slender beams or hinges that deflect under load while maintaining precision, particularly in micro-electro-mechanical systems (MEMS) for sensors and actuators. In MEMS applications, flexure-based grippers or mirrors operate without joints, relying on material properties like Young's modulus 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 geometry is optimized to approximate ideal rotational behavior while accommodating large deflections without fatigue.^[69] The analysis of serial spatial mechanisms, such as robotic arms, commonly employs the Denavit-Hartenberg (DH) parameters to model kinematics systematically. This convention assigns four parameters to each joint: link length a_i, link twist \alpha_i, joint angle \theta_i, and link offset d_i, which define the homogeneous transformation matrix between consecutive frames. The forward kinematics 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 joints, facilitating both manual and computational analysis in robot design.^[70] The general DH transformation matrix from frame i-1 to i is given by:

{}^{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}

This formulation supports inverse kinematics solutions for trajectory planning, though it assumes revolute or prismatic joints without addressing parallel structures directly.^[70]

Analysis and Mechanics

Kinematics

Kinematics is the study of the geometry of motion in machines, focusing on the positions, velocities, and accelerations of interconnected links without considering the forces or masses involved. This branch of mechanics analyzes how mechanisms achieve desired motions through constraints imposed by joints and links, enabling the prediction of trajectories and speeds in systems ranging from simple linkages to complex assemblies.^[71] A fundamental concept in machine kinematics is the degrees of freedom (DOF), which quantifies the number of independent coordinates required to specify the configuration of a mechanism. For planar mechanisms, Gruebler's equation provides the DOF as follows:

\text{DOF} = 3(n - 1) - 2j - h

where n is the total number of links, j is the number of lower pairs (such as revolute or prismatic joints that constrain two degrees of freedom), and h is the number of higher pairs (such as point or line contacts that constrain only one degree of freedom). This equation, derived from counting the constraints in a closed kinematic chain, ensures mechanisms are neither overconstrained (DOF < 1, forming a structure) nor underconstrained (DOF > 1, allowing unintended motions). For example, a four-bar linkage with four links, four lower pairs, and no higher pairs yields DOF = 1, enabling controlled motion from a single input.^[71]^[72] Velocity analysis in kinematics determines the linear and angular velocities of links relative to one another, often using graphical or analytical methods to satisfy compatibility at joints. A key technique involves identifying instantaneous centers of velocity (IC), points where the velocity is zero at a given instant, about which a link appears to rotate purely. For a link in plane motion, the IC can be located by the intersection of perpendiculars to velocity vectors at two points on the link, allowing velocity magnitudes to be computed as v = \omega \times r, where \omega is the angular velocity and r the distance from the IC. Graphical methods, such as velocity polygons, construct vector diagrams by adding relative velocities at joints, providing a visual representation of the velocity field in mechanisms like slider-crank systems. These approaches are essential for ensuring smooth operation and avoiding interferences in multi-link chains.^[73]^[74] Acceleration analysis extends velocity considerations to capture changes in motion, particularly in mechanisms with combined rotation and sliding. When a point slides along a rotating link, the total acceleration includes the Coriolis component, arising from the coupling of translational and rotational motions:

\mathbf{a}_{\text{Coriolis}} = 2 \mathbf{v}_{\text{rel}} \times \boldsymbol{\omega}

where \mathbf{v}_{\text{rel}} is the relative velocity of the sliding point along the link, and \boldsymbol{\omega} is the angular velocity of the link; this vector is perpendicular to both \mathbf{v}_{\text{rel}} and \boldsymbol{\omega}, directed to account for the apparent deflection in the rotating frame. In sliding links, such as the piston in a slider-crank mechanism, this component must be added to centripetal, tangential, and relative accelerations to obtain the complete acceleration diagram, ensuring accurate prediction of inertial effects in kinematic simulations. Graphical acceleration polygons incorporate this term to resolve accelerations at joints iteratively.^[75]^[76] In practical applications, kinematic principles underpin path generation, where mechanisms are synthesized to guide a specific point along a prescribed trajectory, such as in robotic arms or automotive linkages. By specifying multiple pose positions (position and orientation) and applying inversion techniques or optimization, designers solve for link dimensions that approximate the desired path, often using four-bar or six-bar linkages for precision. For instance, in a path-generating four-bar mechanism, the coupler point's trajectory is analyzed via kinematic chains to minimize deviation from the target curve, with DOF constrained to unity for deterministic motion. This synthesis relies on velocity and acceleration analyses to verify timing and smoothness, enabling efficient designs in engineering tasks like contour following.^[77]^[78]

Dynamics

In machine dynamics, the study of forces and torques that cause motion builds upon kinematic descriptions of paths and velocities by incorporating causal interactions. Newton's second law for linear motion, expressed as \mathbf{F} = m \mathbf{a}, relates the net force on a body to its mass and acceleration, enabling the prediction of how applied forces alter the trajectory of machine components.^[79] Similarly, for rotational motion, the analogous form \boldsymbol{\tau} = I \boldsymbol{\alpha} connects torque to the moment of inertia and angular acceleration, which is essential for analyzing rotating elements like shafts and flywheels in machinery.^[80] Balancing in machines addresses unbalanced forces and moments arising from reciprocating or rotating masses, which can lead to vibrations and structural fatigue. In engines, primary forces occur at the fundamental frequency of the crankshaft rotation, while secondary forces appear at twice that frequency due to nonlinear kinematics in mechanisms like the slider-crank.^[81] For a slider-crank mechanism, the primary unbalanced force is given by F_{p1} = m r \omega^2 \cos \theta, where m is the reciprocating mass, r the crank radius, \omega the angular velocity, and \theta the crank angle; this can be partially countered by rotating counterweights on the crankshaft.^[82] Secondary forces, F_{s2} = m r \omega^2 (r/l) \cos 2\theta, where l is the connecting rod length, are typically smaller but require additional balancers, such as geared counter-rotating shafts, to mitigate in multi-cylinder engines.^[83] Vibration analysis in machines focuses on oscillatory responses to dynamic loads, with the natural frequency determining resonance risks. For a simple spring-mass system modeling machine isolators or suspensions, the undamped natural frequency is \omega_n = \sqrt{k/m}, where k is the stiffness and m the mass; excitation near this frequency amplifies amplitudes, potentially causing failure.^[84] Damping ratios influence decay rates, and modal analysis extends this to multi-degree-of-freedom systems in complex machinery like turbines. Energy methods provide an alternative to force-based analysis by tracking work and power transfers. The work-energy principle states that the net work done on a machine element equals the change in its kinetic energy, W = \Delta KE, facilitating efficiency calculations in cyclic operations.^[85] In lossless systems, conservation of mechanical energy holds, where total kinetic plus potential energy remains constant, KE + PE = \text{constant}, aiding the study of conservative mechanisms without explicit force resolution.^[86]

Design and Control

Machine Design Principles

Machine design principles provide a structured methodology to develop reliable and efficient mechanical systems, ensuring they meet functional requirements while minimizing risks of failure. The process begins with needs analysis, also known as task clarification, where engineers identify the problem, establish requirements, and develop a comprehensive product specification that includes constraints such as performance, cost, and safety. This phase ensures the design aligns with user needs and commercial viability.^[87] Following needs analysis, conceptual design involves abstracting the essential problem, establishing functional structures for energy, material, and signal flows, and generating solution principles to create concept variants. These variants are evaluated against technical and economic criteria to select the optimal approach, often using sketches or basic models to explore feasibility without detailed geometry. Embodiment design then refines the selected concept into a preliminary layout, verifying function, strength, and spatial compatibility through iterative refinement. Tools like CAD software, such as SolidWorks, facilitate this stage by enabling 3D modeling, simulation of design variations, and early detection of issues like stress concentrations or interference, reducing the need for physical prototypes.^[87]^[88] Key factors in machine design include safety margins to account for uncertainties in loads, materials, and manufacturing. Safety factors, defined as the ratio of failure load to allowable load, typically range from 1.5 to 4 depending on load type and conditions; for example, 1.5 applies to static loads with well-known materials and conditions, while 2 to 4 is used for fatigue or impact loads to prevent yielding or fracture. For ductile materials under complex stress states, the von Mises failure theory predicts yielding when the equivalent stress exceeds the yield strength, calculated as \sigma' = \sqrt{\frac{(\sigma_x - \sigma_y)^2 + (\sigma_y - \sigma_z)^2 + (\sigma_z - \sigma_x)^2 + 6(\tau_{xy}^2 + \tau_{yz}^2 + \tau_{zx}^2)}{2}} for triaxial cases, providing a conservative criterion that ignores local stress concentrations due to material redistribution upon yielding.^[89]^[90] Optimization in machine design employs finite element analysis (FEA) to evaluate stress distribution and refine geometries for performance. FEA divides the model into discrete elements to simulate loads, revealing areas of high stress and enabling adjustments like material changes or shape modifications to minimize weight while maintaining integrity; for instance, using shell elements for thin components ensures accurate stress predictions with efficient computation. This technique integrates inputs from mechanical dynamics, such as load paths, to validate designs iteratively.^[91] Adherence to standards like ASME Y14.5 ensures precise communication of design intent through geometric dimensioning and tolerancing (GD&T), defining symbols, rules, and tolerance zones for part features to control form, orientation, location, and runout. This standard promotes manufacturability and interchangeability by specifying functional relationships, reducing ambiguity in drawings and inspections.^[92]

Controllers and Automation

Controllers and automation systems regulate machine operation by monitoring performance and adjusting inputs to achieve desired outputs, ensuring stability, efficiency, and precision in mechanical processes. These systems range from simple mechanical devices to sophisticated digital architectures that integrate sensors, actuators, and computational algorithms. In machine engineering, controllers maintain variables such as speed, position, or temperature, while automation extends this to sequential or repetitive tasks, reducing human intervention and enhancing productivity.^[93] Open-loop control systems operate without feedback, relying on predefined inputs like timers or fixed sequences to command machine actions, suitable for predictable environments where disturbances are minimal.^[94] In contrast, closed-loop systems incorporate feedback by continuously measuring the actual output via sensors and comparing it to a setpoint, adjusting the control signal to minimize the error, defined as error = setpoint - measured\ value.^[95] A prominent example of closed-loop control is the proportional-integral-derivative (PID) controller, which combines proportional response to current error, integral action to eliminate steady-state offsets, and derivative anticipation of future errors for smoother regulation.^[96] Historically, one of the earliest feedback controllers was James Watt's centrifugal governor, patented in 1788, which automatically adjusted steam flow to a rotary steam engine by using flyballs to sense speed variations and modulate a throttle valve, maintaining constant rotational speed despite load changes.^[97] This mechanical innovation marked a foundational step in automatic regulation, enabling reliable power delivery in early industrial machinery.^[98] In the modern era, programmable logic controllers (PLCs), introduced in the late 1960s by Dick Morley at Bedford Associates, revolutionized industrial automation by replacing hardwired relay systems with reprogrammable digital logic for sequencing machine operations in manufacturing environments.^[99] The first PLC, the Modicon 084, deployed in 1969, facilitated flexible control of assembly lines and process plants, supporting ladder logic programming for reliability in harsh conditions.^[100] Advancements in the 2020s have integrated artificial intelligence, particularly neural networks, into adaptive control for machines facing uncertain or nonlinear dynamics, where traditional PID may falter. Neural network-based controllers learn from data to approximate complex models and adjust parameters online, as demonstrated in real-time deep neural network architectures for nonlinear systems tracking.^[101] More recent developments as of 2025 include deep reinforcement learning (DRL) for predictive self-adapting robot control and integration of digital twins with neural networks for real-time adaptive systems, such as in automotive suspension, enhancing robustness in dynamic environments.^[102]^[103] Automation levels in machines progress from semi-automated systems, such as computer numerical control (CNC) machines that execute programmed paths with operator oversight for setup and loading, to fully automated setups in Industry 4.0 featuring collaborative robots (cobots).^[104] CNC systems, using closed-loop feedback for axis positioning, represent semi-automation by handling precise milling or turning while requiring human intervention for material changes.^[105] Full automation, exemplified by Industry 4.0 cobots, integrates sensors for safe human-robot collaboration, enabling adaptive tasks like assembly in smart factories without barriers, as outlined in sociotechnical frameworks for enhanced productivity.^[106] Emerging as of 2025, Industry 5.0 builds on this by emphasizing human-centric collaboration between AI, machines, and workers for resilient and sustainable manufacturing.^[107] These levels often integrate with machine design principles to balance human oversight and autonomous operation.

Specialized Machines

Computing Machines

Computing machines represent a class of devices engineered for systematic information processing and computation, evolving from rudimentary mechanical aids to sophisticated electronic and quantum systems. These machines manipulate data through predefined operations, enabling tasks ranging from arithmetic calculations to complex simulations. The development of computing machines has been pivotal in advancing human capability to handle abstract and large-scale information, laying the foundation for modern digital technology. Early mechanical precursors emerged in the 17th and 19th centuries as attempts to automate arithmetic. Blaise Pascal invented the Pascaline in 1642, a gear-based device capable of addition and subtraction to assist with tax computations, marking the first mechanical calculator designed for practical use.^[108] Nearly two centuries later, Charles Babbage conceived the Analytical Engine in 1834, a programmable mechanical computer that incorporated punch cards for input and control, inspired by Jacquard looms, and featured components like a mill for arithmetic and a store for memory, though it was never fully built.^[109] These inventions demonstrated the feasibility of mechanizing logical operations but were limited by mechanical complexity and lack of electronic speed. The transition to electronic computing accelerated in the mid-20th century, grounded in theoretical foundations. Alan Turing formalized the concept of a universal machine in his 1936 paper "On Computable Numbers," describing an abstract device capable of simulating any algorithm through a tape-based read-write mechanism, which became the theoretical basis for general-purpose computers.^[110] This idea materialized in hardware with ENIAC, completed in 1945, the first programmable electronic general-purpose digital computer, built for the U.S. Army to compute artillery firing tables using vacuum tubes for over 5,000 additions per second.^[111]^[112] The architecture of modern computers traces to John von Neumann's 1945 report on EDVAC, which outlined a stored-program design separating processing unit, memory, and input-output, allowing instructions and data to reside in the same memory space for flexibility.^[113] Contemporary computing machines build on these principles, incorporating binary logic and scaling through miniaturization. Binary logic, where information is represented as 0s and 1s corresponding to Boolean true/false states, was applied to electrical circuits by Claude Shannon in his 1937 master's thesis, enabling the design of reliable digital switches fundamental to all electronic computers.^[114] Moore's Law, observed by Gordon Moore in 1965, predicted that transistor density on integrated circuits would double approximately every two years, driving exponential growth in computing power; by 2025, this scaling has approached physical limits due to atomic scales and heat dissipation, prompting innovations like 3D stacking.^[115] Quantum computing extends these boundaries, as exemplified by IBM's Osprey processor announced in 2022 with 433 superconducting qubits, enabling parallel computations for problems intractable on classical machines, such as molecular simulations. More recently, as of November 2025, IBM announced the Nighthawk processor, advancing toward fault-tolerant quantum systems with improved coherence and error correction capabilities.^[116]^[117]

Molecular Machines

Molecular machines are nanoscale devices, typically operating at the atomic or molecular level, that perform mechanical work through chemical or physical processes, often mimicking the functionality of biological systems. These machines convert energy from sources such as chemical reactions, light, or proton gradients into directed motion or force generation, enabling tasks like transport, synthesis, and assembly at scales where thermal fluctuations dominate. Unlike macroscopic machines, molecular machines must contend with pervasive Brownian motion, yet they achieve functionality by harnessing these random thermal movements in a directed manner.^[118] In biological systems, molecular machines exemplify efficient energy transduction at the cellular level. ATP synthase, a rotary motor embedded in mitochondrial and chloroplast membranes, harnesses proton gradients across the membrane to drive the synthesis of adenosine triphosphate (ATP), the cell's primary energy currency, through a 120-degree stepwise rotation of its central rotor. This enzyme's F1 domain rotates unidirectionally, powered by the proton motive force, producing up to three ATP molecules per full revolution. Similarly, kinesin is a linear motor protein that facilitates intracellular transport by walking processively along microtubules, carrying vesicles and organelles toward the cell periphery at speeds of about 800 nm per second while hydrolyzing ATP for each 8-nm step. These natural motors operate in aqueous environments where the thermal energy scale, given by kT at room temperature (approximately 298 K), is about $4.1 \times 10^{-21} J, underscoring their ability to generate directed motion against diffusive chaos.^[119]^[120]^[121]^[118] Synthetic molecular machines draw inspiration from these biological counterparts, with significant advances recognized by the 2016 Nobel Prize in Chemistry awarded to Jean-Pierre Sauvage, Sir J. Fraser Stoddart, and Bernard L. Feringa for designing and synthesizing molecular machines. Feringa's pioneering work introduced the first light-driven unidirectional rotary motor in 1999, based on overcrowded alkenes that undergo 360-degree rotations around a central carbon-carbon double bond upon sequential ultraviolet and visible light irradiation, followed by thermal helix inversions. These motors demonstrate autonomous, directional rotation at the molecular scale, with rotation rates tunable by light wavelength and temperature. Emerging applications of synthetic molecular machines include targeted drug delivery via nanobots, particularly those constructed using DNA origami techniques developed in the 2000s. DNA origami enables the folding of long single-stranded DNA into precise nanostructures, such as reconfigurable nanocapsules that can encapsulate drugs like doxorubicin and release them in response to pH changes in tumor microenvironments, enhancing specificity and reducing systemic toxicity in cancer therapy. For instance, pH-responsive DNA origami structures have demonstrated controlled release at acidic pH levels (around 5.0), with studies showing up to 60% release efficiency under combined stimuli and high cellular uptake.^[122]^[123]^[124] These systems leverage Brownian motion for diffusion while using external triggers to rectify motion for precise navigation and actuation. Recent advances as of 2025 include self-driving molecular machines powered by enzymatic oxidation-reduction cycles and programmable robotic platforms for synthesizing complex molecular machines.^[125]^[126]

Societal Impact

Mechanization and Productivity

Mechanization has profoundly influenced economic productivity by enabling faster and more efficient production processes, particularly in agriculture and manufacturing. In the 19th century, the introduction of the mechanical reaper by Cyrus McCormick dramatically boosted agricultural output in the United States, increasing farms' potential yield at least tenfold by allowing a single man and horse to harvest large fields that previously required extensive manual labor.^[127] This innovation contributed to significant GDP growth in agrarian economies, as mechanized harvesting reduced labor needs and expanded cultivable land, fueling the expansion of the U.S. agricultural sector during the Industrial Revolution.^[128] The adoption of machines also drove major labor shifts from rural agrarian work to urban industrial employment across Europe. For instance, in Britain, the share of the labor force in agriculture declined from about 40% in 1800 to less than 10% by 1900, as workers migrated to factories enabled by steam-powered machinery and other inventions of the Industrial Revolution.^[129] Similar patterns emerged elsewhere, such as in Belgium where agricultural employment fell from 62% to 38% over the same period, reflecting a broader transition that increased factory-based manufacturing and overall economic output.^[129] Quantitative metrics underscore these gains, with total factor productivity (TFP)—often measured via the Solow residual—attributing roughly 50% or more of post-World War II U.S. economic growth to technological advancements, including mechanization. A seminal case study is Henry Ford's 1913 implementation of the moving assembly line for the Model T, which slashed vehicle assembly time from 12 hours to 1.5 hours per car, boosting productivity and enabling mass production that transformed the automotive industry and contributed to broader industrial efficiency.^[130] These developments illustrate how machines have historically amplified economic output by optimizing resource use and scaling operations.

Ethical and Environmental Considerations

The proliferation of machines, particularly through automation, has raised significant ethical concerns regarding job displacement. In the manufacturing sector, automation contributed to a substantial decline in employment, with U.S. manufacturing jobs falling by approximately 35% from 19.6 million in 1979 to 12.8 million in 2019, driven largely by technological advancements and productivity gains.^[131] Between 2000 and 2010 alone, nearly 6 million manufacturing positions were lost, exacerbating economic inequality and requiring workforce reskilling efforts.^[132] As of 2025, U.S. manufacturing employment has stabilized at approximately 13 million jobs, though AI advancements continue to drive reskilling needs.^[133] Additionally, in decision-making machines powered by artificial intelligence (AI), biases inherent in training data can perpetuate discrimination, as highlighted in analyses of algorithmic fairness where skewed datasets lead to unequal outcomes in areas like hiring and lending.^[134] For instance, studies have shown that AI systems in recruitment can amplify gender and racial biases if not mitigated through diverse data and auditing protocols.^[135] Environmentally, machine production and operation contribute to resource depletion, notably the extraction of rare earth elements (REEs) essential for electric vehicle (EV) motors and batteries. REE mining generates toxic waste and habitat destruction, with each ton of rare earths producing up to 2,000 tons of toxic waste, straining global supplies projected to meet rising clean energy demands.^[136] Electronic waste (e-waste) from discarded machines further compounds the issue, with global generation reaching 62 million tonnes in 2022—equivalent to 7.8 kg per person—and projected to increase by 32% to 82 million tonnes by 2030 if recycling rates remain low at 22.3%.^[137] Data centers supporting AI-driven machines also impose a heavy carbon footprint, accounting for about 1% of global energy-related greenhouse gas emissions in 2024, with projections estimating a rise to 1.4% by 2030 due to surging computational demands.^[138] Regulatory frameworks address these challenges by enforcing safety and sustainability standards. The EU Machinery Directive 2006/42/EC establishes essential health and safety requirements for machine design and construction, ensuring risk assessments and protective measures to prevent accidents across the European market.^[139] Complementing this, circular economy initiatives promote recyclable machine designs, such as the EU's Waste Electrical and Electronic Equipment (WEEE) Directive, which mandates producers to facilitate disassembly, reuse, and material recovery to minimize waste and resource use.^[140] Looking toward sustainable advancements, the 2020s have seen the emergence of green robotics inspired by biological systems, emphasizing low-energy efficiency. For example, bio-inspired designs mimicking reptilian locomotion enable robots to navigate rough terrain with minimal power consumption, reducing operational environmental impacts through optimized mechanics and AI control.^[141] These approaches, including soft robotics derived from natural movements, support eco-friendly applications in monitoring and remediation while aligning with broader goals of energy-efficient automation.^[142]

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Design of chainless bicycle transmission system using four linkages ...
Two types of models were made using the same principle. These two types of bicycle system designs use a four linkages connecting mechanism. The system motion ...<|separator|>
[60]
[PDF] CAMS - De Anza College
A cam that moves the follower axially, or parallel to the axis of the cam, is called a cylindrical cam or drum cam. ... The drive mechanism may be a. 17. Name ...Missing: disk | Show results with:disk
[61]
Cam followers | SKF
SKF cam followers (stud-type track rollers) are designed to run on all types of tracks and to be used in cam drives, conveyor systems, etc.
[62]
Motion Diagrams - CAM MECHANISMS
The equations relating the follower displacement, velocity and acceleration to the cam rotation angle are: Within the curves we have thus far seen, cycloidal ...
[63]
Cam Design - CAM MECHANISMS
These cams exist in sewing machines in toys, in recording instruments. ... Typical application is toys, automatic screw cutting machines, sewing machines, etc.
[64]
[PDF] Cam Chap 1 PM 6 - TEquipment
Many sewing machines use cams to obtain patterned stitching. If you go to a health club, you use cams to actuate many of the weight training machines.
[65]
A Platform with Six Degrees of Freedom - D. Stewart, 1965
First published June 1965. A Platform with Six Degrees of Freedom. D. StewartView all authors and affiliations. Volume 180, Issue 1 · https://doi.org/10.1243 ...
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Antenna Pointing Mechanisms - Moog Inc.
Antenna Pointing Mechanisms (APMs) point antenna bore sight to its target and track to maintain RF link. APMs are typically two-axis gimbals.
[67]
Design of Compliant Mechanisms: Applications to MEMS
Abstract. Compliant mechanisms are single-piece flexible structures that deliver the desired motion by undergoing elastic deformation as opposed to jointed ...
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A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
Jun 4, 2021 · ... A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices” (Denavit, J., and Hartenberg, R. S., 1955, ASME J. ... PDF. Open the PDF ...
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Chapter 4. Basic Kinematics of Constrained Rigid Bodies
4.4.1 Gruebler's Equation ... The definition of the degrees of freedom of a mechanism is the number of independent relative motions among the rigid bodies. For ...Degrees of Freedom of a Rigid... · Degrees of Freedom of Planar...
[70]
Mobility criteria : Grueblers equation for mechanism design
Nov 15, 2024 · Gruebler's equation is commonly used to calculate the mobility of planar mechanisms. It is expressed as: M = 3(N-1) – 2J-H
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[PDF] Kinematics of Rigid Bodies Instant Centers or Instantaneous Centers
Mar 5, 2007 · This simply means that the body is instantaneously rotating about an external point. The instant center can change in time. Example: Rolling ...
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12.7: Instantaneous Center of Zero Velocity - Engineering LibreTexts
Aug 18, 2024 · Instantaneous Center of Zero Velocity is a graphical technique that can help simplify relative motion problems.Finding the Instantaneous... · Finding ICs when velocities... · Worked Problems
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[PDF] UNIT 2 KINEMATICS OF LINKAGE MECHANISMS - Sathyabama
The sliding link has two relative velocities, the radial and the tangential. They are normal to each other and the true velocity relative to A is the vector sum ...
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Kinematics of Linkage Mechanisms - BrainKart
Nov 16, 2016 · Coriolis Acceleration:Ac = 2 (dr/dt). In a direction perpendicular to the link. A slider attached to ground experiences only sliding ...
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Kinematic Synthesis of Adjustable Mechanisms—Part 2: Path ...
Adjustment of the path generator mechanism is accomplished by moving a fixed pivot. Mechanisms adjustable for different approximate straight line motions, for ...
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https://www.brainkart.com/article/Kinematics-of-Linkage-Mechanisms_6279/
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9 Newton's Laws of Dynamics - Feynman Lectures
In order to use Newton's laws, we have to have some formula for the force; these laws say pay attention to the forces. If an object is accelerating, some ...
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10.7 Newton's Second Law for Rotation – University Physics Volume 1
In this section, we introduce the rotational equivalent to Newton's second law of motion and apply it to rigid bodies with fixed-axis rotation.Missing: machine | Show results with:machine
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Design and Dynamic Analysis of Different Balancing Mechanisms ...
One of the conventional approaches to balance the primary unbalanced force in the slider-crank mechanism is by adding counterweights to the crankshaft, ...<|separator|>
[80]
Shaking moment cancellation of self-balanced slider–crank ...
This paper presents a solution for improving the balancing of double slider–crank mechanical systems. In these systems the shaking force balancing is achieved ...
[81]
Dynamic Balancing of a Single Crank-Double Slider Mechanism ...
This article presents a systematic investigation of the dynamic balancing of a singlecrank-double slider mechanism of which the coupler links have symmetric ...
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Differential Equations - Mechanical Vibrations
Nov 16, 2022 · In this section we will examine mechanical vibrations. In particular we will model an object connected to a spring and moving up and down.
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[PDF] Lecture L12 - Work and Energy - MIT OpenCourseWare
... principle of work and energy, and states that the mechanical work done on a particle is equal to the change in the kinetic energy of the particle. External ...
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Conservation of Energy & Work-Energy Principle
Aug 5, 2022 · The relation between the energy conservation principle, the work-energy principle, and the mechanical energy balance.
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Systematic Engineering Design
Pahl and Beitz divided their method into a number of broad phases, each with a set of basic steps. 1. Start off with product planning and a clarification of the ...
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[PDF] Analysis Guide for Machine Designers - SolidWorks
This guide describes key design issues, benefits of SOLIDWORKS analysis, and how analysis tools help evaluate designs, reduce costs, and identify issues.Missing: steps embodiment
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Factors of Safety - Roy Mech
The factors of safety listed below are based on the yield strength.. Material properties known in detail.
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None
### Summary of Von Mises Failure Theory for Ductile Materials in Machine Design Context
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3 Steps to Improve FEA Models - Ansys
Dec 2, 2020 · An important step in improving an FEA model is model simplification. However, the model must be simplified in the right way to achieve accurate analyses.
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Y14.5 - Dimensioning and Tolerancing - ASME
In stockProduct Options. The Y14. 5 standard is considered the authoritative guideline for the design language of geometric dimensioning and tolerancing (GD&T.)
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Principles of PID Controllers | Zurich Instruments
In the context of control strategies, an open-loop control system refers to a controller whose action is determined based on predetermined input values without ...
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Introduction: PID Controller Design
A PID controller is a feedback compensator that captures system history and anticipates future behavior. It uses proportional, integral, and derivative gains.PID Overview · Open-Loop Step Response · Proportional-Integral Control
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[PDF] PID Control
The PID controller is the most common form of feedback. It was an es- sential element of early governors and it became the standard tool when.
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Brief History of Feedback Control - F.L. Lewis
In 1788 Watt completed the design of the centrifugal flyball governor for regulating the speed of the rotary steam engine. This device employed two pivoted ...
[96]
ECE 486 Control Systems
In 1788, James Watt patents the centrifugal governor for controlling the speed of a steam engine. The governor combines sensing, actuation, and control. The ...
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Historical Engineers: Richard Morley and the Programmable Logic ...
Oct 15, 2018 · Richard Morley is credited as the person who helped modernize industrial facilities with the invention of the programmable logic controller.
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History - PLC/PAC Tutorial Place
The Programmable Logic Controller (PLC) was conceived by Dick Morley on January 1, 1968. Mr. Morley's PLC, which at the time was called a PC for Programmable ...
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Neural Network-based Flight Control Systems: Present and Future
Jun 11, 2022 · As the first review in this field, this paper presents an in-depth mathematical view of Intelligent Flight Control Systems (IFCSs), particularly ...
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SINUMERIK CNC automation system - Siemens US
SINUMERIK is the perfect automation CNC system for machine tools - from Job-Shop manufacturing through large series production.
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15 Types of CNC Machines and How to Automate Them
Nov 8, 2022 · You can automate almost any CNC machine with a robot, though some are easier to integrate with an automation solution than others.
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Cobots in Industry 4.0: A Roadmap for Future Practice Studies on ...
Jul 19, 2021 · We propose a research agenda for social practice and workplace studies to explore the sociotechnical environment of Industry 4.0 involving cobots.
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Blaise Pascal Invents a Calculator: The Pascaline
Mathematician and philosopher Blaise Pascal Offsite Link invented an adding machine, the Pascaline Offsite Link.
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The Engines | Babbage Engine - Computer History Museum
It was programmable using punched cards, an idea borrowed from the Jacquard loom used for weaving complex patterns in textiles. The Engine had a 'Store' where ...Missing: source | Show results with:source
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[PDF] ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ...
Detailed description of the universal machine. A table is given below of the behaviour of this universal machine. The. •m-configurations of which the machine ...
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ENIAC - CHM Revolution - Computer History Museum
ENIAC (Electronic Numerical Integrator And Computer), built between 1943 and 1945—the first large-scale computer to run at electronic speed without being slowed ...Missing: source | Show results with:source
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[PDF] First draft report on the EDVAC by John von Neumann - MIT
June 30, 1945. This is an exact copy of the original typescript draft as obtained from the University of Pennsylvania. Moore School Library except that a ...
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Applications of Boolean Algebra: Claude Shannon and Circuit Design
As a graduate student at MIT, Claude Shannon (1916-2001) applied symbolic logic to electrical circuit design.<|separator|>
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Press Kit: Moore's Law - Intel Newsroom
Moore's Law is the observation that the number of transistors on an integrated circuit will double every two years with minimal rise in cost.
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IBM Unveils 400 Qubit-Plus Quantum Processor and Next ...
Nov 9, 2022 · The new 433 qubit 'Osprey' processor brings us a step closer to the point where quantum computers will be used to tackle previously unsolvable problems.
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Brownian Motors - Physics Today
Nov 1, 2002 · In comparison, a molecular motor moving through water exchanges about 4 × 10−21 J (the thermal energy kT at room temperature) with its ...
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The six steps of the complete F1-ATPase rotary catalytic cycle - Nature
Aug 3, 2021 · F1Fo ATP synthase is a biological rotary motor that utilizes a rotary catalytic mechanism to couple proton translocation across a membrane ...
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Magic-angle-spinning NMR structure of the kinesin-1 motor domain ...
Nov 10, 2022 · The kinesin superfamily of proteins (KIFs) are motors that transport cargos and organelles along microtubules to specific destinations using ATP ...<|separator|>
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WALKING ON TWO HEADS: THE MANY TALENTS OF KINESIN
Yeast Kar3 is a minus-end microtubule motor protein that destabilizes microtubules preferentially at the minus ends. ... Mutation of the axonal transport motor ...
[115]
DNA Origami Delivery System for Cancer Therapy with Tunable ...
The findings indicate that DNA origami nanostructures represent an efficient delivery system for Dox, resulting in high degrees of internalization and increased ...Figure 1 · Figure 2 · Folding Of Dna Origami...
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Reconfigurable DNA Origami Nanocapsule for pH-Controlled ...
Apr 16, 2019 · We present a DNA origami nanocapsule that can be loaded with cargo and reversibly opened and closed by changing the pH of the surrounding solution.Methods · Nanocapsule Design And... · Aunp-Dna Conjugate...
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Cyrus McCormick - Lemelson-MIT
... world's first mechanical reaper to the public. McCormick had singlehandedly increased farms' potential yield at least tenfold, with minimal effort by farmers.Missing: productivity | Show results with:productivity
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Reaping the Benefits of the Reaper | Richmond Fed
The reaper broke the harvest-labor bottleneck by allowing the farmer "to reap as much as he could sow." This big step toward automation allowed farms to become ...
[119]
5.4.2 Labour in Modern History (ca. 1800–1900)
Feb 20, 2023 · This chapter will give an overview of the most important changes that took place in the agricultural, manufacturing, and service sectors as well as the social ...
[120]
Henry Ford and the Moving Assembly Line - Twelve Year History
Aug 25, 2023 · The moving assembly line began in 1913, reducing chassis assembly time from 12 to 1.5 hours, but created repetitive work and high worker ...
[121]
Forty years of falling manufacturing employment
Nov 20, 2020 · Manufacturing employment peaked in 1979 at 19.6 million, then fell to 12.8 million in 2019, a 35% decrease, and never fully recovered after ...Missing: displacement | Show results with:displacement
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[PDF] The Transformation of Manufacturing and the Decline in US ...
Six million manufacturing jobs disappeared between 2000 and 2010, with much of the job loss occurring prior to the start of the Great Recession. In the years ...
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Ethical concerns mount as AI takes bigger decision-making role
Oct 26, 2020 · AI presents three major areas of ethical concern for society: privacy and surveillance, bias and discrimination, and perhaps the deepest, most ...
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Ethics and discrimination in artificial intelligence-enabled ... - Nature
Sep 13, 2023 · This study aims to address the research gap on algorithmic discrimination caused by AI-enabled recruitment and explore technical and managerial solutions.Missing: seminal | Show results with:seminal
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Not So “Green” Technology: The Complicated Legacy of Rare Earth ...
Aug 12, 2021 · Both methods produce mountains of toxic waste, with high risk of environmental and health hazards. For every ton of rare earth produced, the ...
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Global e-Waste Monitor 2024: Electronic Waste Rising Five Times ...
Mar 20, 2024 · A record 62 million tonnes (Mt) of e-waste was produced in 2022, Up 82% from 2010;; On track to rise another 32%, to 82 million tonnes, in 2030; ...
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AI: Five charts that put data-centre energy use – and emissions
Sep 15, 2025 · The agency estimates that data-centre emissions will reach 1% of CO2 emissions by 2030 in its central scenario, or 1.4% in a faster-growth ...
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Directive 2006/42/EC - machinery directive - EU-OSHA
Jun 13, 2024 · Directive 2006/42/EC on machinery lays down health and safety requirements for the design and construction of machinery, placed on the European market.
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Circular Economy - Environment - European Commission
Due for adoption in 2026, the Circular Economy Act aims to establish a Single Market for secondary raw materials, increase the supply of high-quality recycled ...Missing: machine | Show results with:machine
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(PDF) Bio-inspired Energy-Efficient Robot: Mimicking Reptilian ...
Sep 1, 2025 · This paper details the biological rationale, mechanical design, control systems, simulation, and practical applications of this robot. It ...
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Biologically-inspired soft robots for environmental sustainability
This webinar highlighted how by combining biology and robotics we can create bio-inspired soft robots that can be completely sustainable.