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Wedge

A wedge is a simple machine characterized by a triangular shape with two inclined planes joined at a sharp edge, thick at one end and tapering to a thin point at the other, designed to split, lift, or secure objects by directing force along its sloping surfaces.^[1] It functions by transforming an input force applied to its broader base into a greater output force at the tip, thereby multiplying mechanical advantage and making tasks like cutting or separating materials more efficient with less effort.^[2] The wedge has been one of the six classical simple machines recognized since ancient times, alongside the lever, wheel and axle, pulley, inclined plane, and screw, and it operates on the principle of converting linear motion into a splitting or holding action.^[3] Archaeological evidence indicates its use dates back to prehistoric eras, when early humans employed naturally jagged stones as rudimentary wedges for skinning animals and processing food, evolving into more refined tools by around 3000 BC in ancient Egypt, where wooden wedges were utilized to fracture large stone blocks for pyramid construction.^[4] In modern applications, wedges appear in everyday tools such as axes for chopping wood, knives for slicing, chisels for carving, doorstops for securing doors, and even nails or pins that hold materials together by embedding their tapered forms.^[5] These devices not only reduce the force required for separation—often achieving mechanical advantages greater than 5 depending on the angle of the incline—but also play critical roles in engineering, from splitting logs in forestry to stabilizing structures in construction.^[1]

Definition and Principles

Physical Description

The wedge is one of the six classical simple machines, defined as a device consisting of two inclined planes joined at a sharp edge to form a triangular or tapered shape.^[1] This configuration allows the wedge to be driven into materials by applying force to its thicker end, thereby redirecting the force along the sloping surfaces.^[6] Unlike compound machines, the wedge operates without internal moving parts, relying solely on its fixed geometry to alter the direction of applied force.^[7] The geometric properties of a wedge are characterized by its length along the inclined surface (L), the height or thickness at the thick end (t), and the angle of inclination (θ) between each plane and the base.^[8] These dimensions determine the wedge's efficiency in force application; a longer L relative to t results in a smaller θ, which distributes force more gradually.^[9] The cross-section of a typical wedge forms an isosceles triangle, with the apex representing the sharp edge and the base the thick end, as illustrated in basic diagrams of simple machines where the inclined planes converge symmetrically.^[1] Common materials for wedges include wood for its ease of shaping and availability, metal such as steel for enhanced durability and sharpness retention, and stone in contexts requiring resistance to wear.^[10] Modern variants may incorporate plastics or composites for lightweight, corrosion-resistant applications in specialized tools.^[11]

Fundamental Mechanics

The fundamental mechanics of a wedge operate on the principle of force transformation, where an input force applied along the length of the wedge generates a larger output force perpendicular to its surfaces, enabling the separation or lifting of objects. This process adheres to Newton's laws of motion, particularly the second law (F = ma), as the applied force accelerates the wedge into the material, resolving into components that overcome resistance through normal and shear stresses.^[12] A wedge functions as two inclined planes positioned back-to-back, forming a tapered structure that distributes the input force over an extended path. The input force along the slope resolves into a normal component perpendicular to the contact surface and a parallel component that counters friction, allowing the wedge to penetrate and exert separating forces on the opposing sides. This duality with the inclined plane amplifies the effective force output by increasing the distance over which the work is applied, in line with the conservation of energy in ideal conditions.^[12] The ideal mechanical advantage (IMA) of a wedge is given by the equation:

\text{IMA} = \frac{L}{t}

where L is the length along the slope of the wedge and t is the thickness (or height) at the wide end. This ratio quantifies the theoretical amplification of force without considering losses, derived from the geometry of the inclined planes.^[12] In practice, friction significantly influences wedge performance through the coefficient of friction \mu, which opposes motion and dissipates energy as heat. During insertion, kinetic friction acts along the sliding surfaces to resist penetration, requiring greater input force than the ideal case, while static friction predominates during removal or holding, potentially creating a self-locking effect where the wedge remains in place without additional force if \mu is sufficiently high. The distinction between static (\mu_s) and kinetic (\mu_k) coefficients—typically \mu_s > \mu_k—means extraction often demands more force than insertion due to the higher static threshold that must be overcome.^[13]^[14]

Historical Development

Ancient Origins

The earliest evidence of wedge tools dates to the Paleolithic era, where they were employed for practical tasks such as splitting wood and bone. Archaeological excavations have uncovered bone wedges from approximately 80,000 to 60,000 years ago at Sibudu Cave in KwaZulu-Natal, South Africa, which show use-wear patterns consistent with woodworking and splitting activities. Earlier examples include modified bone tools from 1.7 to 1.2 million years ago, interpreted as wedges used by early hominins to fracture wood and process animal remains.^[15]^[16] In key ancient civilizations, wedges facilitated monumental engineering feats. Around 2600 BCE, during the construction of Egypt's pyramids, workers utilized wooden wedges to quarry limestone and granite blocks from bedrock. This technique involved chiseling grooves or exploiting natural fissures in the stone, inserting dry wooden wedges, and then soaking them with water to cause expansion and controlled splitting, enabling the extraction of massive stones for structures like the Great Pyramid of Giza.^[17]^[18] The invention of the wedge cannot be attributed to a single individual but emerged from prehistoric tool-making practices among early human populations, evolving from simple lithic and organic materials. While no specific pre-1000 BCE texts directly reference wedge tools, their widespread adoption is evident in archaeological contexts across Eurasia and Africa. Culturally, the wedge held significant importance in early human engineering, allowing communities to split logs for building shelters and process materials for survival. For instance, at sites like Kalambo Falls in Zambia, wooden wedges from over 300,000 years ago aided in constructing platforms and handling timber, demonstrating their role in enabling more complex habitation and resource management. This foundational tool also contributed to flint knapping techniques, where wedge-like strikes helped shape sharp edges for cutting implements.^[19]

Evolution in Technology

During the medieval period (circa 1000-1500 CE), advancements in metallurgy enabled the widespread use of iron and steel wedges, which offered superior durability and strength compared to earlier wooden variants. Archaeological evidence from sites like medieval York reveals iron wedges among common metal finds, underscoring their role in everyday craftsmanship, particularly woodworking and carpentry.^[20] The Industrial Revolution of the 19th century introduced mechanization to material processing, with steam engines powering sawmills and drilling equipment that increased efficiency in cutting wood and stone, reducing reliance on manual labor.^[21] In the 20th century, wedge technology evolved toward precision engineering, with shims serving as adjustable wedges in machining and assembly processes to achieve micron-level alignments. In automotive assembly lines, steel and later plastic shims ensured accurate positioning of components, minimizing vibrations and enhancing machinery longevity—a practice refined during the mass-production era starting in the 1910s.^[22] In aerospace, shims have been used in assembly for fine-tuning alignments and load distribution, supporting advancements in manufacturing and aviation from the mid-20th century.^[23] These innovations prioritized tolerances and adaptability. Since 2020, 3D printing has revolutionized wedge fabrication by enabling the rapid production of custom designs tailored for robotics, where lightweight, geometry-specific wedges enhance mobility and gripping mechanisms in prototypes.^[24] Concurrently, sustainable bio-based composites—derived from renewable sources like plant fibers and biopolymers—have been developed for tools and structural applications to mitigate environmental impacts of conventional metals and plastics, offering comparable strength with biodegradability and reducing carbon footprints.^[25]^[26]

Practical Applications

Cutting and Splitting

The wedge functions as a fundamental tool for cutting and splitting by applying concentrated force along a narrow edge, generating shear stresses that surpass the material's resistance to deformation and fracture. This mechanism allows the wedge to initiate cracks or separations in materials such as wood, rock, or biological tissues by distributing input force over a minimal contact area, thereby exceeding the shear strength threshold and propagating failure along planes of weakness.^[27] In practical applications, axes, chisels, and knives exemplify wedges tailored for dividing diverse materials: axes split wood by driving into grain lines, chisels fracture rock through targeted impacts, and knives slice flesh or softer substances with minimal resistance. The sharp edge of these tools amplifies pressure at the point of contact, enabling the applied force to overcome the material's shear strength and create clean divisions without requiring excessive overall energy.^[28]^[29] Representative examples include hydraulic log splitters used in forestry operations, where a powered wedge penetrates and expands along wood fibers to process large logs efficiently for fuel or timber. Geological hammers, equipped with chisel-like wedge tips, facilitate precise sample collection by splitting layered rock formations along natural fissures during field surveys. In culinary contexts, knives with blade angles of 15-20 degrees enable precision cutting of vegetables and meats, balancing sharpness for low-force slicing with durability against edge dulling.^[30]^[31]^[32] The wedging action in splitting firewood typically involves inserting the tool into a pre-scored or natural crack and striking the broad end to drive it deeper, promoting radial expansion and separation along the grain, in contrast to the slicing motion of blades that shears material progressively with a drawing cut. Safety considerations emphasize maintaining edge sharpness to prevent slippage and uncontrolled strikes, as dull edges increase the risk of tool deflection, while monitoring material fatigue in the wedge itself—such as micro-cracks from repeated impacts—avoids catastrophic failure during use.^[33]^[34]

Fastening and Separation

The wedge functions as a fastening device by being inserted into a confined space, where it applies lateral pressure to secure objects against movement or to adjust alignments. For instance, a doorstop wedge exploits friction and the inclined plane principle to resist door closure by wedging under the door and creating a normal force that counters sliding forces.^[35] Similarly, shims—thin, tapered wedge-shaped pieces of metal or plastic—are placed between machinery components to fine-tune alignments, compensating for tolerances and ensuring precise positioning during installation or maintenance.^[36] In practical applications, wooden wedges are employed in tree felling to direct the fall of timber by inserting them into the back cut, providing leverage to overcome natural lean and guide the tree's descent safely.^[37] Pitons, which are metal wedges hammered into rock cracks, serve as temporary holds in rock climbing, expanding to grip the rock faces and support climbers or ropes through frictional locking.^[38] Expandable hydraulic wedges in construction allow for the lifting of heavy loads in tight spaces, where pressurized fluid drives the wedge to spread and elevate structures like machinery bases or building elements with controlled force up to 16 tons.^[39] Reversible wedging techniques enable non-destructive separation of joined materials, relying on the wedge's ability to apply gradual pressure for insertion and removal without permanent alteration. In bookbinding, tapered wooden wedges are used to gently separate sewn signatures or lift covers during repair, allowing conservators to access and realign components while preserving the original structure. In archaeological artifact extraction, similar reversible wedges facilitate the controlled splitting of encasing soil or stone matrices around delicate items, minimizing damage during recovery from sites.^[40] A specialized application appears in dentistry, where wooden or plastic dental wedges are inserted interproximally to separate teeth slightly, creating space for matrix placement during composite restorations and protecting adjacent gingival tissues.^[41] This technique ensures precise adaptation of restorative materials without trauma to surrounding structures.^[42]

Mechanical Analysis

Mechanical Advantage

The actual mechanical advantage (AMA) of a wedge is defined as the ratio of the output force to the input force, where the output force is the perpendicular separating force applied to the material, and the input force is the effort applied parallel to the wedge's length to drive it forward.^[12] The ideal mechanical advantage (IMA), assuming no energy losses, quantifies the force amplification based on geometry alone and equals the velocity ratio (VR) in frictionless conditions.^[12] For a symmetric wedge, the IMA is given by \text{IMA} = \frac{L}{t}, where L is the horizontal length from the tip to the thick end, and t is the thickness at the thick end.^[12] This can also be expressed using the wedge angle \theta (the included angle between the two faces) as \text{IMA} = \frac{1}{2 \tan(\theta/2)}. The derivation follows from the right-triangle geometry of each half of the wedge: \tan(\theta/2) = \frac{t/2}{L}, so $2 \tan(\theta/2) = \frac{t}{L}, and inverting yields \frac{L}{t} = \frac{1}{2 \tan(\theta/2)}.^[12] The input force acts along the wedge's length (typically horizontal), providing the effort to overcome resistance and insert the wedge. The output force acts perpendicular to this direction (vertical for horizontal insertion), splitting the material by exerting normal forces on the sloped faces. In a vector diagram, the input force \mathbf{F}_\text{in} points along the positive horizontal axis. Each sloped face experiences a normal force \mathbf{N} perpendicular to the surface; for the upper face (inclined at \theta/2 to horizontal), \mathbf{N} has a vertical component N \cos(\theta/2) upward and a horizontal component N \sin(\theta/2) opposing insertion. The symmetric lower face contributes equally, so the total output force is $2 N \cos(\theta/2) (separating) and the total horizontal resistance is $2 N \sin(\theta/2), with the ideal ratio governed by the geometric IMA.^[12] The IMA increases with narrower wedge angles (smaller \theta), as \tan(\theta/2) decreases, amplifying force but requiring greater insertion distance for equivalent separation.^[43] Surface conditions influence the AMA; rough surfaces increase frictional losses, reducing AMA below IMA, while lubrication minimizes friction for higher efficiency approaching the ideal.^[43] As an example, for a wedge with L = 20 cm and t = 2 cm, \text{IMA} = 20 / 2 = 10. Here, VR = IMA = 10, meaning the input displacement is 10 times the output separation in ideal conditions.^[12]

Efficiency and Limitations

The efficiency of a wedge as a simple machine is defined by the formula \eta = \frac{AMA}{IMA} \times 100\%, where \eta represents efficiency, AMA is the actual mechanical advantage (output force divided by input force), and IMA is the ideal mechanical advantage (input distance divided by output distance, based on geometry alone).^[12] This metric quantifies the ratio of useful work output to total input work, with real-world wedges experiencing energy losses from friction, material deformation, and other dissipative forces.^[12] For instance, in wood-splitting applications, friction can reduce efficiency, as the input force must overcome both separation and sliding resistance along the wedge flanks.^[44] Key limitations arise from friction-induced sticking, particularly in dry or fibrous materials like wood, where the wedge can bind tightly, requiring additional force to extract or advance it and reducing overall effectiveness.^[44] Under high loads, material deformation occurs, with the wedge itself potentially bending or plastically deforming if constructed from insufficiently robust alloys, while the target material may exhibit uneven splitting or chipping.^[45] Edge wear further compromises performance, as repeated impacts dull the cutting tip, increasing the effective angle and amplifying friction over time.^[46] Environmental factors exacerbate these issues; temperature variations cause differential thermal expansion between the wedge and target material, potentially leading to misalignment or increased stress concentrations in applications like ultrasonic testing wedges.^[47] Metal wedges are susceptible to corrosion in humid or saline environments, which weakens structural integrity and promotes pitting along the edges.^[48] Performance also varies by material hardness: wedges penetrate soft substances like green wood more easily but risk embedding without clean separation, whereas hard, dry materials demand greater force and heighten fracture risks for both tool and workpiece.^[44] Mitigation strategies include applying lubricants, such as light machine oil or dry lubricants, to the wedge flanks to minimize friction and prevent sticking during wood splitting.^[49] Anti-stick coatings, like PTFE-based formulations, enhance release properties and reduce adhesion in industrial wedging operations.^[50] In precision engineering, nanoscale limitations further constrain wedge utility, as strain gradient effects and atomic-scale material instabilities—such as blocked phase transitions in metallic wedges—limit achievable sharpness and deformation control below 100 nm.^[51]

Comparison to Other Simple Machines

The wedge shares with the lever the fundamental purpose of amplifying an applied force to perform work more efficiently, yet it differs in its fixed geometry and directional application; while a lever pivots around a fulcrum to redirect force over a distance, often allowing movable components for lifting or balancing loads, the wedge operates through linear insertion without a pivot, concentrating force along a tapered edge for precise, directional separation or holding.^[12] Closely related to the inclined plane, the wedge functions as a portable, dual-sided version of this simple machine, consisting of two inclined planes joined at their thin ends to form a triangular shape, enabling localized force application for tasks like splitting or prying that a stationary ramp cannot achieve.^[52]^[53] In contrast to the screw, which incorporates rotational motion via a helical inclined plane wrapped around a cylinder for fastening or lifting, the wedge relies solely on linear motion without rotation, making it unsuitable for continuous turning but ideal for one-time insertions. Similarly, unlike the wheel and axle or pulley, which facilitate rotational or vertical redirection of force to reduce friction in rolling or lifting scenarios, the wedge emphasizes lateral expansion to overcome resistance in splitting, without altering motion to circular paths.^[12]^[54] In compound machines, the wedge often combines with other simple machines to enhance functionality; for instance, a can opener integrates a lever for leverage with a wedge-shaped blade for cutting, while the teeth of a saw act as multiple small wedges driven by linear or rotational input to slice materials progressively.^[54] A bolt exemplifies this in fastening, where the screw's threads provide rotational grip akin to an inclined plane, augmented by the wedge-like head to secure against surfaces.^[55] What distinguishes the wedge among the six classical simple machines is its unique capacity to both receive input motion in one direction and produce output motion in multiple perpendicular directions simultaneously, transforming a single axial push into opposing lateral forces that can separate, secure, or elevate objects in ways unattainable by the unidirectional redirection of pulleys or the pivoted amplification of levers.^[52]^[35]

Modern Variants and Innovations

In micro/nano-scale applications, wedge principles have been integrated into micro-electro-mechanical systems (MEMS) through chevron-shaped thermal actuators, which utilize angled beam structures to convert thermal expansion into precise linear motion for sensor actuation. These post-2010 developments enable sub-micron displacements in compact devices, enhancing precision in applications like optical alignment and inertial sensing. For instance, a 2019 test structure design demonstrated chevron actuators achieving fracture strength measurements in MEMS thin films with deflections of 3.5 μm at 3.3 V under controlled heating, outperforming traditional electrostatic methods in force amplification.^[56] A comprehensive review of electrothermal actuators highlights their role in generating forces in the µN to mN range with low voltage operation, making them suitable for integrated sensor arrays in harsh environments.^[57] In biomedical engineering, expandable vascular stents employ wedge-like radial expansion mechanisms to dilate narrowed arteries, with significant advancements approved by the FDA in the 2000s. These devices, often balloon-expandable, function analogously to a wedge by applying outward force to fracture plaque and support vessel walls, improving blood flow in conditions like coronary artery disease. The Cypher sirolimus-eluting stent, approved in 2003, exemplified this by achieving over 90% procedural success in clinical trials, reducing restenosis rates to below 10% compared to bare-metal stents. Similarly, the Taxus paclitaxel-eluting stent, cleared in 2004, utilized a similar expansion principle, demonstrating sustained patency in over 80% of patients at one-year follow-up. Crimping tools with wedge-shaped elements further refine deployment, ensuring uniform expansion during procedures.^[58] Robotics and AI have incorporated self-adjusting wedge mechanisms in soft grippers to handle irregular objects, leveraging deformable structures for adaptive grasping. A 2022 hybrid soft gripper design uses internal wedges within vacuum-actuated fingers and palms to control deformation, allowing conformal contact with non-uniform shapes like fruits or tools while minimizing damage. This enables stable gripping across varied geometries, with the wedges tailoring bending angles for stability. Integrating force and pressure sensors enhances adaptability, as seen in sensorized variants that adjust wedge positions in real-time via AI feedback, achieving high success rates in grasping unstructured items in dynamic environments.^[59] Sustainable innovations in agriculture feature biodegradable wedge-shaped tools for plant propagation, reducing plastic waste and supporting eco-friendly cultivation amid climate challenges. Emerging 2020s research has developed wedge-form substrates and trays from natural materials like cassava starch and wastepaper, facilitating root initiation in cuttings without synthetic foams. For example, MACAW (manure, cassava starch, and wastepaper) biodegradable seedling trays, tested in 2025 field trials, promoted 20% faster germination in crops like tomatoes compared to conventional plugs, fully decomposing in soil within six months.^[60] These designs incorporate climate-adaptive features, such as moisture-retaining structures for extreme drought or flood conditions, aligning with frameworks like adaptation wedges that prioritize resilience in vulnerable regions. Offshore propagation systems using biodegradable paper bags, introduced in 2025, further enable substrate-free rooting in energy-efficient setups.^[61]

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Design of a test structure based on chevron-shaped thermal actuator ...
Nov 8, 2019 · HIGHLIGHTS. Presented a novel test structure based on chevron-shaped actuator to measure the fracture strength of MEMS thin films.
[59]
Review of Electrothermal Actuators and Applications - MDPI
The chevron actuators use the total thermal expansion which is constrained in one direction. On the other hand, the bimorph actuator relies on the difference in ...
[60]
Understanding the requirements of self-expandable stents for heart ...
2.2. A crimping head composed by 12 movable wedges disposed about a rotational axis, crimped the stents from their nominal diameter until 15 mm. The ...Missing: principle | Show results with:principle
[61]
Sensorized Reconfigurable Soft Robotic Gripper System for ...
Three fingers and a palm constitute the gripper, all of which are vacuum actuated. Internal wedges are used to tailor the deformation of a soft outer ...
[62]
(PDF) Design and Efficacy of MACAW (Manure, Cassava Starch ...
Jun 2, 2025 · Design and Efficacy of MACAW (Manure, Cassava Starch, and Wastepaper) Biodegradable Seedling Trays for Enhancing Plant Growth. May 2025.Missing: propagation | Show results with:propagation
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Biodegradable paper bags replaces substrate in new propagation ...
Jan 27, 2025 · "This advanced propagation system roots cuttings offshore in special biodegradable paper bags, requiring minimal energy and no substrate. The ...