wedge product

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A wedge is a triangular shaped
tool A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates ba ...
, and is a portable
inclined plane An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six clas ...
, and one of the six
simple machine A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...
s. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
applied to its blunt end into forces perpendicular ( normal) to its inclined surfaces. The
mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
of a wedge is given by the ratio of the length of its slope to its width..''McGraw-Hill Concise Encyclopedia of Science & Technology'', Third Ed., Sybil P. Parker, ed., McGraw-Hill, Inc., 1992, p. 2041. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle. The force is applied on a flat, broad surface. This energy is transported to the pointy, sharp end of the wedge, hence the force is transported. The wedge simply transports energy in the form of friction and collects it to the pointy end, consequently breaking the item.

# History

Wedges have existed for thousands of years. They were first made of simple stone. Perhaps the first example of a wedge is the
hand axe A hand axe (or handaxe or Acheulean hand axe) is a prehistoric stone tool with two faces that is the longest-used tool in human history, yet there is no academic consensus on what they were used for. It is made from stone, usually flint or che ...
biface A hand axe (or handaxe or Acheulean hand axe) is a prehistoric stone tool with two faces that is the longest-used tool in human history, yet there is no academic consensus on what they were used for. It is made from stone, usually flint or cher ...
and Olorgesailie), which is made by chipping stone, generally
flint Flint, occasionally flintstone, is a sedimentary cryptocrystalline form of the mineral quartz, categorized as the variety of chert that occurs in chalk or marly limestone. Flint was widely used historically to make stone tools and start fir ...
, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or
mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or
prismatic joint A prismatic joint is a one- degree-of-freedom kinematic pair which constrains the motion of two bodies to sliding along a common axis, without rotation; for this reason it is often called a slider (as in the slider-crank linkage) or a sliding ...
. The origin of the wedge is not known. In ancient Egyptian
quarries A quarry is a type of open-pit mine in which dimension stone, rock, construction aggregate, riprap, sand, gravel, or slate is excavated from the ground. The operation of quarries is regulated in some jurisdictions to reduce their envir ...
,
bronze Bronze is an alloy consisting primarily of copper, commonly with about 12–12.5% tin and often with the addition of other metals (including aluminium, manganese, nickel, or zinc) and sometimes non-metals, such as phosphorus, or metalloids such ...
wedges were used to break away blocks of stone used in construction.
Wood Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin ...
en wedges that swelled after being saturated with water, were also used. Some
indigenous peoples of the Americas The Indigenous peoples of the Americas are the inhabitants of the Americas before the arrival of the European settlers in the 15th century, and the ethnic groups who now identify themselves with those peoples. Many Indigenous peoples of the Am ...
used
antler Antlers are extensions of an animal's skull found in members of the Cervidae (deer) family. Antlers are a single structure composed of bone, cartilage, fibrous tissue, skin, nerves, and blood vessels. They are generally found only on males ...
wedges for splitting and working wood to make
canoes A canoe is a lightweight narrow water vessel, typically pointed at both ends and open on top, propelled by one or more seated or kneeling paddlers facing the direction of travel and using a single-bladed paddle. In British English, the term ...
, dwellings and other objects.

# Uses of a wedge

Wedges are used to lift heavy objects, separating them from the surface upon which they rest. J. M. McCarthy and Leo Joskowitz, “Kinematic Synthesis,” Formal Engineering Design Synthesis, (J. Cagan and E. Antonson, eds.), Cambridge Univ. Press, 2002.
/ref> Consider a block that is to be lifted by a wedge. As the wedge slides under the block, the block slides up the sloped side of a wedge. This lifts the weight ''F''B of the block. The horizontal force ''F''A needed to lift the block is obtained by considering the velocity of the wedge ''v''A and the velocity of the block ''v''B. If we assume the wedge does not dissipate or store energy, then the power into the wedge equals the power out. or :$\frac = \frac.$ The velocity of the block is related to the velocity of the wedge by the slope of the side of the wedge. If the angle of the wedge is ''α'' then :$v_\mathrm = v_\mathrm \tan\alpha, \!$ which means that the mechanical advantage :$MA = \frac = \frac.$ Thus, the smaller the angle ''α'' the greater the ratio of the lifting force to the applied force on the wedge. This is the
mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
of the wedge. This formula for mechanical advantage applies to cutting edges and splitting operations as well as to lifting. They can also be used to separate objects, such as blocks of cut stone.
Splitting maul A splitting maul also known as a ''block buster'', ''block splitter'', ''chop and maul'', ''sledge axe'', ''go-devil'' or ''hamaxe'' is a heavy, long-handled axe used for splitting a piece of wood along its grain. One side of its head is like a ...
s and splitting wedges are used to split wood along the grain. A narrow wedge with a relatively long
taper Taper may refer to: * Part of an object in the shape of a cone (conical) * Taper (transmission line), a transmission line gradually increasing or decreasing in size * Fishing rod taper, a measure of the flexibility of a fishing rod * Conically t ...
used to finely adjust the distance between objects is called a shim, and is commonly used in carpentry. The tips of forks and nails are also wedges, as they split and separate the material into which they are pushed or driven; the shafts may then hold fast due to friction.

# Blades and wedges

The blade is a compound inclined plane, consisting of two inclined planes placed so that the planes meet at one edge. When the edge where the two planes meet is pushed into a solid or fluid substance it overcomes the resistance of materials to separate by transferring the force exerted against the material into two opposing forces normal to the faces of the blade. The blade's first known use by humans was the sharp edge of a flint stone that was used to cleave or split animal tissue, e.g. cutting meat. The use of
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in fro ...
or other metals led to the development of
knives A knife ( : knives; from Old Norse 'knife, dirk') is a tool or weapon with a cutting edge or blade, usually attached to a handle or hilt. One of the earliest tools used by humanity, knives appeared at least 2.5 million years ago, as evidence ...
for those kinds of tasks. The blade of the knife allowed humans to cut meat, fibers, and other plant and animal materials with much less force than it would take to tear them apart by simply pulling with their hands. Other examples are
plows A plough or plow ( US; both ) is a farm tool for loosening or turning the soil before sowing seed or planting. Ploughs were traditionally drawn by oxen and horses, but in modern farms are drawn by tractors. A plough may have a wooden, iron or ...
, which separate soil particles,
scissors Scissors are hand-operated shearing tools. A pair of scissors consists of a pair of metal blades pivoted so that the sharpened edges slide against each other when the handles (bows) opposite to the pivot are closed. Scissors are used for cutt ...
which separate fabric,
axe An axe ( sometimes ax in American English; see spelling differences) is an implement that has been used for millennia to shape, split and cut wood, to harvest timber, as a weapon, and as a ceremonial or heraldic symbol. The axe has man ...
s which separate wood fibers, and
chisels A chisel is a tool with a characteristically shaped cutting edge (such that wood chisels have lent part of their name to a particular grind) of blade on its end, for carving or cutting a hard material such as wood, stone, or metal by hand, str ...
and
planes Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...
which separate wood. Wedges,
saw A saw is a tool consisting of a tough blade, wire, or chain with a hard toothed edge. It is used to cut through material, very often wood, though sometimes metal or stone. The cut is made by placing the toothed edge against the material and mo ...
s and
chisels A chisel is a tool with a characteristically shaped cutting edge (such that wood chisels have lent part of their name to a particular grind) of blade on its end, for carving or cutting a hard material such as wood, stone, or metal by hand, str ...
can separate thick and hard materials, such as wood, solid stone and hard metals and they do so with much less force, waste of material, and with more precision, than crushing, which is the application of the same force over a wider area of the material to be separated. Other examples of wedges are found in
drill bit Drill bits are cutting tools used in a drill to remove material to create holes, almost always of circular cross-section. Drill bits come in many sizes and shapes and can create different kinds of holes in many different materials. In order ...
s, which produce circular holes in solids. The two edges of a drill bit are sharpened, at opposing angles, into a point and that edge is wound around the shaft of the drill bit. When the drill bit spins on its axis of rotation, the wedges are forced into the material to be separated. The resulting cut in the material is in the direction of rotation of the drill bit while the helical shape of a bit allows the removal of the cut material.

# Examples for holding objects faster

Wedges can also be used to hold objects in place, such as
engine An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power gene ...
parts (
poppet valve A poppet valve (also called mushroom valve) is a valve typically used to control the timing and quantity of gas or vapor flow into an engine. It consists of a hole or open-ended chamber, usually round or oval in cross-section, and a plug, usual ...
s),
bicycle A bicycle, also called a pedal cycle, bike or cycle, is a human-powered or motor-powered assisted, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A is called a cyclist, or bicyclist. Bic ...
parts (
stem Stem or STEM may refer to: Plant structures * Plant stem, a plant's aboveground axis, made of vascular tissue, off which leaves and flowers hang * Stipe (botany), a stalk to support some other structure * Stipe (mycology), the stem of a mushro ...
s and eccentric
bottom bracket The bottom bracket on a bicycle connects the crankset (chainset) to the bicycle and allows the crankset to rotate freely. It contains a spindle to which the crankset attaches, and the bearings that allow the spindle and crankset to rotate. The ...
s), and
door A door is a hinged or otherwise movable barrier that allows ingress (entry) into and egress (exit) from an enclosure. The created opening in the wall is a ''doorway'' or ''portal''. A door's essential and primary purpose is to provide security b ...
s. A wedge-type door stop (door wedge) functions largely because of the friction generated between the bottom of the door and the wedge, and the wedge and the floor (or other surface).

The mechanical advantage or MA of a wedge can be calculated by dividing the height of the wedge by the wedge's width: :$\rm MA=$ The more acute, or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical advantage it will yield. A wedge will bind when the wedge included angle is less than the arctangent of the coefficient of friction between the wedge and the material. Therefore, in an elastic material such as wood, friction may bind a narrow wedge more easily than a wide one. This is why the head of a splitting maul has a much wider angle than that of an axe.

*
Axe An axe ( sometimes ax in American English; see spelling differences) is an implement that has been used for millennia to shape, split and cut wood, to harvest timber, as a weapon, and as a ceremonial or heraldic symbol. The axe has man ...
Wheel chock Wheel chocks (or chocks) are wedges of sturdy material placed closely against a vehicle's wheels to prevent accidental movement. Chocks are placed for safety in addition to setting the brakes. The bottom surface is sometimes coated in rubber ...
* Froe *
Knife A knife ( : knives; from Old Norse 'knife, dirk') is a tool or weapon with a cutting edge or blade, usually attached to a handle or hilt. One of the earliest tools used by humanity, knives appeared at least 2.5 million years ago, as evidence ...
*
Log splitter A log splitter is a piece of machinery or equipment used for splitting firewood from softwood or hardwood logs that have been pre-cut into sections (rounds), usually by chainsaw or on a saw bench. Many log splitters consist of a hydraulic pump or ...
*
Nail (fastener) In woodworking and construction, a nail is a small object made of metal (or wood, called a tree nail or "trunnel") which is used as a fastener, as a peg to hang something, or sometimes as a decoration. Generally, nails have a sharp point on one ...
*
Plug and feather Plug and feather, also known as plugs and wedges, feather and wedges, wedges and shims, pins and feathers and feather and tare, refers to a technique and a three-piece tool set used to split stone. Description Each set consists of a metal wedge ...
* Pushpin * Quoin (printing) *
Splitting maul A splitting maul also known as a ''block buster'', ''block splitter'', ''chop and maul'', ''sledge axe'', ''go-devil'' or ''hamaxe'' is a heavy, long-handled axe used for splitting a piece of wood along its grain. One side of its head is like a ...
and splitting wedges *
Scalpel A scalpel, lancet, or bistoury is a small and extremely sharp bladed instrument used for surgery, anatomical dissection, podiatry and various arts and crafts (either called a hobby knife or an X-acto knife.). Scalpels may be single-use disposa ...
*
Scissors Scissors are hand-operated shearing tools. A pair of scissors consists of a pair of metal blades pivoted so that the sharpened edges slide against each other when the handles (bows) opposite to the pivot are closed. Scissors are used for cutt ...
*
Wheel and Axle The wheel and axle is a simple machine consisting of a wheel attached to a smaller axle so that these two parts rotate together in which a force is transferred from one to the other. The wheel and axle can be viewed as a version of the lever, wit ...
*
Sickle A sickle, bagging hook, reaping-hook or grasshook is a single-handed agricultural tool designed with variously curved blades and typically used for harvesting, or reaping, grain crops or cutting succulent forage chiefly for feeding livestock, ...

# References

{{Authority control Mechanics Tools Simple machines