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| [[File:Wedge-1.jpg|thumb|A wood splitting wedge]]
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| A '''wedge''' is a [[triangle|triangular]] shaped tool, a compound and portable [[inclined plane]], and one of the six classical [[simple machine]]s. It can be used to separate two objects or portions of an object, lift up
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| an object, or hold an object in place. It functions by converting a [[force]] applied to its blunt end into forces perpendicular ([[Surface normal|normal]]) to its inclined surfaces. <!-- this link is broken <ref>{{Citation | title = Wedges and screws | url = http://em-ntserver.unl.edu/Negahban/em223/note16/note16.htm | accessdate = 2009-07-29}}.</ref> --> The [[mechanical advantage]] of a wedge is given by the ratio of the length of its slope to its width.<ref name="bowser">{{Citation | last = Bowser | first = Edward Albert | title = An elementary treatise on analytic mechanics: with numerous examples | publisher = D. Van Nostrand Company | pages= 202–203 | year = 1920 | edition = 25th | url = http://books.google.com/?id=mE4GAQAAIAAJ}}.</ref><ref name="CEST">''McGraw-Hill Concise Encyclopedia of Science & Technology'', Third Ed., Sybil P. Parker, ed., McGraw-Hill, Inc., 1992, p. 2041.</ref> 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.
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| ==History==
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| [[Image:Flint hand axe.JPG|thumb|left|120px|Flint hand axe found in [[Winchester]]]]
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| Perhaps the first example of a wedge is the hand axe, also see [[biface]] and [[Olorgesailie]]. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or [[mechanical advantage]] is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or [[prismatic joint]].
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| The origin of the wedge is not known. In [[ancient Egypt]]ian [[quarry|quarries]], [[bronze]] wedges were used to break away blocks of stone used in construction. [[Wood]]en wedges that swelled after being saturated with water, were also used. Some [[indigenous peoples of the Americas]] used [[antler]] wedges for splitting and working wood to make [[canoes]], dwellings and other objects.
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| ==Use of a wedge for lifting and separating==
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| Wedges are used to lift heavy objects, separating them from the surface upon which they rest.<ref>[http://books.google.com/books?id=m5DK0FSuqysC&pg=PA321&lpg=PA321&dq=“Kinematic+Synthesis,”+Formal+Engineering+Design+Synthesis&source=bl&ots=AZKlvmnPcA&sig=xe0EeLgCy8v4OIdZ_SnbK8igdrc&hl=en&ei=qcbVTsyEKo6FsAL1vsCRDw&sa=X&oi=book_result&ct=result&resnum=3&ved=0CEYQ6AEwAg#v=onepage&q&f=false J. M. McCarthy and Leo Joskowitz, “Kinematic Synthesis,” Formal Engineering Design Synthesis, (J. Cagan and E. Antonson, eds.), Cambridge Univ. Press, 2002.]</ref>
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| 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<sub>B</sub> of the block. The horizontal force F<sub>A</sub> needed to lift the block is obtained by considering the velocity of the wedge v<sub>A</sub> and the velocity of the block v<sub>B</sub>. If we assume the wedge does not dissipate or store energy, then the power into the wedge equals the power out, so
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| :<math> P = F_A v_A = F_B v_B, \!</math>
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| or
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| :<math>\frac{F_B}{F_A} = \frac{v_A}{v_B}. </math>
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| 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
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| :<math> v_B = v_A \tan\alpha, \!</math>
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| which means
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| :<math> MA = \frac{F_B}{F_A} = \frac{1}{\tan\alpha}. </math>
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| 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]] of the wedge. This formula for mechanical advantage applies to cutting edges and splitting operations as well as to lifting.
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| They can also be used to separate objects, such as blocks of cut stone. [[Splitting maul]]s and splitting wedges are used to split wood along the grain. A narrow wedge with a relatively long [[taper]] used to finely adjust the distance between objects is called a [[shim (engineering)|shim]], and is commonly used in carpentry.
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| The tips of forks and [[nail (engineering)|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.
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| ==Blades and wedges==
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| 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.
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| First known to be used by humans in the [[knife]] to separate animal tissue, the blade allowed humans to separate meat, fibers, and other plant and animal materials, with much less force than it would take to tear them by simply pulling them apart. Blades can separate solid material, as with [[plows]] that separate soil particles, [[scissors]] and [[Kitchen shears|shears]] to cut flexible materials, [[axe]]s to separate wood fibers, and [[chisels]] and [[plane (tool)|planes]] to remove precise portions of wood.
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| Wedges, [[saw]]s and [[chisels]] can separate thick and hard materials, such as wood, including solid stone and hard metals, with much less force, less waste of material, and more precision, than [[crusher|crushing]]. Saws have many chisel-like "teeth" along their cutting surface to transfer linear or circular motion to counteract the normal force of the surface to be cut.
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| [[Drills]] produce circular holes in solids by rotating a chisel around its center, with the edge sharpened at opposing angles on either side of the rotation axis, so as to cut in the direction of rotation. [[Twist drill]]s provide one or more [[helix|heliacally]] twisted chisels formed out of grooves cut along the side of the bit, to help evacuate cuttings from the drill hole, by using the same inclined plane principle as the [[archimedean screw]].
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| ==Examples for holding fast==
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| Wedges can also be used to hold objects in place, such as [[Internal combustion engine|engine]] parts ([[poppet valve]]s), [[bicycle]] parts ([[Stem (bicycle part)|stem]]s and [[Eccentric (mechanism)|eccentric]] [[bottom bracket]]s), and [[door]]s.
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| A wedge-type [[door stop (furniture)|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).
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| == Mechanical advantage ==
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| [[Image:Wedge-diagram.svg|thumb|100px|Cross-section of a splitting wedge with its length oriented vertically. A downward force produces forces perpendicular to its inclined surfaces.]]
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| The mechanical advantage of a wedge can be calculated by dividing the length of the slope by the wedge's width:<ref name="bowser"/>
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| :<math>\rm MechanicalAdvantage={Length \over Width}</math>
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| The more [[acute angle|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.<ref name="CEST"/>
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| However, 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.
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| ==See also==
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| * [[Axe]]
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| * [[Blade]]
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| * [[Knife]]
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| * [[Log splitter]]
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| * [[Plug and feather]]
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| * [[Pushpin]]
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| * [[Splitting maul]]
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| * [[Scalpel]]
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| * [[Scissors]]
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| * [[Screw]]
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| * [[Chock (wheel)|Wheel chock]]
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| * [[Wheel and Axle]]
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| ==References==
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| {{Commons category|Wedges}}
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| {{reflist}}
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| {{Simple machines}}
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| [[Category:Mechanics]]
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| [[Category:Tools]]
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| [[Category:Simple machines]]
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I just wish I am useful in one way here.
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