Wedge (mechanical device)

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A wood splitting wedge

A wedge is a triangular shaped tool, a compound and portable inclined plane, and one of the six classical simple machines. 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 applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width.^[1]^[2] 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.

History

Flint hand axe found in Winchester

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.

The origin of the wedge is not known. In ancient Egyptian quarries, bronze wedges were used to break away blocks of stone used in construction. Wooden 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.

Use of a wedge for lifting and separating

Wedges are used to lift heavy objects, separating them from the surface upon which they rest.^[3]

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, so

$P=F_{A}v_{A}=F_{B}v_{B},\!$

${\frac {F_{B}}{F_{A}}}={\frac {v_{A}}{v_{B}}}.$

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

$v_{B}=v_{A}\tan \alpha ,\!$

which means

$MA={\frac {F_{B}}{F_{A}}}={\frac {1}{\tan \alpha }}.$

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.

They can also be used to separate objects, such as blocks of cut stone. Splitting mauls 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, 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.

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 shears to cut flexible materials, axes to separate wood fibers, and chisels and planes to remove precise portions of wood.

Wedges, saws 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 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.

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 drills provide one or more 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.

Examples for holding fast

Wedges can also be used to hold objects in place, such as engine parts (poppet valves), bicycle parts (stems and eccentric bottom brackets), and doors.

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).

Mechanical advantage

Cross-section of a splitting wedge with its length oriented vertically. A downward force produces forces perpendicular to its inclined surfaces.

The mechanical advantage of a wedge can be calculated by dividing the length of the slope by the wedge's width:^[1]

${\rm {MechanicalAdvantage={Length \over Width}}}$

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.^[2]

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.

References

Wikimedia Commons has media related to Wedges.

↑ 1.0 1.1 Bowser, Edward Albert (1920), An elementary treatise on analytic mechanics: with numerous examples (25th ed.), D. Van Nostrand Company, pp. 202–203 .
↑ 2.0 2.1 McGraw-Hill Concise Encyclopedia of Science & Technology, Third Ed., Sybil P. Parker, ed., McGraw-Hill, Inc., 1992, p. 2041.
↑ J. M. McCarthy and Leo Joskowitz, “Kinematic Synthesis,” Formal Engineering Design Synthesis, (J. Cagan and E. Antonson, eds.), Cambridge Univ. Press, 2002.

v t e Simple machine

Classical simple machines	Inclined plane Lever Pulley Screw Wedge Wheel and axle

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