Editing Machine (section)

== Simple machines ==
{{main|Simple machine}}
[[File:Table of Mechanicks, Cyclopaedia, Volume 2.png|thumb|''[[Chambers' Cyclopædia]]'' (1728) has a table of simple mechanisms.<ref name="Mechanicks">{{Citation |last=Chambers |first=Ephraim |year=1728 |title=Table of Mechanicks |work=Cyclopaedia, A Useful Dictionary of Arts and Sciences |volume=2 |location=London, England |page=528, Plate 11 }}.</ref> Simple machines provide a "vocabulary" for understanding more complex machines.]]

The idea that a machine can be decomposed into simple movable elements led [[Archimedes]] to define the [[lever]], [[pulley]] and [[screw]] as [[simple machines]]. By the time of the Renaissance this list increased to include the [[wheel and axle]], [[Wedge (mechanical device)|wedge]] and [[inclined plane]]. The modern approach to characterizing machines focusses on the components that allow movement, known as [[joint (mechanics)|joints]].

Wedge (hand axe): Perhaps the first example of a device designed to manage power is the [[hand axe]], also called [[biface]] and [[Olorgesailie]]. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or [[wedge (mechanical device)|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]].

Lever: The [[lever]] is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If ''a'' is the distance from the pivot to the point where the input force is applied and ''b'' is the distance to the point where the output force is applied, then ''a/b'' is the [[mechanical advantage]] of the lever. The fulcrum of a lever is modeled as a hinged or [[revolute joint]].

Wheel: The [[wheel]] is an important early machine, such as the [[chariot]]. A wheel uses the law of the lever to reduce the force needed to overcome [[friction]] when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.

[[File:Kinematics of Machinery - Figure 21.jpg|thumb|right|alt=Illustration of a Four-bar linkage from Kinematics of Machinery, 1876|[[s:The Kinematics of Machinery|''The Kinematics of Machinery'' (1876)]] has an illustration of a [[four-bar linkage]].]]
The classification of [[simple machine]]s to provide a strategy for the design of new machines was developed by [[Franz Reuleaux]], who collected and studied over 800 elementary machines.<ref>[[Francis C. Moon|Moon, F. C.]], [http://kmoddl.library.cornell.edu/facets/moon61899.htm The Reuleaux Collection of Kinematic Mechanisms at Cornell University, 1999] {{webarchive|url=https://web.archive.org/web/20150518064706/http://kmoddl.library.cornell.edu/facets/moon61899.htm |date=2015-05-18 }}</ref> He recognized that the classical [[simple machine]]s can be separated into the lever, pulley and wheel and axle that are formed by a body rotating about a hinge, and the inclined plane, wedge and screw that are similarly a block sliding on a flat surface.<ref>Hartenberg, R.S. & J. Denavit (1964) [http://kmoddl.library.cornell.edu/bib.php?m=23 Kinematic synthesis of linkages] {{webarchive|url=https://web.archive.org/web/20110519063139/http://kmoddl.library.cornell.edu/bib.php?m=23 |date=2011-05-19 }}, New York: McGraw-Hill, online link from [[Cornell University]].</ref>

Simple machines are elementary examples of [[kinematic chain]]s or [[linkage (mechanical)|linkages]] that are used to model [[mechanical systems]] ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a [[kinematic pair]] called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the [[kinematic pair]] called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.

This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the rotary joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints called a [[mechanism (engineering)|mechanism]] .<ref name="Uicker2003"/>

Two levers, or cranks, are combined into a planar [[four-bar linkage]] by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a [[six-bar linkage]] or in series to form a robot.<ref name="Uicker2003"/>