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| {{About|the concept in physics|the [[Internet forum]] software|Simple Machines Forum}}
| | ӏm Williams and was born on 2 Octobeг 1972. My hobbies are Running and Insect collecting.<br><br>Also visit my homepɑge: family vacation ԁestination ([http://Www.Picnicbasketcity.com/traveling-when-older-how-to-be-comfortable/ linked resource site]) |
| [[File:Table of Mechanicks, Cyclopaedia, Volume 2.png|thumb|250px|Table of simple mechanisms, from [[Chambers' Cyclopedia]], 1728.<ref name="Mechanicks">{{Citation |last=Chambers |first=Ephraim |year=1728 |title=Table of Mechanicks |work=Cyclopaedia, A Useful Dictionary of Arts and Sciences |volume=Volume 2 |location=London, England |page=528, Plate 11 }}.</ref> Simple machines provide a "vocabulary" for understanding more complex machines.]]
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| A '''simple machine''' is a non-motorized device that changes the direction or magnitude of a [[force]].<ref name="Paul-Roy-Mukherjee-2005">{{Citation |last=Paul |first=Akshoy |last2=Roy |first2=Pijush |last3=Mukherjee |first3=Sanchayan |title=Mechanical sciences: engineering mechanics and strength of materials |year=2005 |publisher=Prentice Hall of India |isbn=81-203-2611-3 |page=215 |postscript=.}}</ref> In general, a simple machine can be defined as one of the simplest mechanisms that provide [[mechanical advantage]] (also called [[lever]]age).<ref name="Asimov1988">{{Citation |last=Asimov |first=Isaac |title=Understanding Physics |year=1988 |publisher=Barnes & Noble |location=New York, New York, USA |isbn=0-88029-251-2 |url=http://books.google.com/books?id=pSKvaLV6zkcC&pg=PA88&dq=Asimov+simple+machine&cd=1#v=onepage&q&f=false |page=88 |postscript=.}}</ref>
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| Usually the term refers to the six classical simple machines which were defined by [[Renaissance]] scientists:<ref>{{cite book
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| |last=Anderson
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| |first=William Ballantyne
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| |title=Physics for Technical Students: Mechanics and Heat
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| |year=1914
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| |publisher=McGraw Hill
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| |location=New York, USA
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| |url=http://books.google.com/books?id=Pa0IAAAAIAAJ&pg=PA112
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| |accessdate=2008-05-11
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| |pages=112–122}}</ref>
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| * [[Lever]]
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| * [[Wheel and axle]]
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| * [[Pulley]]
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| * [[Inclined plane]] (ramp)
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| * [[Wedge (mechanical device)|Wedge]] (moving ramp)
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| * [[Screw (simple machine)|Screw]]
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| A simple machine is an elementary device that has a specific movement (often called a [[mechanism (engineering)|mechanism]]), which can be combined with other devices and movements to form a [[machine (mechanical)|machine]]. Thus simple machines are considered to be the "building blocks" of more complicated [[machine (mechanical)|machine]]s. This analytical view of [[machine (mechanical)|machine]]s as decomposable into simple machines first arose in the Renaissance as a [[neoclassicism|neoclassical]] amplification of [[ancient Greece|ancient Greek]] texts on technology,<ref name="Usher">{{cite book
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| |last=Usher
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| |first=Abbott Payson
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| |authorlink=
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| |coauthors=
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| |title=A History of Mechanical Inventions
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| |publisher=Courier Dover Publications
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| |year=1988
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| |location=USA
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| |pages=98
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| |url=http://books.google.com/books?id=xuDDqqa8FlwC&pg=PA196#v=snippet&q=wedge%20and%20screw&f=false
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| |doi=
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| |isbn=0-486-25593-X
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| |postscript=.}}</ref> and is still a central part of [[engineering]] in today's age of [[applied science]]. For example, wheels, levers, and pulleys are all used in the mechanism of a [[bicycle]].<ref name="Prater1994">{{Citation
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| |last=Prater
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| |first=Edward L.
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| |year=1994
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| |title=Basic machines
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| |url=http://www.constructionknowledge.net/public_domain_documents/Div_1_General/Basic_Skills/Basic%20Machines%20NAVEDTRA%2014037%201994.pdf
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| |publisher=U.S. Navy Naval Education and Training Professional Development and Technology Center, NAVEDTRA 14037
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| |postscript=.}}</ref><ref name="USBureauNavalPersonnel1971">{{Citation
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| |author=U.S. Navy Bureau of Naval Personnel
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| |year=1971
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| |url=http://www.webpal.org/SAFE/aaarecovery/5_simple_technology/basic_machines.pdf
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| |title=Basic machines and how they work
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| |publisher=Dover Publications
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| |postscript=.}}</ref> Between the simple machines and complex assemblies, several intermediate classes can be defined, which may be termed "compound machines"<ref name="U_Virginia_elementary_curriculum">{{Citation
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| |url=http://galileo.phys.virginia.edu/outreach/8thgradesol/compoundmachine.htm
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| |title=Compound machines
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| |publisher=University of Virginia Physics Department
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| |accessdate=2010-06-11
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| |postscript=.}}</ref><ref name="Asimov1988"/><ref name="Wallenstein2002">{{cite conference |last=Wallenstein |first=Andrew |title=Foundations of cognitive support: Toward abstract patterns of usefulness |date=June 2002 |booktitle=Proceedings of the 9th Annual Workshop on the Design, Specification, and Verification of Interactive Systems |publisher=Springer |url=http://books.google.com/books?id=G9sZf7D24a8C&pg=PA136&vq=simple+machines&source=gbs_search_r&cad=1_1&sig=dynXLdHrC2AX55hDds_zGQRJv_U |accessdate=2008-05-21 |page=136 |postscript=.}}</ref> or "[[machine element]]s".<ref name="Matthews-ASME-2e-2005">{{Citation |last=Matthews |first=Clifford |last2=[[ASME]] |title=ASME engineer's data book |page=249 |publisher=[[ASME]] Press |year=2005 |edition=2nd |url=http://books.google.com/books?id=dPS2KU0gj-8C&pg=PA249 |isbn=978-0-7918-0229-8 |postscript=.}}</ref> The mechanical advantage of a compound machine is simply the product of the mechanical advantages of the simple machines of which it is composed.
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| Various authors have compiled lists of simple machines and machine elements, sometimes lumping them together under a single term such as "simple machines",<ref name="Mechanicks"/> "basic machines",<ref name="Prater1994"/> "compound machines",<ref name="U_Virginia_elementary_curriculum"/> or "machine elements"; the use of the term "simple machines" in this broader [[word sense|sense]] is a departure from the neoclassical sense of the six essential simple machines, which is why many authors prefer to avoid its use, preferring the other terms (such as "machine element"). In all cases, the theme of an analytical and synthetic connection from simple to compound to complex is at work. A page from a 1728 text by Ephraim Chambers<ref name="Mechanicks"/> (in the figure to the right) shows more machine elements. By the late 1800s, [[Franz Reuleaux]]<ref name="Reuleaux1876">{{Citation |last=Reuleaux |first=F. |origyear=1876 |year=1963 |title=The kinematics of machinery (translated and annotated by A.B.W. Kennedy) |publisher=reprinted by Dover |location=New York, New York, USA |postscript=.}}</ref> identified hundreds of machine elements (calling them "simple machines"). Models of these devices can be found at [[Cornell University]]'s KMODDL website.<ref name="KMODDL">{{Citation |author=Cornell University |authorlink=Cornell University |title=Reuleaux Collection of Mechanisms and Machines at Cornell University |url=http://kmoddl.library.cornell.edu/rx_collection.php |publisher=Cornell University |postscript=.}}</ref>
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| ==History==
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| The idea of a "simple machine" originated with the Greek philosopher [[Archimedes]] around the 3rd century BC, who studied the "Archimedean" simple machines: lever, pulley, and [[Screw (simple machine)|screw]].<ref name="Asimov1988"/><ref name="Chiu">{{Citation
| |
| | last = Chiu
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| | first = Y. C.
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| | authorlink =
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| | coauthors =
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| | title = An introduction to the History of Project Management
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| | publisher = Eburon Academic Publishers
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| | year = 2010
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| | location = Delft
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| | pages = 42
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| | url = http://books.google.com/books?id=osNrPO3ivZoC&pg=PA42&dq=%22heron+of+alexandria%22++load+motion#v=onepage&q=%22heron%20of%20alexandria%22%20%20load%20motion&f=false
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| | doi =
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| | isbn = 90-5972-437-2}}</ref> He discovered the principle of [[mechanical advantage]] in the lever.<ref>{{cite book
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| |last=Ostdiek
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| |first=Vern
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| |coauthors=Bord, Donald
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| |title=Inquiry into Physics
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| |year=2005
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| |publisher=Thompson Brooks/Cole
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| |isbn=0-534-49168-5
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| |url=http://books.google.com/books?id=7kz2pd14hPUC&pg=PA123
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| |accessdate=2008-05-22
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| |page=123}}</ref> Later Greek philosophers defined the classic five simple machines (excluding the [[inclined plane]]) and were able to roughly calculate their mechanical advantage.<ref name="Usher">{{cite book
| |
| | last = Usher
| |
| | first = Abbott Payson
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| | authorlink =
| |
| | coauthors =
| |
| | title = A History of Mechanical Inventions
| |
| | publisher = Courier Dover Publications
| |
| | year = 1988
| |
| | location = USA
| |
| | pages = 98
| |
| | url = http://books.google.com/books?id=xuDDqqa8FlwC&pg=PA196#v=snippet&q=wedge%20and%20screw&f=false
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| | doi =
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| | isbn = 0-486-25593-X}}</ref> [[Heron of Alexandria]] (ca. 10–75 AD) in his work ''Mechanics'' lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw,<ref name="Chiu" /> and describes their fabrication and uses.<ref>{{cite conference
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| | first = Viktor
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| | last = Strizhak
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| | coauthors = Igor Penkov, Toivo Pappel
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| | title = Evolution of design, use, and strength calculations of screw threads and threaded joints
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| | booktitle = HMM2004 International Symposium on History of Machines and Mechanisms
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| | pages =
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| | publisher = Kluwer Academic publishers
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| | year = 2004
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| | location =
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| | url = http://books.google.com/books?id=FqZvlMnjqY0C&printsec=frontcover&dq=%22archimedean+simple+machine%22&source=gbs_summary_r&cad=0
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| | doi =
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| | id = ISBN 1-4020-2203-4
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| | accessdate = 2008-05-21
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| |page=245}}</ref> However the Greeks' understanding was limited to the [[statics]] of simple machines; the balance of forces, and did not include [[Dynamics (mechanics)|dynamics]]; the tradeoff between force and distance, or the concept of [[Work (physics)|work]].
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| During the [[Renaissance]] the dynamics of the ''Mechanical Powers'', as the simple machines were called, began to be studied from the standpoint of how much useful work they could perform, leading eventually to the new concept of mechanical [[work (physics)|work]]. In 1586 Flemish engineer [[Simon Stevin]] derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist [[Galileo Galilei]] in 1600 in ''Le Meccaniche'' ("On Mechanics").<ref name="Krebs">{{cite book
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| |last=Krebs
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| |first=Robert E.
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| |title=Groundbreaking Experiments, Inventions, and Discoveries of the Middle Ages
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| |year=2004
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| |publisher=Greenwood Publishing Group
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| |isbn=0-313-32433-6
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| |url=http://books.google.com/books?id=MTXdplfiz-cC&pg=PA163&dq=%22mechanics+Galileo+analyzed%22#v=onepage&q=%22mechanics%20Galileo%20analyzed%22&f=false
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| |accessdate=2008-05-21
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| |page=163}}</ref><ref name="Stephen">{{cite book
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| | last = Stephen
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| | first = Donald
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| | authorlink =
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| | coauthors = Lowell Cardwell
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| | title = Wheels, clocks, and rockets: a history of technology
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| | publisher = W. W. Norton & Company
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| | year = 2001
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| | location = USA
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| | pages = 85–87
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| | url = http://books.google.com/books?id=BSfpFLV1nkAC&pg=PA86&dq=%22simple+machine%22+galileo#v=onepage&q=%22simple%20machine%22%20galileo&f=false
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| | doi =
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| | isbn = 0-393-32175-4}}</ref> He was the first to understand that simple machines do not create [[energy]], only transform it.<ref name="Krebs" />
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| The classic rules of sliding [[friction]] in machines were discovered by [[Leonardo da Vinci]] (1452–1519), but remained unpublished in his notebooks. They were rediscovered by [[Guillaume Amontons]] (1699) and were further developed by [[Charles-Augustin de Coulomb]] (1785).<ref>{{cite book
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| | last = Armstrong-Hélouvry
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| | first = Brian
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| | authorlink =
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| | coauthors =
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| | title = Control of machines with friction
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| | publisher = Springer
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| | year = 1991
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| | location = USA
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| | pages = 10
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| | url = http://books.google.com/books?id=0zk_zI3xACgC&pg=PA10&dq=friction+leonardo+da+vinci+amontons+coulomb#v=onepage&q=friction%20leonardo%20da%20vinci%20amontons%20coulomb&f=false
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| | doi =
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| | isbn = 0-7923-9133-0}}</ref>
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| <!-- I am commenting this section out because the references are not substantial and there is no question about what the Renaissance scientists considered to be simple machines. I think this section is confusing to readers.
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| ==Alternate definitions==
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| Any list of simple machines is somewhat arbitrary; the central idea is that every mechanism that manipulates force should be able to be understood as a combination of devices on the list. Some variations that have been proposed to the classical list of six simple machines:
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| * Some exclude the wedge from the list of simple machines, as it is a moving inclined plane.<ref name="Asimov1988"/>
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| * The screw, being a [[helical]] inclined plane,<ref>[http://cnx.org/content/m13594/latest/ Simple machine elements: The screw is basically an inclined plane wrapped around a cylinder]</ref> is sometimes also excluded.<ref>{{cite book
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| |last=Carhart
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| |first=Henry S.
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| |coauthors=Chute, Horatio N.
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| |title=Physics with Applications
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| |year=1917
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| |publisher=Allyn & Bacom
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| |pages=159–160
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| |url=http://books.google.com/books?id=4T0AAAAAYAAJ&pg=RA1-PA160
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| |accessdate=2008-05-20}}</ref> This position is less accepted because a screw converts a rotational force ([[torque]]) to a linear force.
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| * It has been said that the pulley, and wheel and axle can be viewed as unique forms of levers, leaving only the lever and the inclined plane as simple machines from which all others can be derived.<ref>{{cite web
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| |last=Isbell
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| |first=Pam
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| |title=Simple machines, or are they?
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| |year=2001
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| |work=Grade 5–7 lesson plan
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| |publisher=2001 National Teacher Training Institute
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| |url=http://www.myetv.org/education/ntti/lessons/2001_lessons/simplemachines.cfm
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| |accessdate=2008-05-13}}</ref><ref name="Clute">{{cite book
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| |last=Clute
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| |first=Willard N.
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| |title=Experimental General Science
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| |year=1917
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| |publisher=P. Blakiston's Son & Co.
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| |location=Philadelphia
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| |pages=188
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| |url=http://books.google.com/books?id=OuFHAAAAIAAJ&pg=PA188
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| |accessdate=2008-05-20}}</ref><ref name="BNET">{{cite web
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| |title=Mechanical Advantage and Simple Machines
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| |year=2002
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| |work=BNET Business Network
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| |publisher=CNET
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| |url=http://findarticles.com/p/articles/mi_gx5226/is_2002/ai_n19143765/pg_1
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| |accessdate=2008-05-21}}</ref><ref name="Beiser">{{cite book
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| |last=Beiser
| |
| |first=Arthur
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| |year=2004
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| |title=Schaum's Outline of Applied Physics
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| |publisher=McGraw-Hill
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| |url=http://books.google.com/books?id=soKguvJDgmsC&dq=Hydraulic+%22simple+machines%22&cad=0
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| |isbn=0-07-142611-6
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| |accessdate=2008-05-21
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| |page=145}}</ref>
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| * [[Hydraulic]] systems can also provide amplification of force, so some say they should be added to the list.<ref name="BNET"/><ref>This was first suggested by [[Blaise Pascal]] in the 17th century: {{cite book
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| |last=Meli
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| |first=Domenico Bertolini
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| |title=Thinking with Objects:The Transformation of Mechanics in the 17th Century
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| |year=2006
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| |publisher=JHU Press
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| |isbn=0-8018-8427-6
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| |url=http://books.google.com/books?id=qbS_0qAB3_cC&dq=Hydraulic+%22simple+machines%22&cad=0}} p.175</ref><ref>{{cite web
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| |title=Mechanical Advantage - Simple Machines
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| |work=MCAT Exam preparation
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| |date=January 7, 2008
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| |publisher=Eduturca
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| |url=http://www.eduturca.com/mcat-exam/mechanical-advantage-simple-machines-mcat.html
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| |accessdate=2008-05-21}}</ref>
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| -->
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| ==Mechanical advantage==
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| A simple machine has an applied force that [[Mechanical work|work]]s against a load force. If there are no [[friction]] losses, the work done on the load is equal to the work done by the applied force. This allows an increase in the output force at the cost of a proportional decrease in the distance moved by the load. The ratio of the output force to the input force is the [[mechanical advantage]] of the machine.
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| If the simple machine does not dissipate or absorb energy, then its mechanical advantage can be calculated from the machine's geometry. For example, the mechanical advantage of a [[lever]] is equal to the ratio of its [[lever arm]]s. A simple machine with no [[friction]] or [[Elasticity (physics)|elasticity]] is often called an ''[[ideal machine]]''.<ref name="Uicker2003">{{Citation |first=John J. |last=Uicker, Jr. |first2=Gordon R. |last2=Pennock |first3=Joseph E. |last3=Shigley |year=2003 |title=Theory of Machines and Mechanisms |edition=third |publisher=Oxford University Press |location=New York |isbn=978-0-19-515598-3 |doi= }}</ref><ref>{{Citation |first=Burton |last=Paul |year=1979 |title=Kinematics and Dynamics of Planar Machinery |publisher=Prentice Hall |isbn=978-0-13-516062-6 |doi= }}</ref>
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| For an ideal simple machine the rate of energy in, or [[power (physics)|power]] in, equals the rate of energy out, or power out, that is
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| :<math>P_{in} = P_{out}.\!</math>
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| Because [[power (physics)|power]] is the product of a force and the velocity of its point of application, the applied force times the velocity the input point moves, ''v<sub>in</sub>'', must be equal to the load force times the velocity the load moves, ''v<sub>out</sub>'', given by
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| :<math>F_{in}v_{in} = F_{out}v_{out}.\,</math>
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| So the ratio of output to input force, the [[mechanical advantage]], of a frictionless machine is equal to the "''velocity ratio''"; the ratio of input velocity to output velocity:
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| :<math>MA = \frac{F_{out}}{F_{in}} = \frac{v_{in}}{v_{out}} \,</math> (Ideal Mechanical Advantage)
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| In the [[screw (simple machine)|screw]], which uses rotational motion, the input force should be replaced by the [[torque]], and the velocity by the angular velocity the shaft is turned.
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| ==Compound machine==
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| A ''compound machine'' is a [[machine (mechanical)|machine]] formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example a [[Vise|bench vise]] consists of a lever (the vise's handle) in series with a screw, and a simple [[gear train]] consists of a number of [[gear]]s ([[Wheel and axle|wheels and axles]]) connected in series.
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| The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is
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| :<math>\mathrm{MA}_{compound} = \frac {F_{\mathrm{out} n}} {F_{\mathrm{in} 1}}. \,</math>
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| Because the output force of each machine is the input of the next, <math>F_{out 1}=F_{in 2} \,</math> and <math> F_{out k} =F_{in k+1} \,</math>, this mechanical advantage is also given by,
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| :<math>\mathrm{MA}_{compound} = \frac {F_{out 1}} {F_{in 1}} \frac {F_{out 2}} {F_{in 2}} \ldots\frac {F_{out n}} {F_{in n}}. \,</math>
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| Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it,
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| :<math>\mathrm{MA}_{compound} = \mathrm{MA}_1 \mathrm{MA}_2 \ldots\mathrm{MA}_n \,</math>
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| ==Energy losses and efficiency==
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| Machines lose energy through friction, deformation and wear, which is dissipated as heat. This means the power out of the machine is less than power in. The ratio of power out to power in is the [[Mechanical efficiency|efficiency]] η of the machine, and is a measure of the energy losses,
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| :<math>\eta = \frac{P_{out}}{P_{in}}. \, </math>
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| The velocity ratio of a machine is fixed by its dimensions, so it is the mechanical advantage that is reduced by the losses, that is
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| :<math>MA = \frac{F_{out}}{F_{in}} = \eta \frac{v_{in}}{v_{out}}.</math>
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| So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency ''η''. So a machine that includes losses such as friction, deformation and wear, will not be able to move as large a load as a corresponding ideal machine using the same input force.
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| The efficiency of a compound machine is the product of the efficiencies of the series of simple machines that form it,
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| :<math>\eta_{compound} = \eta_1 \eta_2 \ldots \eta_n.\,</math>
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| ==Kinematic chains==
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| [[File:Kinematics of Machinery - Figure 21.jpg|thumb|right|200px|alt=Illustration of a Four-bar linkage from Kinematics of Machinery, 1876|Illustration of a four-bar linkage from [http://en.wikisource.org/wiki/The_Kinematics_of_Machinery Kinematics of Machinery, 1876]]]Simple machines are elementary examples of [[kinematic chain]]s 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.
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| 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"/>
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| <!-- This section on self-locking applies to the inclined plane, wedge and screw but uses a general approach rather than a direct analysis. I recommend that a direct analysis be provided in the articles on each of these devices.
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| ==Self-locking machines==
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| In many simple machines, if the load force ''F<sub>out</sub>'' on the machine is high enough in relation to the input force ''F<sub>in</sub>'', the machine will move backwards, with the load force doing work on the input force.<ref name="Gujral2">{{cite book
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| | last = Gujral
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| | first = I.S.
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| | authorlink =
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| | coauthors =
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| | title = Engineering Mechanics
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| | publisher = Firewall Media
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| | year = 2005
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| | location =
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| | pages = 382
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| | url = http://books.google.com/books?id=JM0OG-XUyu0C&pg=PA382&dq=%22simple+machine%22+self-locking#v=onepage&q=%22simple%20machine%22%20self-locking&f=false
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| | doi =
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| | isbn = 81-7008-636-1}}</ref> So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called "''reversible''", "''non-locking''" or "''overhauling''" machines, and the backward motion is called "''overhauling''". However in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a "''self-locking''", "''nonreversible''", or "''non-overhauling''" machine.<ref name="Gujral2" /> These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left.
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| Self-locking occurs mainly in those machines which have large areas of sliding contact and therefore large frictional losses: the [[screw (simple machine)|screw]], [[inclined plane]], and [[wedge (mechanical device)|wedge]]:
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| *The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
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| *In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
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| *A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.
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|
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| A machine will be self-locking if and only if its efficiency ''η'' is below 50%:<ref name="Gujral2" />
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| :<math>\eta \equiv \frac {F_{out}/F_{in} }{d_{in}/d_{out} } < 0.50 \,</math>
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| Whether a machine is self-locking depends on both the friction forces ([[Coefficient of friction|coefficient of static friction]]) between its parts, and the distance ratio ''d<sub>in</sub>/d<sub>out</sub>'' (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.
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| ===Derivation===
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| When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy<ref name="Rao">{{cite book
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| | last = Rao
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| | first = S.
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| | authorlink =
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| | coauthors = R. Durgaiah
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| | title = Engineering Mechanics
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| | publisher = Universities Press
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| | year = 2005
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| | location =
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| | pages = 82
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| | url = http://books.google.com/books?id=vRR4FKAkJl4C&pg=PA80&dq=%22simple+machine%22+%22mechanical+advantage%22#v=onepage&q=%22simple%20machine%22%20%22&f=false
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| | doi =
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| | isbn = 81-7371-543-2}}</ref><ref name="Goyal">{{cite book
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| | last = Goyal
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| | first = M. C.
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| | authorlink =
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| | coauthors = G. S. Raghuvanshi
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| | title = Engineering Mechanics
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| | publisher = PHI Learning Private Ltd.
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| | year = 2009
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| | location = New Delhi
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| | pages = 202
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| | url = http://books.google.com/books?id=vRR4FKAkJl4C&pg=PA82#v=onepage&q&f=false
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| | doi =
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| | isbn = 81-203-3789-1}}</ref>
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| :<math>W_{i1,2} = W_{load} + W_{fric} \qquad \qquad (1)\,</math>
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| When it moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction ''W<sub>fric</sub>'' is the same
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| :<math>W_{load} = W_{i2,1} + W_{fric} \,</math>
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| When the input force is removed, the machine will self-lock if the work dissipated in friction is greater than the work done by the load force moving it backwards
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| :<math>W_{load} < W_{fric} \,</math>
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| From (1)
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| :<math>W_{load} < W_{i1,2} - W_{load} \,</math>
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| :<math>2W_{load} < W_{i1,2} \,</math>
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| :<math>\eta \equiv \frac {W_{load}}{W_{i1,2}} < \frac {1}{2} \,</math>
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| -->
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| ==Classification of machines==
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| The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.
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| However, a more successful strategy was identified by [[Franz Reuleaux]], who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are 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], New York: McGraw-Hill, online link from [[Cornell University]].</ref>
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| 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 [[revolute joint]], [[prismatic joint|sliding joint]], [[cam|cam joint]] and [[gear train|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.<ref name="Uicker2003"/>
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| ==See also==
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| * [[Machine (mechanical)]]
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| * [[Mechanism (engineering)]]
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| * [[Linkage (mechanical)]]
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| * [[Four-bar linkage]]
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| * [[Six-bar linkage]]
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| * [[Gear train]]
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| * [[Power (physics)]]
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| ==References==
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| {{Reflist|30em}}
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| {{Machines}}
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| {{DEFAULTSORT:Simple Machine}}
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| [[Category:Mechanical engineering]]
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| [[Category:Simple machines| ]]
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