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| [[File:ATHLETE robot climbing a hill.jpg|thumb|300px|The [[JPL]] [[mobile robot]] [[ATHLETE]] is a platform with six serial chain legs ending in wheels.]]
| | Hi there, I am Yoshiko Villareal but I by no means truly liked that title. Delaware has always been my residing place and will never move. What she loves doing is bottle tops collecting and she is attempting to make it a occupation. My job is a messenger.<br><br>Here is my website ... [http://ernrduo.woobi.Co.kr/xe/?document_srl=582849 ernrduo.woobi.Co.kr] |
| [[File:JSC2001-01725.jpg|thumb|300px|The arms, fingers and head of the [[Lyndon B. Johnson Space Center|JSC]] [[Robonaut]] are modeled as kinematic chains.]]
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| [[File:SteamEngine Boulton&Watt 1784.png|thumb|right|300px|alt=Boulton & Watt Steam Engine|The movement of the [[Watt steam engine|Boulton & Watt steam engine]] is studied as a system of rigid bodies connected by joints forming a kinematic chain.]]
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| [[File:Modele cinematique corps humain.svg|thumb|A model of the human skeleton as a kinematic chain allows positioning using forward and inverse kinematics.]]
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| '''Kinematic chain''' refers to an assembly of [[Rigid body|rigid bodies]] connected by [[Joint (mechanics)|joints]] that is the [[mathematical model]] for a [[mechanical system]].<ref name=Reuleaux1876>[[Franz Reuleaux|Reuleaux, F.]], 1876 [http://books.google.com/books?id=WUZVAAAAMAAJ&printsec=frontcover&dq=kinematics+of+machinery&hl=en&sa=X&ei=qpn4Tse-E9SasgLcsZytDw&ved=0CEQQ6AEwAQ#v=onepage&q=kinematics%20of%20machinery&f=false ''The Kinematics of Machinery,''] (trans. and annotated by A. B. W. Kennedy), reprinted by Dover, New York (1963)</ref> As in the familiar use of the word [[chain]], the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the [[kinematic]] model for a typical robot [[manipulator]].<ref name="McCarthy2010">J. M. McCarthy and G. S. Soh, 2010, [http://books.google.com/books?id=jv9mQyjRIw4C&pg=PA231&lpg=PA231&dq=geometric+design+of+linkages&source=bl&ots=j6TS1043qE&sig=R5ycw5DximWrQOEVshfiytflD6Q&hl=en&sa=X&ei=0Zj4TuiCFvCGsgKyvO3FAQ&ved=0CGAQ6AEwBQ#v=onepage&q=geometric%20design%20of%20linkages&f=false ''Geometric Design of Linkages,''] Springer, New York.</ref>
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| Mathematical models of the connections, or joints, between two links are termed [[kinematic pair]]s. Kinematic pairs model the hinged and sliding joints fundamental to [[robotics]], often called ''lower pairs'' and the surface contact joints critical to [[cam]]s and [[gear]]ing, called ''higher pairs.'' These joints are generally modeled as [[holonomic constraints]]. A [[kinematic diagram]] is a schematic of the mechanical system that shows the kinematic chain.
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| The modern use of kinematic chains includes compliance that arises from flexure joints in precision mechanisms, link compliance in [[compliant mechanism]]s and [[micro-electro-mechanical systems]], and cable compliance in cable robotic and [[tensegrity]] systems.<ref>Larry L. Howell, 2001, [http://books.google.com/books/about/Compliant_mechanisms.html?id=tiiSOuhsIfgC Compliant mechanisms], John Wiley & Sons.</ref>
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| <ref>Alexander Slocum, 1992, [http://books.google.com/books?id=uG7aqgal65YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Precision Machine Design], SME</ref>
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| == Mobility formula ==
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| The [[degrees of freedom (mechanics)|degrees of freedom]], or ''mobility,'' of a kinematic chain is the number of parameters that define the configuration of the chain.<ref name="McCarthy2010"/><ref name=Uicker2003>J. J. Uicker, G. R. Pennock, and J. E. Shigley, 2003, '''Theory of Machines and Mechanisms,''' Oxford University Press, New York.</ref>
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| A system of ''n'' rigid bodies moving in space has ''6n'' degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M=6(N-1), where N=n+1 is the number of moving bodies plus the fixed body.
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| Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints ''c'' that a joint imposes in terms of the joint's freedom ''f'', where ''c=6-f''. In the case of a hinge or slider, which are one degree of freedom joints, have ''f=1'' and therefore ''c=6-1=5''.
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| The result is that the mobility of a kinematic chain formed from ''n'' moving links and ''j'' joints each with freedom ''f<sub>i</sub>'', ''i=1, ..., j,'' is given by
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| :<math> M = 6n - \sum_{i=1}^j\ (6 - f_i) = 6(N-1 - j) + \sum_{i=1}^j\ f_i </math>
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| Recall that ''N'' includes the fixed link.
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| ==Analysis of kinematic chains==
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| The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form [[algebraic equations]] that are solved to determine the configuration of the chain associated with specific values of input parameters, called [[degrees of freedom (mechanics)|degrees of freedom]].
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| The constraint equations for a kinematic chain are obtained using [[rigid transformation]]s [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of ''n'' links connected in series has the kinematic equations,
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| :<math>[T] = [Z_1][X_1][Z_2][X_2]\ldots[X_{n-1}][Z_n],\!</math>
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| where [T] is the transformation locating the end-link---notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the [[forward kinematics]] equations of the serial chain.<ref>J. M. McCarthy, 1990, ''Introduction to Theoretical Kinematics,'' MIT Press, Cambridge, MA.</ref>
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| Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called ''loop equations''.
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| The complexity (in terms of calculating the [[forward kinematics|forward]] and [[inverse kinematics]]) of the chain is determined by the following factors:
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| * Its [[topology]]: a serial chain, a [[parallel manipulator]], a [[tree (graph theory)|tree]] structure, or a [[graph theory|graph]].
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| * Its [[Euclidean geometry|geometrical]] form: how are neighbouring [[kinematic pair|joints]] spatially connected to each other?
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| '''Explanation:-'''<br>
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| Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.<ref name="Uicker2003"/>
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| ==Synthesis of kinematic chains==
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| The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed ''kinematic synthesis.''<ref name="Hartenberg1964">R. S. Hartenberg and J. Denavit, 1964, ''Kinematic Synthesis of Linkages,'' McGraw-Hill, New York.</ref>
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| Perhaps the most developed formulation of kinematic synthesis is for [[four-bar linkage]]s, which is known as [[Burmester theory]].<ref>Suh, C. H., and Radcliffe, C. W., '''Kinematics and Mechanism Design,''' John Wiley and Sons, New York, 1978.</ref><ref>Sandor,G.N.,andErdman,A.G.,1984,AdvancedMechanismDesign:AnalysisandSynthesis, Vol. 2. Prentice-Hall, Englewood Cliffs, NJ.</ref><ref>Hunt, K. H., '''Kinematic Geometry of Mechanisms,''' Oxford Engineering Science Series, 1979</ref>
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| [[Ferdinand Freudenstein]] is often called the father of modern kinematics for his contributions to the kinematic synthesis of [[Linkage (mechanical)|linkages]] beginning in the 1950s. His use of the newly developed computer to solve ''Freudenstein's equation'' became the prototype of [[computer-aided design]] systems.<ref name="Hartenberg1964"/>
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| This work has been generalized to the synthesis of spherical and spatial mechanisms.<ref name="McCarthy2010"/>
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| ==See also==
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| * [[Denavit-Hartenberg parameters]]
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| * [[Chebychev–Grübler–Kutzbach criterion]]
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| * [[Configuration space]]
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| * [[Machine (mechanical)]]
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| * [[Mechanism (engineering)]]
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| * [[Six-bar linkage]]
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| * [[Simple machines]]
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| * [[Six degrees of freedom]]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Kinematic Chain}}
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| [[Category:Computer graphics]]
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| [[Category:3D computer graphics]]
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| [[Category:Computational physics]]
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| [[Category:Robot kinematics]]
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| [[Category:Virtual reality]]
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| [[Category:Mechanical engineering]]
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| [[Category:Mechanisms]]
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| [[Category:Diagrams]]
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| [[Category:Classical mechanics]]
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| [[Category:Kinematics]]
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Hi there, I am Yoshiko Villareal but I by no means truly liked that title. Delaware has always been my residing place and will never move. What she loves doing is bottle tops collecting and she is attempting to make it a occupation. My job is a messenger.
Here is my website ... ernrduo.woobi.Co.kr