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Kinematic chain refers to an assembly of rigid bodies connected by joints that is the mathematical model for a mechanical system.〔Reuleaux, F., 1876 (''The Kinematics of Machinery,'' ) (trans. and annotated by A. B. W. Kennedy), reprinted by Dover, New York (1963)〕 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.〔J. M. McCarthy and G. S. Soh, 2010, (''Geometric Design of Linkages,'' ) Springer, New York.〕 Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called ''lower pairs'' and the surface contact joints critical to cams and gearing, 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. The modern use of kinematic chains includes compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems.〔Larry L. Howell, 2001, (Compliant mechanisms ), John Wiley & Sons.〕 〔Alexander Slocum, 1992, (Precision Machine Design ), SME〕 == Mobility formula == The degrees of freedom, or ''mobility,'' of a kinematic chain is the number of parameters that define the configuration of the chain.〔〔J. J. Uicker, G. R. Pennock, and J. E. Shigley, 2003, Theory of Machines and Mechanisms, Oxford University Press, New York.〕 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. 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''. The result is that the mobility of a kinematic chain formed from ''n'' moving links and ''j'' joints each with freedom ''fi'', ''i=1, ..., j,'' is given by : Recall that ''N'' includes the fixed link. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「kinematic chain」の詳細全文を読む スポンサード リンク
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