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- W31081353 abstract "In the previous chapter, direct and inverse kinematics equations establishing the relationship between the joint variables and the end-effector position and orientation were derived. In this chapter, differential kinematics is presented which gives the relationship between the joint velocities and the corresponding end-effector linear and angular velocity. This mapping is described by a matrix, termed geometric Jacobian, which depends on the manipulator configuration. Alternatively, if the end-effector location is expressed with reference to a minimal representation in the operational space, it is possible to compute the Jacobian matrix via differentiation of the direct kinematics function with respect to the joint variables. The resulting Jacobian, termed analytical Jacobian, in general differs from the geometric one. The Jacobian constitutes one of the most important tools for manipulator characterization; in fact, it is useful for finding singular configuration, analyzing redundancy, determining inverse kinematics algorithms, describing the mapping between forces applied to the end effector and resulting torques at the joints (statics) and, as will be seen in the following chapters, for deriving dynamic equations of motion and designing operational space control schemes. Finally, the kineto-static duality concept is illustrated, which is at the basis of the definition of velocity and force manipulability ellipsoids." @default.
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- W31081353 date "2000-01-01" @default.
- W31081353 modified "2023-09-25" @default.
- W31081353 title "Differential Kinematics and Statics" @default.
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