Analytical derivation and application of the Jacobian matrix of parallel kinematic manipulators
J. Brinker, M. Lorenz, S.C. Eddine and B. Corves
https://doi.org/10.19124/ima.2015.001.24
Abstract
This paper describes two major aspects within the research fields of robotics: First, the analytical derivation of the Jacobian matrix of mechanisms with complex kinematics and second, the performance evaluation of redundantly actuated parallel kinematic manipulators with different types of actuators. For mechanisms with simple kinematics, the Jacobian matrix can usually be obtained by straightforward derivation and differentiation of the closure equation. Complex architectures, however, require comprehensive analytical approaches. Accordingly, an existing method to determine the Jacobian based on selection matrices is applied to a 3-RPRRR mechanism. In order to characterize and evaluate corresponding structures, the concept of power manipulability ellipsoids is applied. Thus, the common problem of the Jacobian’s inhomogeneity due to a mixed translational and/or rotational drive configuration is avoided.
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