Jacobian-based Derivation of Dynamics Equations of Elastic Parallel Manipulators

K. Stachera, F. Wobbe, and W. Schumacher


elastic parallel manipulators, dynamics computation, dy namics modelling, Jacobian matrix


This article presents two approaches for the deriva tion of dynamics equations of elastic parallel manipulators. These are based on the standard Lagrange-D’Alembert for mulation extendend by the consideration of (even redun dant) elasticities.They start up from different points of view on the dynamics of the parallel manipulators. The first one reduces the parallel manipulator to a tree-structure, the se cond one deals with the manipulator as a compact struc ture. These different ways lead to the same equation of motion. In addition, a new method for the derivation of the Jacobian matrix of the elastic parallel manipulator will be presented. For verification an analytical model of the pla nar parallel elastic manipulator FIVE-BAR is derived with the presented approaches and compared with a numerical model in form of a DYMOLA-model.

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