Jacobian-based derivation of dynamics equations of elastic parallel manipulators

Authors:
Krzysztof Stachera;Frank Wobbe;Walter Schumacher
Affiliations:
Technical University of Braunschweig;Technical University of Braunschweig;Technical University of Braunschweig
Venue:
AsiaMS '07 Proceedings of the IASTED Asian Conference on Modelling and Simulation
Year:
2007

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Abstract

This article presents two approaches for the derivation of dynamics equations of elastic parallel manipulators. These are based on the standard Lagrange-D'Alembert formulation extendend by the consideration of (even redundant) 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 second one deals with the manipulator as a compact structure. 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 planar parallel elastic manipulator Five-Bar is derived with the presented approaches and compared with a numerical model in form of a DYMOLA-model.