Original scientific paper
Differential-Geometric Modelling and Dynamic Simulation of Multibody Systems
Andreas MÜLLER
; University Duisburg-Essen Chair of Mechanics and Robotics, Germany
Zdravko TERZE
; Faculty of Mechanical Engineering and Naval Architecture of the University of Zagreb, Zagreb, Croatia
Abstract
A formulation for the kinematics of multibody systems is presented, which uses Lie group concepts. With line coordinates the kinematics is parameterized in terms of the screw coordinates of the joints. Thereupon, the Lagrangian motion equations are derived, and explicit expressions are given for the objects therein. It is shown how the kinematics and thus the motion equations can be expressed without the introduction of body-fixed reference frames. This admits the processing of CAD data, which refers to a single (world) frame. For constrained multibody systems, the Lagrangian motion equations are projected to the constraint manifold, which yields the equations of Woronetz. The mathematical models for numerical integration routines of MBS are surveyed and constraint gradient projective method for stabilization of constraint violation is presented.
Keywords
CAD; Constraint violation; Lagrange equations; Lie groups; Multibody systems; Numerical integration; Woronetz equations
Hrčak ID:
50594
URI
Publication date:
31.12.2009.
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