Dissertation presented to the Mechanical Engineering Department of PUC-Rio as part of requirements to obtain the degree of : Master in sciences of mechanical engineering
Advisor: Prof. Rubens Sampaio, Ph.D.
June 1996

Abstract

This dissertation presents an introduction to the multibody dynamics with rigid and flexible parts, through the exposition of the following steps: modeling, simulation and control. The modeling of multibody systems emphasizes finite rotations representation, flexibility characterization and symbolic formulation of equations of motion. Finite rotations representation is done using several classical parameters, namely Euler's and Bryant's angles, Euler's and Rodrigues' parameters, rotational vector, conformal rotational vector and quaternions. Parameters singularities are analyzed, through the comparison of different parameters systems. Flexibilty characterization is done using the assumed modes method. Equations of motion formulation is achieved through Lagrange's and Maggi-Kane's equations and then implemented in MATLAB (tm) Symbolic Math Toolbox. State space equations are then derived from the symbolic math results in order to study the linear control of multibody systems. Two control strategies are considered: pole placement and optimal control. Simulation of some numerical examples of dynamics and control of multibody systems is done with emphasis to the choice of the integration algorithm. All steps are achieved inside MATLAB (tm) environment, using its symbolic function for modeling, linearization and control functions for controller design, and integration algorithms and graphical functions for simulation.

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