Abstract

This paper addresses modeling issues that arise in the formulation of the equations of motion for the flexible multibody mechanical systems intended for space applications and designed according to ground test results. A planar multibody system consisting of two flexible links interconnected by two revolute joints and a payload at its free end is proposed for the investigations. In addition to the gravity and transverse deflections (most common two conditions adopted for the research in this field), the foreshortening effects, the axial deflections and the work done by the system’s own weight on the elastic deflections are also taken into consideration. Since the slender link assumption is made, the Euler-Bernoulli Beam theory is considered sufficient and satisfactory for describing the behavior of the deformed link components. The Lagrangian formulation in conjunction with assumed displacement field method is then implemented to develop the equations of motion for the system. After achieving the analytical model for the system, a linearization about various system configurations transforms the fully coupled nonlinear differential equations into standard eigenvalue problems. In doing so, the roles played by gravity, foreshortening and system’s own weight (‘weight-load’) on the dynamic behavior of the system undergoing ground testing are examined. For analysis, the fundamental frequency of the system is chosen as a measurement index. Finally, parametric studies focusing on the mass properties of payload, lower and upper links, and actuators are undertaken to address the stability problems. Results indicate that the ‘weight-load’ exhibits interesting effects on the ‘foreshortening and stability’, hence, merits further investigation.

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