DYNAMICS OF CONTROLLED MOTION OF ELASTIC SYSTEMS SUBJECT TO FINITE DISPLACEMENTS AND ROTATIONS

摘要

When performing various operations, for example, unfolding, orientation, or automated assembly, engineering systems (e.g., cranes, manipulation robots, or space vehicles and structures) and their members can be subjected to finite displacements and rotations. Such motions can excite unsteady vibrations. These vibrations reduce the accuracy and increase the time of the operations and lead to various disturbances. A number of issues related to the dynamics and control of flexible manipulation robots have been considered in [1]. Mathematical models and methods for the analysis and solution of some problems of mechanics of flexible space structures have been presented in [2, 3]. In many cases, it is necessary that the residual elastic vibrations after the operation has been accomplished have been completely damped or reduced to an acceptable minimum level. To that end, as a rule, various dampers or means for active suppression of unsteady vibrations are commonly utilized [4]. In [5], for the case of rotation of a rod that can perform small vibrations by a finite angle, it is shown that for an appropriate dynamic or kinematic control law designed for the rotation of the rod, one can reduce the level of the residual vibrations by adjusting the relationship between the natural vibration frequencies of the rod. In the present paper, the approach of [5] is developed for an arbitrary spatial elastic system that performs finite translations and rotations between two states of rest, with these motions being accompanied by elastic vibrations with finite strains.