Abstract
In this paper, a modelling method and an accurate numerical procedure are presented to simulate the dynamical responses of a multi-cable driven parallel suspension platform system. For such systems, the cables might become slack due to external excitations and due to the fact that cables can become tensionless when been pushed in longitudinal direction. In lateral and torsional directions, the constraint forces between the cables and platform can be positive as well as negative. This paper will deal with the non-smooth cable vibrations (in longitudinal, lateral and torsional directions) by taking into account the slackness of the cables. Firstly, the Lagrange equation with constraints is used to derive the equations of motion of the multi-cable suspension platform. Then, by expressing the equations of motion and constraint equations at velocity level, a non-smooth algorithm is used to numerically solve the equations. Finally, the numerical results are compared with an ADAMS simulation, and the two results agree well with each other. Moreover, the results in this paper significantly improve the numerical results used in the analysis of the dynamics for multi-cable systems which usually neglect the lateral properties of the cables.
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