ABSTRACT In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange’s equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for non-smooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices.

中文翻译：

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带导向装置的多缆驱动并联平台动力学建模

摘要 在本文中，提出了一个数学模型来数值模拟多缆悬挂平台中的动态响应，同时考虑了松弛的缆索和导向装置。考虑了缆索的状态变化（松弛与张紧），并用互补条件方程进行数学描述，导向轮和井壁之间的相互作用由 Heaviside 阶跃函数描述。利用带约束的拉格朗日方程导出系统的动力学方程，并应用针对多体动力学非光滑现象的非光滑广义α算法对方程进行数值求解。仿真结果显示了不同纵向激励下不同缆索激励时平台的动态响应和缆索张力特性。此外，结果还说明了缆索张力差异如何影响导向装置施加在井壁上的压力。