The dynamics and vibration characteristics of a 3-UPU parallel mechanism isolator are investigated by theoretical modeling, numerical simulation, and experimental study. The system consists of two platforms, three linear motors, and the Hook hinges. Firstly, the dynamical mathematical model of this vibration isolator is innovatively established and solved by using the discrete-time transfer matrix method of the multibody system (MS-DT-TMM). According to the modeling principle, the transfer matrix of each component is derived, including the upper and lower platforms, Hooke hinges, and linear motors. Then, the dynamical equation of the overall system is obtained by multiplying all transfer matrices. Secondly, the solution of equation is calculated through the setting of boundary conditions. The numerical simulation is carried out according to the known parameters. The dynamical and vibration analysis of the isolation platform is performed, involving the displacement and force characteristics of the branches. Furthermore, in view of the fact that the Hooke hinges and linear motors are simplified as spatial elastic hinges in modeling. The vibration suppression effect caused by adjusting spring stiffness and damping coefficient is discussed. The simulation results verified the correctness of the MS-DT-TMM method through the comparison with ADAMS simulation results. Finally, the prototype of the vibration isolator is constructed and assembled, and the vibration experiment is conducted. By testing the responses of the isolation device mounted on the vibration table, the natural frequency of the isolator is obtained. The purpose of this experiment is to avoid resonance when it is applied as a vibration isolator in the future. This paper provides a theoretical basis for the later vibration research and control scheme design of the 3-UPU parallel vibration isolation platform.

中文翻译：

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基于MS-DT-TMM的3-UPU直线电机并联隔振平台建模与振动分析

通过理论建模、数值模拟和实验研究，研究了 3-UPU 并联机构隔振器的动力学和振动特性。该系统由两个平台、三个线性电机和 Hook 铰链组成。首先，利用多体系统的离散时间传递矩阵法(MS-DT-TMM)，创新地建立并求解了该隔振器的动力学数学模型。根据建模原理，推导出各部件的传递矩阵，包括上下平台、虎克铰链、直线电机等。然后，通过将所有传递矩阵相乘得到整个系统的动力学方程。其次，通过设置边界条件来计算方程的解。根据已知参数进行数值模拟。对隔震平台进行动力和振动分析，涉及分支的位移和受力特性。此外，鉴于胡克铰链和直线电机在建模中被简化为空间弹性铰链。讨论了调整弹簧刚度和阻尼系数引起的振动抑制效果。仿真结果通过与ADAMS仿真结果的对比验证了MS-DT-TMM方法的正确性。最后，搭建并组装了隔振器样机，并进行了振动实验。通过测试安装在振动台上的隔振装置的响应，得到隔振器的固有频率。本实验的目的是为了在以后作为隔振器应用时避免共振。该论文为3-UPU并联隔振平台的后期振动研究和控制方案设计提供了理论依据。