空间刚柔耦合并联机构系统的频率特性分析

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对空间刚柔耦合并联机构系统的固有频率特性进行分析。建立一种空间有限元梁单元新模型,基于有限元法和Lagrange方程导出有限元梁单元的运动微分方程。通过分析动平台运动参量与运动支链间的运动关系,得到刚柔耦合并联机构系统的运动学约束条件,并由Newton-Euler方程得到系统动平台的动力学模型。根据系统的运动学约束条件和动平台的动力学模型,经过各个单元运动微分方程的有机组装,导出刚柔耦合并联机构系统的整体动力学方程。在此基础上,通过算例3-RRS刚柔耦合并联机构系统的频率特性分析,总结空间刚柔耦合并联机构系统的固有频率与机构基本参量之间的内在规律。结果显示,刚柔耦合并联机构系统的结构尺寸、支链中杆件的截面参量和材料参量等对系统的固有频率都有显著影响。研究对进一步研究刚柔耦合并联机构的动态特性和机构优化设计具有重要的指导意义。 The primary goal of this research is frequency analysis of the spatial flexible-rigid coupled parallel manipulator.A new model of spatial flexible beam element is proposed.The dynamic equation of the spatial flexible beam element is derived based on the finite element theory and Lagrange equations.The kinematic constraint conditions of the movable platform and the sub-chains of the flexible-rigid coupled parallel manipulator are derived,based on the elastic displacements of the movable platform and the sub-chains.The dynamic model of the movable platform is developed based on the Newton-Euler principle.By using the kinematic constraint equations and dynamic model of the moving platform,the overall system dynamic equations of the flexible-rigid coupled parallel manipulator are obtained through assembling the dynamic equations of elements.Then,the natural frequencies of a 3-RRS flexible-rigid coupled parallel manipulator are studied through numerical simulation.From the simulation results,the natural frequencies are relatively sensitive to the structure size,section parameter,and characteristic parameter of material on mechanisms.The results provide important knowledge to researchers to the dynamic analysis and optimal design of flexible-rigid coupled parallel manipulators.