Abstract A modeling approach is proposed for analyzing the natural frequencies of parallel manipulators (PMs) using the global independent generalized displacement coordinates (IGDC). To avoid the constraint equations while solving the dynamic equation, all of the compatibility conditions must be integrated into the overall stiffness and mass matrices. The global IGDC is proposed to solve this problem. We establish one set of nonsingular independent displacement coordinates of the joint connection points using a multipoint constraint element and singularity assessment of the mapping matrix in the workspace. The global IGDC is obtained by combining the coordinates of the joint connection points and the inner nodes of the components. Matrix structural analysis (MSA) is used in combination with the global IGDC to establish the model for analyzing the natural frequencies of the PMs. The 2UPR-RPU and 2UR-2RPU PMs are presented to illustrate the effectiveness of the proposed model. We investigate the influence of the number of element divisions on the natural frequencies considering the member as a single element to ensure accurate and efficient computation of the fundamental frequency of the PMs.

中文翻译：

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使用全局独立广义位移坐标的并联机械臂固有频率分析

摘要 提出了一种使用全局独立广义位移坐标 (IGDC) 分析并联机械手 (PM) 固有频率的建模方法。为了在求解动力学方程时避免约束方程，必须将所有的兼容性条件整合到整体刚度和质量矩阵中。提出了全球IGDC来解决这个问题。我们使用多点约束元素和工作空间中映射矩阵的奇异性评估来建立一组关节连接点的非奇异独立位移坐标。全局 IGDC 是通过结合关节连接点的坐标和组件的内部节点来获得的。矩阵结构分析（MSA）结合全球IGDC建立分析PMs固有频率的模型。提出了 2UPR-RPU 和 2UR-2RPU PM 以说明所提出模型的有效性。我们研究了单元划分数量对固有频率的影响，将成员视为单个元素，以确保准确有效地计算 PM 的基频。