Natural frequency analysis of parallel manipulators using global independent generalized displacement coordinates

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.