Elastodynamic Modeling and Analysis of a 2PRU-UPR Over-constrained Parallel Manipulator

doi:10.3901/JME.2023.21.209

Abstract

Abstract: The elastodynamic modeling of a 2PRU-UPR parallel manipulator with 2R1T 3-DOF (degrees of freedom) is studied based on the global independent generalized displacement coordinates and Lagrange’s equation. First, the links are divided into a number of elements using the Euler-Bernoulli beam element, the dynamic control equation of each element is obtained, and the dynamic control equation of each link can be obtained using the Lagrange’s equation. Second, one set of nonsingular independent displacement coordinates of the joint connection points is established using a multipoint constraint element and singularity assessment of the mapping matrix in the workspace, and the global independent generalized displacement coordinates (IGDC) of the mechanism is obtained by combining the internal node displacement coordinates and independent displacement coordinates of the joint connection points. Finally, the dynamic control equation of the mechanism is established using the Lagrange’s equation and global IGDC. Numerical results of natural frequencies show that the relative error between the finite element model established by the ANSYS Workbench software and the theoretical model is within 3.6%, which verify the correctness of the proposed model. The comparison of computational accuracy and cost of subspace iteration method, static condensation method, and dynamic condensation method for the natural frequency analysis is also presented. The proposed method is also applicable to other parallel and serial mechanisms.

Key words: parallel manipulator, elastodynamic, global independent generalized displacement coordinates, Lagrange’s equation

CLC Number:

TG156

YANG Chao, HUANG Fengli, YE Wei, CHEN Qiaohong. Elastodynamic Modeling and Analysis of a 2PRU-UPR Over-constrained Parallel Manipulator[J]. Journal of Mechanical Engineering, 2023, 59(21): 209-223.

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