Parameters Optimization Design of 3-UPU Parallel Mechanism based on the Spectral Norm

Abstract

For the same type of the parallel mechanism, the structure parameters affect the performance of the movement of kinematics and the static stiffness, so the design of the reasonable structure parameters becomes a key problem in the structural design of parallel mechanism. Taking the 3-UPU parallel mechanism as the research object, an optimum design method of parallel mechanism structure parameters based on the spectral norm is proposed. Firstly, the structure of the parallel mechanism deduces the mathematical model of the end executor and establishes Jacobi matrix, and then the mathematical model of Jacobi matrix condition number is established in the form of spectral norm according to the parallel mechanism dexterity evaluation system in the condition number of the evaluation index. Through the first-order influence coefficient and the eigenvalue of matrix, the analysis of the optimization and simulation is made on the structure parameters of the parallel mechanism whose workspace is known by using the Matlab software. The results show that: in the known workspace and considering the requirements of the design of mechanical structure, when the condition number is 1. $58\leq E\leq 1.72$, the optimized parameters meet the initial design requirements and the data lays a theoretical foundation for the follow-up analysis of the error of parallel mechanism.