ОПРЕДЕЛЕНИЕ ИНДЕКСА УПРАВЛЯЕМОСТИ И ВЫЯВЛЕНИЕ ОСОБЫХ ПОЛОЖЕНИЙ ПАРАЛЛЕЛЬНОГО МАНИПУЛЯТОРА

Abstract

The article presents a model, tools, methodology and results of identifying special provisions when planning the movement of a parallel manipulator such as the Gough-Stewart platform. Special positions are understood as positions having geometric uncertainty, singularity. Singular positions are estimated by analyzing the Jacobian matrix using its singular value decomposition. The calculation of the Jacobi matrix and its singular values is performed using special libraries of the high-level Python programming language. The presence of special positions in the workspace is analyzed using the dexterity index, which characterizes the ratios of the singular values of the singular value decomposition of the Jacobian matrix. A series of computational experiments are carried out to calculate the dexterity index, identify and analyze special positions in the working area. The results of a computational experiment for various design versions of the platform, which differ in the ratio of the radii of the movable platform and the fixed base, are presented. The analysis of the characteristic features of the formation of singularity zones in their working zones is carried out and design options are identified that have the maximum dexterity index of the working area. The presented approach is applicable in the framework of the development, modernization, optimization of structural elements of parallel structure manipulators.