ANALYSIS OF THE SINGULARITIES INFLUENCE ON THE FORWARD KINEMATICS SOLUTION AND THE GEOMETRY OF THE WORKSPACE OF THE GOUGH-STEWART PLATFORM

Abstract

One of the obligatory requirements for parallel mechanisms design is the exclusion from the workspace of singularities in which the mechanism loses its controllability and malfunctions may occur. The analysis of the workspace of the mechanisms of a parallel structure is more complicated than that for the mechanisms of a serial structure, especially if the mechanism has more than three degrees of freedom. The article considers the problem of analyzing the influence of singularities on the solution of the forward kinematics and the geometry of the workspace 3/6 of the Gough-Stewart platform (commercial name - "Hexapod"). A numerical algorithm for solving the forward kinematics of platform has been developed. It is based on the direct use of the system of equations of the platform's kinematic constraints. Approximation of the set of solutions to the system of equations is based on deterministic methods of global optimization. An analysis of the change in the number of forward kinematics near the zone of singularities is performed. The analysis consists of two stages. The first stage consists in solving the forward kinematics for the position and orientation of the platform, at which singularities arises. The second stage consists in solving the forward kinematics for the case of a singularity and the case near a singularity. As a result of solving the forward kinematics, a different number of forward kinematics solutions for different cases was revealed. An algorithm has been synthesized that makes it possible to determine a singularity-free workspace free for given ranges of change in the platform orientation angles specified by Euler angles. An analysis of the dependence of the change in the volume of the workspace depending on the range of change in the angles of the platform orientation was carried out. The algorithms are implemented programmatically in the C++ programming language. The modeling was performed using parallel computing and the implementation of the export of three-dimensional models of the positions of the platform and workspace to the universal format of three-dimensional models STL.