НЕОДНОЗНАЧНІСТЬ ТА СИНГУЛЯРНІСТЬ МЕХАНІЗМІВ ПАРАЛЕЛЬНОЇ СТРУКТУРИ ТИПУ БІГЛАЙД

Abstract

The article deals with the issues of planning and obtaining shaping trajectories of the mechanisms of a parallel structure of the biglide type. The possibilities of forming functional trajectories of a biaxial two-coordinate biglide in the direct problem in the form of generalized coordinates of the degrees of freedom and the inverse problem in the form of gripper pole coordinates are considered. The conditions for the occurrence of ambiguity in the position of the mechanism in direct and inverse problems are revealed. To avoid ambiguity, it is proposed to control the process of forming a trajectory using an additional parameter. In the process of computer 3-D modeling, singular configurations of the biaxial bigglide mechanism with parallel guides were studied. Analytical models for the formation of trajectories are developed and kinematic conditions are proposed for avoiding locking processes in the mechanism in singular configurations. Singular configurations with quasi-zero and negative stiffness have been found for the mechanism of a parallel structure of the biglide type. Using the Lagrange principle of virtual (possible) displacements, analytical models of the generalized stiffness coefficients of the mechanism are obtained depending on the formed configuration. Configurations with quasi-zero stiffness correspond to zero values of the stiffness coefficients, and for negative stiffness, a characteristic transition through a singular configuration. Analytical expressions for the relative rigidities of the biglide mechanism are obtained and diagrams of their change for different configurations are constructed. The influence of the design parameters of the biglide on the value of the relative generalized stiffness of the entire mechanism has been studied. It has been established that within the range of configuration angle change from 0 to 12° and from 45° to 80°, the values of relative stiffness coefficients are much higher than within the range from 15° to 45°, which allows controlling the rigidity of the mechanism and having a positive effect on the positioning accuracy of the pole. biglide.