Development of the Mathematical Model of Movement of the Output Robot Rotating on the Basis of Positioning Possibility Analysis

Abstract

The construction of a mathematical model of motion of the output link of an industrial robot with six degrees of freedom is considered in the study of the accuracy of its positioning. The mathematical model of the robot includes the solution of the inverse kinematics problem, the solution of the direct problem of dynamics, and also the problem of the position of the working point of the robot. Significant influence on the characteristics of control systems of complex mechatronic objects, such as manipulation robots, is provided by their kinematic and dynamic parameters, for the use of which in the implementation of the SS, it is necessary to give their detailed mathematical description. To solve this problem, two directions are used. The first is to create an accurate kinematic model of the manipulator, which makes it possible to uniquely determine its spatial configuration, which in turn will enable us to describe the laws of displacement of the working member. The second direction is the description of the dynamic characteristics and relationships existing in the manipulator, which will allow describing its behavior when moving along a given trajectory. The peculiarity of the model is the registration of deviations of the trajectory of the output link from the given position. The developed mathematical model will allow to obtain a more complete picture of the process of positioning the output link of the mechatronic complex with allowance for inertial forces and, thereby, to increase its accuracy when working out a spatial trajectory of arbitrary shape.