MATHEMATICAL MODEL FOR DETERMINATION OF TOOL DEVIATIONS FROM THE DESIRED TRAJECTORY IN ROBOTIC MACHINING CONSIDERING THE ROBOT'S STIFFNESS

The article examines the advantages and disadvantages of using industrial robots to control a tool during machining operations. It is concluded that the main drawback of robots is their low stiffness. A mathematical model has been developed to calculate the deviation of the tool from the desired trajectory during robotic machining. To predict deviations, the proposed model uses the virtual joint method, which provides a reasonable compromise between modeling accuracy and computational complexity. The model is implemented in Matlab using the Robotics System Toolbox and a URDF description of the industrial robot. It takes into account external forces and torques, as well as dynamic parameters such as velocity and acceleration of the robot’s links. Tool deviations are calculated in both joint and Cartesian spaces. The article presents the results of model testing on a sample tool trajectory using the ABB IRB 120 industrial robot. Based on the modeling results, it is concluded that the robot’s configuration significantly affects the tool positioning accuracy. It is shown that even in the absence of external loads, an unsuccessful choice of robot configuration can cause significant tool deviations due to gravity. The developed model can be used as a tool to improve the accuracy of robotic machining and to optimize production process parameters.