This paper presents a new method, a fast prediction method based on the Cartesian stiffness model and equivalent spring stiffness (FPM-CSES), to calculate displacement errors of deformation caused by low stiffness for industrial robot. First, the Cartesian stiffness model based on the Jacobian matrix was established for a robot, and then the displacement error model of deformations caused by external force was established based on Cartesian stiffness. Second, the transmission system of the robot's joint was analyzed, and an equivalent method for joint stiffness was presented based on a series spring system. Meanwhile, the stiffness of the key components including the servo motor, harmonic reducer, and timing belt was deduced in detail. Finally, a compared simulation and a measurement experiment were conducted on a 6-joint series robot. It was found that the FPM-CSES could calculate any configuration among the robot's workspace. Compared with the finite element analysis (FEA) method, the presented method is feasible and more efficient. The experimental results showed that the prediction accuracy of the FPM-CSES is rather high, with an average rate of more than 83.72%. Hence, the prediction method presented in this study is simple, fast, and reliable, and could be used to predict and analyze the displacement errors caused by the cutting force, and provide the basis for trajectory planning and error compensation, enhancing the robot's machining performance.
Keywords: Jacobian matrix; finite element analysis; industrial robot; joint stiffness; stiffness model.