Torsional Stiffness Model of an Industrial Robotic Joint Using Fractal Theory

Abstract

It is known that mechanical connections have great influence on the dynamic characteristic of the assembly. In existing methods, the torsional stiffness of the robotic joint is calculated only considering the stiffness of components of the system, which largely reduces the prediction accuracy of the joint stiffness. In the paper, to predict the joint stiffness more accurately, a model is proposed considering influences of the stiffness of all connections existed in a joint system. The normal and tangential stiffness of the contact surface of each connection are calculated by combining the equilibrium analysis of the force and the fractal theory. Then the total stiffness of one robotic joint can be modelled by putting the torsional stiffness of all connections and that of the RV reducer and gear pair in parallel. To verify the proposed model, its simulation result is compared to the stiffness based on the previous technique without considering the influence of connections. The comparison result shows that the proposed model can improve the stiffness-prediction accuracy. This study can be extended to the stiffness modeling of other joint systems and provides a theoretical basis for the dynamic analysis of the robotic system.