Mathematical model and evaluation of dynamic stability of industrial robot manipulator: Universal robot

Robot is an indispensable technology within the context of the Industrial 4.0 revolution, providing a wide range of applications in industry. The stability of a robot's manipulator is contingent upon its associated manipulator settings, hence influencing its overall quality. The assessment of stability has been examined in prior studies using a limited set of manipulator parameters, leading to a deficient comprehension of this phenomenon. In this study, a mathematical model of a flexible six-link manipulator is formulated using Lagrangian mechanics and various parameters. An innovative mathematical framework is developed to establish a correlation between stability and the motor acceleration and moment of inertia for the Universal Robot (UR5). Furthermore, extensive research has been conducted to examine the correlation between stiffness, damping, and deflection in the context of stability. In spite of this, fuzzy logic inference methods are employed to ascertain the relative significance of stiffness, damping, and deflection with regards to stability. Mathematical approaches are employed to validate the numerical values of several manipulator parameters. The findings of the study demonstrate that there is a positive correlation between motor acceleration and stability, indicating that as motor acceleration grows, stability also increases. Conversely, there is a negative correlation between stability and moment of inertia, suggesting that stability reduces as moment of inertia increases. In the case of stiffness, damping, and deflection, stiffness is the most important factor. When stiffness is high, stability is also high. However, when stiffness is minimal, stability is low. The implications of these findings are expected to have a positive impact on enhancing industrial productivity.