FINITE ELEMENT BASED APPROACH TO MATHEMATICAL MODELING OF FLEXIBLE 3DOF ROBOT ARM

This study presents a finite element-based approach to the mathematical modeling and dynamic analysis of a flexible three-degree-of-freedom (3DoF) robot arm under varying boundary conditions. The motivation for this research stems from the increasing demand for lightweight and flexible robotic manipulators in modern engineering applications, where traditional rigid-body assumptions fail to accurately capture structural behavior. Using the Finite Element Method, the flexible links of the robot arm were discritize and modeled to account for distributed mass, stiffness, and damping properties. Two fundamental boundary condition spinned-free and clamped-free were considered to evaluate their influence on system dynamics. Numerical simulations were conducted in a Python-based environment, where the system’s time-domain and frequency-domain responses were analyzed through displacement, velocity, acceleration, phase trajectory, and frequency spectrum plots. The results reveal that the pinned-free configuration exhibits larger displacement amplitudes, lower natural frequencies, and prolonged oscillations due to reduced stiffness at the base. In contrast, the clamped-free configuration demonstrates enhanced stiffness, higher natural frequencies, and faster decay of oscillations, leading to improved stability and control performance. The comparative analysis highlights the critical role of boundary conditions in determining the dynamic behavior of flexible robotic systems. The findings of this study provide valuable insights for the design, modeling, and control of flexible manipulators, particularly in applications requiring high precision and vibration suppression. Ultimately, the research contributes to advancing the development of efficient and reliable flexible robotic systems using robust mathematical modeling techniques.