Mathematical Analysis and SolidWorks-Based 3D Simulation of a Double-Pendulum Robotic Arm

The non-linear dynamics of robotic arm manipulators impose considerable barriers to control and stabilization. The proposed study will help to close the gap between theory and applicationin physics by comparing mathematical modeling with simulations of physical 3D mechanical systems of a manipulator working as a simple double pendulum. The study uses SolidWorks to design the 3D of the first stage and MATLAB to simulate the changes in physical parameters on oscillatory motion. The method included the derivation of the Lagrange equations of a 2-DoF system, creation of the MATLAB/Simulink blocks in mathematical analysis, and execution of a simulation using MATLAB/Simscape Multibody in the 3D visualization. Four models of robots were analyzed, and the numerical results indicated that sine waves were always generated by the mathematical simulation. The sine wave peaked at 57.9 in the case of Franka Emika. By comparison, the 3D model simulation of the same reached the highest point of 56.9 at a definite time delay, highlighting the influence of physical models. The most important results showed that mathematical models are more appropriate for deriving a transfer function but the behavior of robots with similar dimensions and weights was closed when 3D simulation was used. An effective control parameter development of robotic hardware is presented by this dual-modeling methodology, which enables all theoretical designs that are developed to be tested against mechanical realities.