Closed-Loop Vector Formulation in Euler's Complex Numbers for Multi-Loop Planar Mechanisms With N-bars: A Novel Modeling Approach and Algorithm

This paper presents a novel iterative algorithm incorporated in a user-friendly GUI for modeling the kinematics of multiple looped N-bar closed-loop mechanisms. Past research works have used custom coding or expensive commercial software to analyze the mechanisms of specific applications. The proposed algorithm focuses on kinematics and offers a quick, easy-to-use, cost-effective solution to analyze a wide range of generic mechanisms, reducing the need for custom coding and lowering computational costs. The algorithm employs algebraic equations, such as solving complex closed-loop vector equations using the Euler form of complex numbers, to simulate and derive the unknowns necessary to characterise any generic closed-loop mechanism. The Python code implemented in the algorithm adapts to various scenarios by utilising available information on the position, velocity, and acceleration variables of the mechanisms. The simulation tool can display real-time color contour plots (RGB color scale) for linear and angular velocities and accelerations, simulate mechanisms with multiple loops and switch configurations, and find inverse mechanisms. The approach for solving multiple loop problems and the algorithm utilized to solve the configurations, methods, equations used and GUI features implementation are all described in this study. The case study considered for a four-bar mechanism indicates a strong agreement between the results obtained from the proposed kinematics-based simulator and ANSYS software. These results demonstrate the simulator's effectiveness in providing low-cost and user-friendly simulation results for various generic mechanisms involving multiple interconnected loops.