Solving a mechanical system of a multi-arm pendulum

Abstract

The multi-arm pendulum system is a complex mechanical system consisting of interconnected pendulum arms. Understanding the dynamics and behavior of such systems is essential for various applications in physics, engineering, and robotics. This project aims to investigate the multi-arm pendulum system by obtaining Lagrangian functions, solving the equations of motion, and exploring potential applications.

The objectives of the project are as follows:

To obtain Lagrangian functions for both simple and multi-arm pendulum systems, capturing the interrelationships between the system's variables. To solve the equation(s) of motion for the multi-arm pendulum system using analytical and numerical methods, considering the complexity and non-linearity of the system. To establish the relation between the simple and multi-arm pendula, gaining insights into their dynamics and identifying similarities and differences. To investigate potential applications of the multi-arm pendulum system in fields such as robotics, biomechanics, and motion control. The methodology involves deriving the Lagrangian functions for the pendulum systems, solving the equations of motion using numerical techniques like the Runge-Kutta 4th order method, and analyzing the results. MATLAB, a powerful scientific computing library, is used for implementing the numerical solver and visualizing the system's motion.

The project's scope focuses on idealized pendulum systems without considering factors like damping, friction, and non-ideal constraints. Data collection involves simulations and numerical computations. The results are analyzed, and comparisons are made between the multi-arm and simple pendulum systems to gain insights into their dynamics.

The outcomes of the project contribute to a deeper understanding of multi-arm pendulum systems and their relation to simple pendula. This knowledge can be applied in various fields, including robotics, motion control systems, and mechanical design. The findings also highlight the limitations and challenges associated with analyzing complex mechanical systems.