2DoF RRBot EoM

Developed at: Worcester Polytechnic Institute

Project date: October, 2023

GitHub URL: parth-20-07/2-DoF-Revolute-Revolute-robot-arm-Equation-of-Motion

Brief Introduction on Project

I worked on deriving the equation of motion by taking the derivatives of the Lagrangian Function. This method is called as Euler-Lagrange Method.

The Lagrange Equation uses the terms Kinetic and Potential Energy of the system. Where: \(LE = KE - PE\)

The Euler-Lagrangian Equations can be derived by taking a derivative of the Lagrangian Equations. Where,␍

\[ \frac{d}{dt}\frac{\partial L}{\partial \dot{q_{i}}} - \frac{\partial L}{\partial{q_{i}}}= u_{i} \]

This would result in an equation of form \(a\ddot{q} + b\dot{q} + c{q} + d = 0\). We solve for \(\ddot{q_{i}}\) which results in the equation of motion for the system. This system does not contain any form of input. Thus, \(u_{i} = 0\) for all joints.