Table of Contents
The Newton-Euler formulation is a fundamental method used in robotics to analyze the motion of robotic links and joints. It combines Newton’s laws of motion with Euler’s equations to compute forces and torques acting on each part of a robot. This step-by-step guide provides an overview of applying this formulation for effective robot motion analysis.
Understanding the Newton-Euler Formulation
The Newton-Euler method involves two main processes: forward recursion to determine velocities and accelerations, and backward recursion to compute forces and torques. It is particularly useful for serial manipulators with multiple links.
Step 1: Define Robot Parameters
Identify the robot’s link parameters, including link lengths, masses, centers of mass, and moments of inertia. Establish coordinate frames for each link and define joint variables such as angles and velocities.
Step 2: Forward Recursion
Calculate the angular velocities and accelerations of each link starting from the base to the end-effector. Determine linear velocities and accelerations of the centers of mass using recursive equations.
Step 3: Backward Recursion
Compute the forces and torques acting on each link, beginning from the end-effector back to the base. Use Newton’s second law for linear motion and Euler’s equations for rotational motion.
Step 4: Calculate Joint Torques and Forces
Determine the required joint torques and forces to produce the desired motion. These are obtained from the recursive calculations and account for gravity, inertia, and external forces.
- Define link parameters
- Perform forward recursion
- Perform backward recursion
- Compute joint torques and forces