Robot Modeling and Control, 2nd Edition

CHAPTER 6DYNAMICS

This chapter deals with the dynamics of robot manipulators. Whereas the kinematic equations describe the motion of the robot without consideration of the forces and torques producing the motion, the dynamic equations explicitly describe the relationship between force and motion. The equations of motion are important to consider in the design of robots, in simulation and animation of robot motion, and in the design of control algorithms. We introduce the so-called Euler–Lagrange equations, which describe the evolution of a mechanical system subject to holonomic constraints (this term is defined later on). To motivate the Euler–Lagrange approach we begin with a simple derivation of these equations from Newton’s second law for a one-degree-of-freedom system. We then derive the Euler–Lagrange equations from the principle of virtual work in the general case.

In order to determine the Euler-Lagrange equations in a specific situation, one has to form the Lagrangian of the system, which is the difference between the kinetic energy and the potential energy; we show how to do this in several commonly encountered situations. We then derive the dynamic equations of several example robotic manipulators, including a two-link Cartesian robot, a two-link planar robot, and a two-link robot with remotely driven joints.

We also discuss several important properties of the Euler–Lagrange equations that can be exploited to design and analyze feedback control algorithms. Among these ...