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Chapter 3

Robot Dynamics

This chapter provides the background required for the study of robot
manipulator control The arm dynamical equations are derived both in the
second-order differential equation formulation and several state-variable
formulations. Some important properties of the dynamics are introduced. We
show how to include the dynamics of the arm actuators, which may be electric
or hydraulic motors.

3.1 Introduction

Robotics is a complex field involving many diverse disciplines, such as physics,
properties of materials, statics and dynamics, electronics, control theory, vision,
signal processing, computer programming, and manufacturing. In this book
our main interest is control of robot manipulators. The purpose of this chapter
is to study the dynamical equations needed for the study of robot control.
For those desiring a background in control theory, Chapter 2 is provided.
For those desiring a background in the basics of robot manipulators, in Appendix
A we examine the geometric structure of robot manipulators, covering basic
manipulator configurations, kinematics, and inverse kinematics. There we
review as well the manipulator Jacobian, which is essential for control in
Cartesian or workspace coordinates, where the desired trajectories of the arm
are usually specified to begin with.
The robot dynamics are derived in Section 3.2. Lagrangian mechanics are
used in this derivation. In Section 3.3 we review some fundamental properties
of the arm dynamical equation that are essential in subsequent chapters for
the derivation of robot control schemes. These are summarized in Table 3.3.1,
which is referred to throughout the text.
The arm dynamics in Section 3.2 are in the form of a second-order vector

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Copyright © 2004 by Marcel Dekker, Inc.