Robot Modeling and Control, 2nd Edition

CHAPTER 3FORWARD KINEMATICS

The problem of manipulator kinematics is to describe the motion of a manipulator without consideration of the forces and torques causing the motion. The kinematic description is therefore a geometric one. In this chapter we consider the forward kinematics problem for serial link manipulators, which is to determine the position and orientation of the end effector given the values for the joint variables of the robot. This problem is easily solved by attaching coordinate frames to each link of the robot and expressing the relationships among these frames as homogeneous transformations. We use a systematic procedure, known as the Denavit–Hartenberg convention, to attach these coordinate frames to the robot. The position and orientation of the robot end effector is then reduced to a matrix multiplication of homogeneous transformations. We give examples of this procedure for several of the standard configurations that we introduced in Chapter 1.

In subsequent chapters we will consider the problems of velocity kinematics and inverse kinematics. The former problem is to determine the relation between the end-effector velocity and the joint velocities whereas the inverse kinematics problem is to determine the joint variables given the end-effector position and orientation.

3.1 Kinematic Chains

As described in Chapter 1, a robot manipulator is composed of a set of links connected together by joints. The joints can either be very simple, such as a revolute ...