CHAPTER 2
 THE INVERSE KINEMATICS PROBLEM



 Notation and Mathematical Preliminaries The DH Parameters

 A robot manipulator is modelled as an open kinematic chain of rigid bodies (links) connected by joints. A

reference frame is assigned to each link along the chain starting with the base frame F0, assigned to the fixed link, up to the end effector frame Fn, for a manipulator with n degrees of freedom (DOF). The position and orientation of frame Fi=(xi, Yi, zi), with respect to the preceding frame Fi_, are entirely described by the four DH-parameters di, 8Gi, ai and ai (Denavit and Hartenberg 1955). These parameters are illustrated in Figure 2.1 and defined as: di = distance between the common normal to axes zi-1 and z

 and the common normal to zi and zi+1 measured along

 axis zi.

i = the angle of rotation about zi so that xi becomes

 parallel to xi-1 when ei = 0.

a = the length of the common normal to axes zi-1 and zi. ai = the angle of rotation about xi so that zi becomes

 parallel to zi-1 when ai = 0.

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