Fundamentals of Rigid-Body Mechanics

Abstract

The purpose of this chapter is to lay down the foundations of the kineto-statics and dynamics of rigid bodies, as needed in the study of multibody mechanical systems. With this background, we study the kinetostatics and dynamics of robotic manipulators of the serial type in Chapters 4 and 6, respectively, while devoting Chapter 5 to the study of trajectory planning. The latter requires, additionally, the background of Chapter 4. A special feature of this chapter is the study of the relations between the angular velocity of a rigid body and the time-rates of change of the various sets of rotation invariants introduced in Chapter 2. Similar relations between the angular acceleration and the second time-derivatives of the rotation invariants are also recalled, the corresponding derivations being outlined in Appendix A.