<i>Robots and Screw Theory: Applications of Kinematics and Statics to Robotics</i>

Abstract

Robots and Screw Theory: Applications of Kinematics and Statics to Robotics, by Joseph K. Davidson and Kenneth H. Hunt, Oxford University Press, 2004, Great Clarendon Street, Oxford, England. (ISBN 0-19-856245-4). REVIEWED BY GORDON R. PENNOCK1As stated in the preface, the goal of this book is two-fold: (i) to explore the underlying principles of kinematic geometry which are so important for an understanding of rigid body displacements and velocities in a robotic manipulator; and (ii) to explore the principles of the geometry of force systems in as much as they relate to the understanding of the kinematics. The book emphasizes important and long-established principles which provide the reader with a basis for a deeper understanding of the capabilities and the limitations of robot motion. The authors believe that this knowledge can be used effectively to design and control robotic manipulators. The key to the treatment on robotics presented in this book is the Screw, that geometric entity which underlies the mechanics of statics and first-order kinematics. The earliest references to screws can be traced back to the beginning of the 19th century when Poinsot (1806) established the concept that any system of forces applied to a rigid body can be reduced to a single force and a couple. Then Chasles (1832) stated that any rigid body displacement can be conceived as a rotation about a line accompanied by a translation along that line. This type of representation is canonical in form; moreover, it is subject to easy geometrical interpretation. Ball (1900) established a firm physical base for the mathematics of screws when he wrote his treatise on the small oscillations of a rigid body. Although the basis for screw theory in spatial kinematics was introduced almost two hundred years ago, the treatment presented in this text is well-worth reading. The two fundamental concepts in the theory of screws—that the instantaneous motion of a rigid body is a twisting motion about the instantaneous screw axis, and that a system of forces acting upon the rigid body is a wrench acting about a particular screw axis—are the underlying basis for the work in this book. This text builds upon the idea that the kinetostatics of serial and parallel robots is a valuable discipline. This concept was introduced for planar robot manipulators several years ago by Joseph Duffy in his book Statics and Kinematics with Applications to Robotics, published by Cambridge University Press (1996). The book was based solely on the concepts of classical geometry. The author was lamenting that the great developments in geometry of the last century and their application in mechanics have, for the most part, been forgotten or ignored by many researchers in the field of robotics. He attempted to correct this error with a rigorous study of instantaneous kinematics and statics applied to the field of robotics. The Davidson and Hunt text makes a significant step forward in applying geometry to the study of rigid body mechanics, in general, and robot manipulators, in particular. The text expands kinetostatics to spatial robots and integrates into two charts the detailed relationships between instantaneous kinematically equivalent serial and parallel manipulators. The charts are also adapted to parallel manipulators of reduced freedom (for example, those with translating platforms) in a way that leads to simple representations of their behavior. Since the authors are primarily concerned with the geometry of mechanical motion, the most general of which is spatial, it is natural that they employ the well-known theory of screws. The instantaneous screw is fundamental to rigid body motion. An infinitesimal displacement of a rigid body can be reduced to a single twist about a unique screw that has a certain pitch. Similarly, any system of forces and moments that act on the rigid body can be reduced to a single wrench which lies on a unique screw that has a certain pitch. The concept of