This book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw algebra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathematics related to robot theory, design, control and application. All articles in the book were reported at the seventh international symposium on Advances in Robot Kinematics that was organised in June 2000 in the beautiful ancient Mediterranean town of Piran in Slovenia. The preceding symposia of the series took place in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996), and Salzburg (1998).

This book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw algebra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathematics related to robot theory, design, control and application. All articles in the book were reported at the seventh international symposium on Advances in Robot Kinematics that was organised in June 2000 in the beautiful ancient Mediterranean town of Piran in Slovenia. The preceding symposia of the series took place in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996), and Salzburg (1998).

"I do not think at all that I am able to present here any procedure of investiga tion that was not perceived long ago by all men of talent; and I do not promise at all that you can find here anything_ quite new of this kind. But I shall take pains to state in clear words the pules and ways of investigation which are followed by ahle men, who in most cases are not even conscious of foZlow ing them. Although I am free from illusion that I shall fully succeed even in doing this, I still hope that the little that is present here may please some people and have some application afterwards. " Bernard Bolzano (Wissenschaftslehre, 1929) The following book results from aseries of lectures on the mathematical theory of turbulence delivered by the author at the Purdue University School of Aeronautics and Astronautics during the past several years, and represents, in fact, a comprehensive account of the author's work with his graduate students in this field. It was my aim in writing this book to give to engineers and scientists a mathematical feeling for a subject, which because of its nonlinear character has resisted mathematical analysis for many years. On account vii i of its refractory nature this subject was categorized as one of seven "elementary catastrophes." The material presented here is designed for a first graduate course in turbulence. The complete course has been taught in one semester."