The aim of this book is to provide an account of the state of the art in Com putational Kinematics. We understand here under this term that branch of kinematics research involving intensive computations not only of the nu merical type, but also of symbolic as well as geometric nature. Research in kinematics over the last decade has been remarkably ori ented towards the computational aspects of kinematics problems. In fact, this work has been prompted by the need to answer fundamental questions such as the number of solutions, whether real or complex, that a given problem can admit as well as computational algorithms to support geo metric analysis. Problems of the first kind occur frequently in the analysis and synthesis of kinematic chains, when fine displacements are considered. The associated models, that are derived from kinematic relations known as closure equations, lead to systems of nonlinear algebraic equations in the variables or parameters sought. The algebraic equations at hand can take the form of multivariate polynomials or may involve trigonometric functions of unknown angles.

Parallel robots are closed-loop mechanisms presenting very good performances in terms of accuracy, velocity, rigidity and ability to manipulate large loads. They have been used in a large number of applications ranging from astronomy to flight simulators and are becoming increasingly popular in the field of machine-tool industry. This book presents a complete synthesis of the latest results on the possible mechanical architectures, analysis and synthesis of this type of mechanism. It is intended to be used by students (with over 150 exercises and numerous internet addresses), researchers (with over 650 references and anonymous ftp access to the code of some algorithms presented in this book) and engineers (for which practical results, mistakes to avoid, and applications are presented). Since the publication of the first edition (2000) there has been an impressive increase in terms of study and use of this kind of structure that are reported in this book. This second edition has been completely overhauled. The initial chapter on kinematics has been split into Inverse Kinematics and Direct Kinematics. A new chapter on calibration was added. The other chapters have also been rewritten to a large extent. The reference section has been updated to include around 45% new works that appeared after the first edition.

Parallel robots are closed-loop mechanisms presenting very good performances in terms of accuracy, velocity, rigidity and ability to manipulate large loads. They have been used in a large number of applications ranging from astronomy to flight simulators and are becoming increasingly popular in the field of machine-tool industry. This book presents a complete synthesis of the latest results on the possible mechanical architectures, analysis and synthesis of this type of mechanism. It is intended to be used by students (with over 150 exercises and numerous internet addresses), researchers (with over 650 references and anonymous ftp access to the code of some algorithms presented in this book) and engineers (for which practical results, mistakes to avoid, and applications are presented).

Since the publication of the first edition (2000) there has been an impressive increase in terms of study and use of this kind of structure that are reported in this book. This second edition has been completely overhauled. The initial chapter on kinematics has been split into Inverse Kinematics and Direct Kinematics. A new chapter on calibration was added. The other chapters have also been rewritten to a large extent. The reference section has been updated to include around 45% new works that appeared after the first edition.

The trends and progress attained in computational kinematics over a broad class of problems are grouped into six parts describing the main themes: kinematics algorithms, discussing kinematics problems in light of their solution algorithms; kinematics of mechanisms, studying problems related to specific mechanisms; singularities; workspace, discussing the determination of the workspace of given mechanisms; parallel manipulators; and motion and grasp planning, touching on computational geometry. The volume contains a representative sample of the most modern techniques available for kinetics problems, including techniques based on advances in algebraic geometry. Researchers, graduate students and practising engineers in work relating to kinematics, robotics, machine design and computer science should find this work useful.