Synopses & Reviews
This volume provides a state of the art account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated logically into six parts describing the main themes: (i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms; (ii) redundant manipulators; (iii) kinematic and dynamic control in which the link between kinematics and the disciplines of dynamics and control is highlighted; (iv) parallel manipulators; (v) motion planning, touching on computational geometry; (vi) kinematics of mechanisms describing the closed kinematic chains. The volume contains a representative sample of the most modern techniques available for kinematics problems, including some novel techniques described for the first time in a book. It will be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.
Synopsis
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 numer ical type, but also of a symbolic 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 question s such as the number of solutions, whether real or complex, that a given problem can admit. Problems of this kind occur frequently in the analysis and synthesis of kinematic chains, when finite 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. What we mean by algebraic equations here is equations whereby the unknowns are numbers, as opposed to differen tial equations, where the unknowns are functions. The algebraic equations at hand can take on the form of multivariate polynomials or may involve trigonometric functions of unknown angles. Because of the nonlinear nature of the underlying kinematic models, purely numerical methods turn out to be too restrictive, for they involve iterative procedures whose convergence cannot, in general, be guaranteed. Additionally, when these methods converge, they do so to only isolated solu tions, and the question as to the number of solutions to expect still remains."
Table of Contents
Preface.
1. Kinematics Algorithms.
2. Redundant Manipulators.
3. Kinematic and Dynamic Control.
4. Parallel Manipulators.
5. Motion Planning.
6. Kinematics of Mechanisms.