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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.
Inhaltsverzeichnis
1 Kinematics Algorithms.- 1.1 Computations in Kinematics.- 1.2 Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigenproblem.- 1.3 On the Tangent-Half-Angle Substitution.- 1.4 Resultant Methods for the Inverse Kinematics Problem.- 2 Redundant Manipulators.- 2.1 Redundancy Resolution for an Eight-Axis Manipulator.- 2.2 A Mixed Numeric and Symbolic Approach to Redundant Manipulators.- 2.3 Computational Considerations on Kinematics Inversion of Multi-Link Redundant Robot Manipulators.- 2.4 On Finding the Set of Inverse Kinematic Solutions for Redundant Manipulators.- 2.5 The Self-Motion Manifolds of the N-Bar Mechanism.- 3 Kinematic and Dynamic Control.- 3.1 Feedforward Torque Computations with the Aid of Maple V.- 3.2 Nonlinear Control of Constrained Redundant Manipulators.- 3.3 Analysis of Mechanisms by the Dual Inertia Operator.- 4 Parallel Manipulators.- 4.1 Direct Kinematics in Analytical Form of a General Geometry 5-4 Fully-Parallel Manipulator.- 4.2 The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators.- 4.3 The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators.- 4.4 On the Representation of Rigid-Body Motions and its Application to Generalized Platform Manipulators.- 4.5 Algebraic-Geometry Tools for the Study of Kinematics of Parallel Manipulators.- 5 Motion Planning.- 5.1 Singularity Control for Simple Manipulators using 'PathEnergy'.- 5.2 An Investigation of Path Tracking Singularities for Planar 2R Manipulators.- 5.3 Robot Motions with Trajectory Interpolation and Overcorrection.- 5.4 Computational Geometry and Motion Approximation.- 6 Kinematics of Mechanisms.- 6.1 Forward Kinematics of a 3-DOF Variable-Geometry-Truss Manipulator.- 6.2 AnalyticalDetermination of the Intersections of Two Coupler-Point Curves Generated by Two Four-Bar Linkages.- 6.3 On Closed Form Solutions of Multiple-Loop Mechanisms.- 6.4 A Modular Method for Computational Kinematics.- 6.5 Synthesis for Rigid Body Guidance Using Polynomials.- 6.6 Designing Mechanisms for Workspace Fit.
Zusammenfassung
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.
