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Computational Kinematics

  • Book
  • © 1993

Overview

Editors:
  1. Jorge Angeles

    1. Department of Mechanical Engineering, McGill University, Montreal, Canada

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  2. Günter Hommel

    1. Department of Computer Science, Technical University of Berlin, Berlin, Germany

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  3. Peter Kovács

    1. Department of Computer Science, Technical University of Berlin, Berlin, Germany

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Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 28)

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-ix
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  2. Kinematics Algorithms

    1. Front Matter

      Pages 1-1
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    2. Computations in Kinematics

      • Bernard Roth
      Pages 3-14

    3. Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigenproblem

      • Masoud Ghazvini
      Pages 15-26

    4. On the Tangent-Half-Angle Substitution

      • Peter Kovács, Günter Hommel
      Pages 27-39

    5. Resultant Methods for the Inverse Kinematics Problem

      • Jürgen Weiss
      Pages 41-52

  4. Kinematic and Dynamic Control

    1. Front Matter

      Pages 107-107
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    2. Feedforward Torque Computations with the Aid of Maple V

      • Thomas H. Connolly, Friedrich Pfeiffer
      Pages 109-117

    3. Nonlinear Control of Constrained Redundant Manipulators

      • Christoph Woernle
      Pages 119-128

    4. Analysis of Mechanisms by the Dual Inertia Operator

      • M. Shoham, V. Brodsky
      Pages 129-138

  5. Parallel Manipulators

    1. Front Matter

      Pages 139-139
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    2. Direct Kinematics in Analytical Form of a General Geometry 5–4 Fully-Parallel Manipulator

      • Carlo Innocenti, Vincenzo Parenti-Castelli
      Pages 141-152

    3. The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators

      • H. R. Mohammadi Daniali, P. J. Zsombor-Murray, J. Angeles
      Pages 153-164

    4. The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators

      • K. E. Zanganeh, J. Angeles
      Pages 165-173
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mechanical Engineering, McGill University, Montreal, Canada

    Jorge Angeles

  • Department of Computer Science, Technical University of Berlin, Berlin, Germany

    Günter Hommel, Peter Kovács

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