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Singularities of Robot Mechanisms

Numerical Computation and Avoidance Path Planning

  • Book
  • © 2017


  • Presents mechanism singularities, with powerful numerical methods for their computation and avoidance in the general architecture case, solving two open, long-standing problems of robot kinematics
  • Toolbox of methods for exhaustively computing the singularities, determining accurate workspace maps, and planning safe motion paths between given configurations, for mechanisms of arbitrary architecture
  • A companion web page provides open access to implemented versions of the algorithms, input files for the study cases analyzed, and animated versions of many figures in the book

Part of the book series: Mechanisms and Machine Science (Mechan. Machine Science, volume 41)

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About this book

This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves. The theory can be put into practice as well: a companion web page gives open access to implementations of the algorithms and the corresponding input files. Using them, the reader can gain hands-on experience on the topic, or analyse new mechanisms beyond those examined in the text. Overall, the book contributes new tools for robot design, and constitutes a single reference source of knowledge that is otherwise dispersed in the literature.   

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Table of contents (7 chapters)


“The book is valuable from many points of view. One of them is the clear, systematic and synthetic characterization of singularities as an algebraic problem. Another is the abundant use of real-case examples and the care in the graphical display. Moreover, the authors' proposals for a novel numerical computation scheme of singularities and a singularity-free path planning scheme are worth noting.” (Gianni Ferretti, Mathematical Reviews, May 2017)

Authors and Affiliations

  • Kinematics and Robot Design, Institut de Robòtica i Informàtica Industrial (UPC-CSIC), Barcelona, Catalonia, Spain

    Oriol Bohigas, Montserrat Manubens, Lluís Ros

About the authors

Bibliographic Information

  • Book Title: Singularities of Robot Mechanisms

  • Book Subtitle: Numerical Computation and Avoidance Path Planning

  • Authors: Oriol Bohigas, Montserrat Manubens, Lluís Ros

  • Series Title: Mechanisms and Machine Science

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2017

  • Hardcover ISBN: 978-3-319-32920-8Published: 16 September 2016

  • Softcover ISBN: 978-3-319-81399-8Published: 12 June 2018

  • eBook ISBN: 978-3-319-32922-2Published: 08 September 2016

  • Series ISSN: 2211-0984

  • Series E-ISSN: 2211-0992

  • Edition Number: 1

  • Number of Pages: XXI, 184

  • Number of Illustrations: 29 b/w illustrations, 64 illustrations in colour

  • Topics: Robotics and Automation, Vibration, Dynamical Systems, Control, Numerical Analysis, Mathematical and Computational Engineering

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