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Kinematics and Dynamics of Multi-Body Systems pp 75–165Cite as

Multiloop Kinematic Chains

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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 360))

Abstract

The purpose of this chapter is to lay down a methodology for treating the kinematics of multiple loop mechanical systems in an efficient and compact manner. As the kinematics is at the core of any dynamic formulation, this treatment will also provide a suitable means for attaining high-speed dynamic models for complex systems containing several multibody loops. The method basically consists of gradually decomposing a system of highly coupled kinematic constraint equations into hierarchical layers that can be analyzed independently. The core of the constraint equations is hereby formed by the relative kinematics, i.e., the determination of the dependent joint variables as functions of the independent ones. As will be shown, the relative kinematics can be represented as a network of linearly interconnected kinematic transformers, which mirror the individual independent loops. From this network, it is easy to determine the sequence in which the system has to be traversed in order to obtain closed-form solutions, if possible. Regarding the treatment of single multibody loops, methods for mapping the closure equations of the individual multibody loops to a univariate polynomials are described, together with the conditions under which the so established polynomials are of minimal degree. Furthermore, the application of the developed ideas to nonholonomic systems is discussed. All procedures are illustrated by several industrial examples of varying complexity.

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Author information

Authors and Affiliations

  1. G. Mercator University of Duisburg, Duisburg, Germany

    M. Hiller

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  1. M. Hiller
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Editor information

Editors and Affiliations

  1. McGill University, Canada

    J. Angeles

  2. Gerhard Mercator University, Germany

    A. Kecskeméthy

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© 1995 Springer-Verlag Wien

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Hiller, M. (1995). Multiloop Kinematic Chains. In: Angeles, J., Kecskeméthy, A. (eds) Kinematics and Dynamics of Multi-Body Systems. CISM International Centre for Mechanical Sciences, vol 360. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4362-9_4

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  • DOI: https://doi.org/10.1007/978-3-7091-4362-9_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82731-4

  • Online ISBN: 978-3-7091-4362-9

  • eBook Packages: Springer Book Archive

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