Multiloop Kinematic Chains

  • M. Hiller
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 360)


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.


Constraint Equation Multibody System Kinematic Chain Nonholonomic System Revolute Joint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • M. Hiller
    • 1
  1. 1.G. Mercator University of DuisburgDuisburgGermany

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