Spatial Multibody Systems

  • John M. Hansen
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 511)


As for the planar case a set of coordinates are needed to describe position and rotation of the bodies in a spatial mechanical system in order to describe the kinematics. For the translational coordinates that is fairly straight forward, as it merely requires an extra Cartesian coordinate, z. Therefore the position vector r i for a body i becomes
$$ r_i = \left\{ {\begin{array}{*{20}c} x \\ y \\ z \\ \end{array} } \right\}_i $$
For the rotational parameters, however, it is more complex. Since rotation around more than one axis is not commutative as will be shown below; it is not sufficient to add the two additional angles around which the body can rotate to the vector of coordinates.


Angular Velocity Jacobian Matrix Local Coordinate System Planar Case Global Coordinate System 
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  1. Haug, E.J. Computer-Aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon, Ohio, 1989.Google Scholar
  2. Nikravesh, P. E. Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, New Jersey, 1988.Google Scholar
  3. Pedersen, N. L. and Pedersen, M. L. Dynamisk analyse af stive og fleksible 3d-mekanismer. Master thesis, Technical University of Denmark, Lyngby, 1995. (In Danish).Google Scholar

Copyright information

© CISM, Udine 2009

Authors and Affiliations

  • John M. Hansen
    • 1
  1. 1.MAN Diesel SECopenhagen SVDenmark

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