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Intrinsic joint kinematic planning. I: Reassessing the Listing’s law constraint in the control of three-dimensional arm movements

  • D. G. LiebermannEmail author
  • A. Biess
  • J. Friedman
  • C. C. A. M. Gielen
  • T. Flash
Research Article

Abstract

This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing’s law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing’s constraint, the hand paths may be predicted. Four individuals performed ‘extended arm’, ‘radial’, ‘frontal plane’, and ‘random mixed’ movements to visual targets to test Listing’s law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders’ and Listing’s laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between ≈1.7° and 4.7° for the rotation vectors of the upper arm segment and ≈2.6° and 7.5° for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing’s law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.

Keywords

Planning arm posture Joint kinematics Listing’s law 

Notes

Acknowledgments

We gratefully acknowledge the help of Dr. L. Zuk from the University of Tel Aviv and the support of Mrs. E. Nuri. The research was supported in part by the Israeli Ministry of Science and by the Moross Vision and Robotics Laboratory, Weizmann Institute of Science, Israel. Tamar Flash is an incumbent of the Dr. Hymie Moross Professorial Chair.

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • D. G. Liebermann
    • 1
    • 2
    Email author
  • A. Biess
    • 2
  • J. Friedman
    • 2
  • C. C. A. M. Gielen
    • 3
  • T. Flash
    • 2
  1. 1.Department of Physical Therapy, Sackler Faculty of MedicineTel-Aviv UniversityRamat AvivIsrael
  2. 2.Department of Applied Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  3. 3.Department of Medical Physics and BiophysicsUniversity of NijmegenNijmegenThe Netherlands

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