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Application of motor algebra to the analysis of human arm movements

Published online by Cambridge University Press:  01 July 2008

Sigal Berman ,
Dario G. Liebermann  and
Tamar Flash
Sigal Berman*
Affiliation:
Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
Dario G. Liebermann
Affiliation:
Department of Physical Therapy, Tel-Aviv University, Ramat-Aviv, Israel
Tamar Flash
Affiliation:
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
*
*Corresponding author. E-mail: sigalbe@bgu.ac.il
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Summary

Motor algebra, a 4D degenerate geometric algebra, offers a rigorous yet simple representation of the 3D velocity of a rigid body. Using this representation, we study 3D extended arm pointing and reaching movements. We analyze the choice of arm orientation about the vector connecting the shoulder and the wrist, in cases for which this orientation is not prescribed by the task. Our findings show that the changes in this orientation throughout the movement were very small, possibly indicating an underlying motion planning strategy. We additionally examine the decomposition of movements into submovements and reconstruct the motion by assuming superposition of the velocity profiles of the underlying submovements by analyzing both the translational and rotational components of the 3D spatial velocity. This movement decomposition method reveals a larger number of submovement than is found using previously applied submovement extraction methods that are based only on the analysis of the hand tangential velocity. The reconstructed velocity profiles and final orientations are relatively close to the actual values, indicating that single-axis submovements may be the basic building blocks underlying 3D movement construction.

Keywords

Geometric algebraMotor algebraArm motionSpatial velocity
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 435 - 451
Copyright
Copyright © Cambridge University Press 2007

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