Biological Cybernetics

, Volume 57, Issue 4–5, pp 257–274 | Cite as

The control of hand equilibrium trajectories in multi-joint arm movements

  • T. Flash


According to the equilibrium trajectory hypothesis, multi-joint arm movements are achieved by gradually shifting the hand equilibrium positions defined by the neuromuscular activity. The magnitude of the force exerted on the arm, at any time, depends on the difference between the actual and equilibrium hand positions and the stiffness and viscosity about the equilibrium position. The purpose of this paper is to test the validity and implications of this hypothesis in the context of reaching movements. A mathematical description of the behavior of an arm tracking the equilibrium trajectory was developed and implemented in computer simulations. The joint stiffness parameters used in these simulations were derived from experimentally measured static stiffness values. The kinematic features of hand equilibrium trajectories which were derived from measured planar horizontal movements gave rise to the suggestion that the generation of reaching movements involves explicit planning of spatially and temporally invariant hand equilibrium trajectories. This hypothesis was tested by simulating actual arm movements based on hypothetical equilibrium trajectories. The success of the predicted behavior in capturing both the qualitative features and the quantitative kinematic details of the measured movements supports the equilibrium trajectory hypothesis. The control strategy suggested here may allow the motor system to avoid some of the complicated computational problems associated with multi-joint arm movements.


Equilibrium Position Hand Position Joint Stiffness Stiffness Parameter Kinematic Feature 
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 1987

Authors and Affiliations

  • T. Flash
    • 1
    • 2
  1. 1.Department of Brain and Cognitive SciencesMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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