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

Biol Cybern. 1987;57(4-5):257-74. doi: 10.1007/BF00338819.


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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Arm / physiology*
  • Biomechanical Phenomena
  • Elasticity
  • Hand / physiology*
  • Humans
  • Joints / physiology*
  • Mathematics
  • Models, Neurological
  • Movement
  • Muscles / innervation*
  • Muscles / physiology