The basis of a simple synergy: Reconstruction of joint equilibrium trajectories during unrestrained arm movements

Mark L. Latash, Alexander S. Aruin, Vladimir M. Zatsiorsky

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36 Scopus citations


The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the elbow and of the wrist during fast voluntary movements in one of the joints. Natural movement variability was used as the source of perturbations that are necessary to reconstruct ETs based on a series of trials at the same motor task. Time patterns of muscle torques were calculated using the inverse dynamics technique. A second-order linear model was used to calculate the instantaneous position of the joint compliant characteristic at different times during the movement. ETs in the focal joint were N-shaped, similar to ETs described earlier for single-joint movements. ETs in the non-focal joint represented a single oscillatory cycle whose peaks were timed similarly to the peaks of the N-shaped ETs in the focal joint. Peak-to-peak ET amplitude in the wrist during elbow movements could be of a similar amplitude or even bigger than peak-to-peak ET amplitude in the elbow while the actual trajectory in the wrist was an irregular, low-amplitude flapping, and the actual trajectory in the elbow was a typical, sigmoid curve. An explicit relation among control variables to the two joints is suggested as the foundation of a simple synergy whose purpose is to preserve control over the trajectory of the limb's endpoint in the presence of joint coupling.

Original languageEnglish (US)
Pages (from-to)3-30
Number of pages28
JournalHuman Movement Science
Issue number1
StatePublished - Feb 1999

All Science Journal Classification (ASJC) codes

  • Biophysics
  • Orthopedics and Sports Medicine
  • Experimental and Cognitive Psychology


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