Skip to main content
Log in

Theoretical Analysis of the Force and Position Synergies in Two-Joint Movements

  • Published:
Neurophysiology Aims and scope


A theoretical approach is proposed to define the force and position singular points (FSPs and PSPs) in the circular, ellipsoidal, and linear planar two-joint movements produced under steady loadings directed along the movement traces. The FSPs coincide with changes in the direction of the force moments acting around the joints; the PSPs show the locations of the extrema at the joint angle trajectories. The force synergy (defined by the location of FSPs) provides a strong influence on the activation synergy; the latter is largely described by correlations between the activities recorded from the muscles participating in the movement. The position synergy (defined by the location of PSPs) is responsible for a hysteresis-related modulation of the activation synergy. Geometrical procedures are proposed to define positions of the FSPs and PSPs along various movement traces; this can provide a general description of the force and position synergies for the movements. The force synergies in the circular movements cover four sectors with diverse loading combinations of the flexor and extensor muscles belonging to different joints. The variability of the synergy effects for changes in the size and position of the circular trajectories is analyzed; the synergy patterns are also considered for ellipsoidal and linear movement traces. A Force Feedback Control Hypothesis is proposed; it allows one to explain the decrease in the number of controlled variables during real multi-joint movements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. M. Santello and J. F. Soechting, “Force synergies for multifingered grasping,” Exp. Brain Res., 133, 457-467 (2000).

    Article  CAS  PubMed  Google Scholar 

  2. P. H. Thakur, A. J. Bastian, and S. S. Hsiao, “Multidigit movement synergies of the human hand in an unconstrained haptic exploration task,” J. Neurosci., 28, 1271-1281 (2008).

    Article  CAS  PubMed  Google Scholar 

  3. I. V. Grinyagin, E. V. Biryukova, and M. A. Maier, “Kinematic and dynamic synergies of human precisiongrip movements,” J. Neurophysiol., 94, 2284-2294 (2005).

    Article  CAS  PubMed  Google Scholar 

  4. J. K. Shim, H. Olafsdottir, V. M. Zatsiorsky, and M. L. Latash, “The emergence and disappearance of multi-digit synergies during force-production tasks,” Exp. Brain Res., 164, 260-270 (2005).

    Article  PubMed  PubMed Central  Google Scholar 

  5. A. W. Hooke, S. Karol, J. Park, et al., “Handwriting: three-dimensional kinetic synergies in circle drawing movements,” Motor Control, 16, 329-352 (2012).

    Article  PubMed  Google Scholar 

  6. C. Castellini and P. van der Smagt, “Evidence of muscle synergies during human grasping,” Biol. Cybern., 107, 233-245 (2013).

    Article  PubMed  Google Scholar 

  7. M. L. Latash, J. P. Scholz, and G. Schoner, “Toward a new theory of motor synergies,” Motor Control, 11, 276-308 (2007).

    Article  PubMed  Google Scholar 

  8. B. Poston, A. Danna-Dos Santos, M. Jesunathadas, et al., “Force-independent distribution of correlated neural inputs to hand muscles during three-digit grasping,” J. Neurophysiol., 104, 1141-1154 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  9. A. V. Lehedza, A. V. Gorkovenko, I. V. Vereshchaka, et al., “Comparative analysis of electromyographic muscle activity of the human hand during cyclic turns of isometric effort vector of wrist in opposite directions,” Fiziol. Zh., 61, No. 2, 3-14 (2015).

    CAS  PubMed  Google Scholar 

  10. T. Tomiak, A. V. Gorkovenko, A. N. Tal’nov, et al., “The averaged EMGs recorded from the arm muscles during bimanual “rowing” movements,” Front. Physiol., 6, No. 349, doi: 10.3389/fphys.2015.00349 (2015).

  11. T. Tomiak, T. I. Abramovych, A. V. Gorkovenko, et al., “The movement- and load-dependent differences in the EMG patterns of the human arm muscles during twojoint movements (a preliminary study),” Front. Physiol., 7, No. 218, doi: 10.3389/fphys.2016.00218 (2016).

  12. P. D. Neilson, M. D. Neilson, and R. T. Bye, “A Riemannian geometry theory of human movement: The geodesic synergy hypothesis,” Human. Mov. Sci., 44, 42-72 (2015).

    Article  Google Scholar 

  13. A. I. Kostyukov, “Muscle hysteresis and movement control: a theoretical study,” Neuroscience, 83, 303-320 (1998).

    Article  CAS  PubMed  Google Scholar 

  14. A. M. Hill, A. M. J. Bull, A. L. Wallace, et al., “Qualitative and quantitative descriptions of glenohumeral motion,” Gait Posture, 27, No. 2, 177-188 (2008).

  15. C. D. Bryce and A. D. Armstrong, “Anatomy and biomechanics of the elbow,” Orthop. Clin. North Am., 39, No. 2, 141-154 (2008).

    Article  PubMed  Google Scholar 

  16. B. M. Van Bolhuis, C. C. Gielen, and G. J. van Ingen Schenau, “Activation patterns of mono- and bi-articular arm muscles as a function of force and movement direction of the wrist in humans,” J. Physiol., 508, 313-324 (1998).

    Article  PubMed  PubMed Central  Google Scholar 

  17. A. V. Gorkovenko, S. Sawczyn, N. V. Bulgakova, et al., “Muscle agonist-antagonist interactions in an experimental joint model,” Exp. Brain Res., 222, 399-414 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  18. T. E. Milner and C. Cloutier, “Damping of the wrist joint during voluntary movement,” Exp. Brain Res., 122, 309-317 (1998).

    Article  CAS  PubMed  Google Scholar 

  19. E. Burde, R. Osu, D. W. Franklin, et al., “The central nervous system stabilizes unstable dynamics by learning optimal impedance,” Nature, 414, 446-449 (2001).

    Article  Google Scholar 

  20. P. L. Gribble and D. J. Ostry, “Independent coactivation of shoulder and elbow muscles,” Exp. Brain Res., 123, 335-360 (1998).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. I. Kostyukov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kostyukov, A.I. Theoretical Analysis of the Force and Position Synergies in Two-Joint Movements. Neurophysiology 48, 287–296 (2016).

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: