Archive of Applied Mechanics

, Volume 82, Issue 3, pp 333–344 | Cite as

What does head movement tell about the minimum number of mechanical degrees of freedom in quiet human stance?

  • Michael Günther
  • Otto Müller
  • Reinhard Blickhan


In this study, we checked experimentally whether anterior–posterior accelerations of the head during quiet human stance are usually below or above known thresholds of the otolith sensor. Thereto, we measured head kinematics with high spatial resolution. Furthermore, we used both these experimental data and computer simulations of two double inverted pendulum (DIP) models in order to verify the validity of DIP models in general. The results are clear cut. First, not only are acceleration thresholds regularly exceeded about once a second but also are velocity thresholds exceeded, albeit probably less frequently. Second, COM and head movement predicted by interwoven DIP model dynamics can not reproduce the mean measured amplitudes at once. Thus, neither the formerly promoted single inverted pendulum nor any DIP model can causally explain the dynamics of quiet human stance. Instead, we suggest to factor in at least three mechanical degrees of freedom. Due to a couple of reasons discussed, the triple inverted pendulum (TIP) model seems to be a promising abstraction implying potential to better understand the dynamics of quiet human stance.


Biomechanical analysis Posture control Double inverted pendulum Computer simulation Attractor 

List of symbols

(time) sequence

An array of values of measured variables (positional or force components) sampled discretely versus time


Acquisition of one (consistent and synchronised) data set containing all (time) sequences of the measured variables


Number of subjects (9)


Number of trials per subject (10)


Number of data points in one trial (1019)


(single) inverted pendulum


Double inverted pendulum


Triple inverted pendulum


Degree of freedom


Ground reaction force


Segment including head, arms and trunk


Centre of mass


Centre of pressure in the plane of the force platform surface


Standard deviation




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  1. 1.
    Alexandrov A.V., Frolov A.A., Horak F.B., Carlson-Kuhta P., Park S.: Feedback equilibrium control during human standing. Biol. Cybern. 93(5), 309–322 (2005)zbMATHCrossRefGoogle Scholar
  2. 2.
    Alexandrov A.V., Frolov A.A., Massion J.: Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling. Biol. Cybern. 84(6), 425–434 (2001)CrossRefGoogle Scholar
  3. 3.
    Allum J.H.J., Mauritz K.H.: Compensation for intrinsic muscle stiffness by short latency reflexes in human triceps surae muscles. J. Neurophysiol. 52(5), 797–818 (1984)Google Scholar
  4. 4.
    Benson A.J., Kass J.R., Vogel H.: European vestibular experiments on the Spacelab-1 mission: 4. Thresholds of perception of whole-body linear oscillation. Exp. Brain Res. 64(2), 264–271 (1986)Google Scholar
  5. 5.
    Benson A.J., Spencer M.B., Stott J.R.: Thresholds for detection of the direction of whole body linear movement in the horizontal plane. Aviat. Space Environ. Med. 57(11), 1088–1096 (1986)Google Scholar
  6. 6.
    Creath R., Kiemel T., Horak F., Peterka R., Jeka J.J.: A unified view of quiet and perturbed stance: simultaneous co-existing excitable modes. Neurosci. Lett. 377(2), 75–80 (2005)CrossRefGoogle Scholar
  7. 7.
    De Nunzio A.M., Nardone A., Schieppati M.: Head stabilization on a continuously oscillating platform: the effect of a proprioceptive disturbance on the balancing strategy. Exp. Brain Res. 165(2), 261–272 (2005)CrossRefGoogle Scholar
  8. 8.
    Edwards W.T.: Effect of joint stiffness on standing stability. Gait Posture 25(3), 432–439 (2007)CrossRefGoogle Scholar
  9. 9.
    Fitzpatrick R., McCloskey D.I.: Proprioceptive, visual and vestibular thresholds for the perception of sway during standing in humans. J. Physiol. 478(Pt 1), 173–186 (1994)Google Scholar
  10. 10.
    Fitzpatrick R.C., Taylor J.L., McCloskey D.I.: Ankle stiffness of standing humans in response to imperceptible perturbation: reflex and task-dependent components. J. Physiol. 454, 533–547 (1992)Google Scholar
  11. 11.
    Gerritsen K.G.M., van den Bogert A.J., Nigg B.M.: Direct dynamics simulation of the impact phase in heel-toe running. J. Biomech. 28(6), 661–668 (1995)CrossRefGoogle Scholar
  12. 12.
    Gruber K., Ruder H., Denoth J., Schneider K.: A comparative study of impact dynamics: wobbling mass model versus rigid body models. J. Biomech. 31(5), 439–444 (1998)CrossRefGoogle Scholar
  13. 13.
    Gundry A.J.: Thresholds of perception for periodic linear motion. Aviat. Space Environ. Med. 49(5), 679–686 (1978)Google Scholar
  14. 14.
    Günther M., Grimmer S., Siebert T., Blickhan R.: All leg joints contribute to quiet human stance: a mechanical analysis. J. Biomech. 42(16), 2739–2746 (2009)CrossRefGoogle Scholar
  15. 15.
    Günther M., Müller O., Blickhan R.: Watching quiet human stance to shake off its straitjacket. Arch. Appl. Mech. 81(3), 283–302 (2011)CrossRefGoogle Scholar
  16. 16.
    Günther M., Otto D., Müller O., Blickhan R.: Transverse pelvic rotation during quiet human stance. Gait Posture 27(3), 361–367 (2008)CrossRefGoogle Scholar
  17. 17.
    Günther M., Putsche P., Leistritz L., Grimmer S.: Phase synchronisation of the three leg joints in quiet human stance. Gait Posture 33(3), 412–417 (2011)CrossRefGoogle Scholar
  18. 18.
    Günther M., Ruder H.: Synthesis of two-dimensional human walking: a test of the λ-model. Biol. Cybern. 89(2), 89–106 (2003)zbMATHCrossRefGoogle Scholar
  19. 19.
    Hahn, U.: Entwicklung mehrgliedriger Modelle zur realistischen Simulation dynamischer Prozesse in biologischen Systemen. Master’s thesis, Eberhard-Karls-Universität, Tübingen (1993)Google Scholar
  20. 20.
    Hsu W.L., Scholz J.P., Schöner G., Jeka J.J., Kiemel T.: Control and estimation of posture during quiet stance depends on multijoint coordination. J. Neurophysiol. 97(4), 3024–3035 (2007)CrossRefGoogle Scholar
  21. 21.
    Kiemel T., Elahi A.J., Jeka J.J.: Identification of the plant for upright stance in humans: multiple movement patterns from a single neural strategy. J. Neurophysiol. 100(6), 3394–3406 (2008)CrossRefGoogle Scholar
  22. 22.
    Kingma H.: Thresholds of perception for periodic linear motion. BMC Ear Nose Throat Disorders 5(1), 5 (2005)CrossRefGoogle Scholar
  23. 23.
    Krieg, M.: Simulation und Steuerung biomechanischer Mehrkörpersysteme. Master’s thesis, Eberhard-Karls-Universität, Tübingen (1992)Google Scholar
  24. 24.
    Kuo A.D.: An optimal state estimation model of sensory integration in human postural balance. J. Neural Eng. 2(3), 235–249 (2005)CrossRefGoogle Scholar
  25. 25.
    Lipfert S., Günther M., Seyfarth A.: Diverging times in movement analysis. J. Biomech. 42(6), 786–788 (2009)CrossRefGoogle Scholar
  26. 26.
    Loram I.D., Lakie M.: Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. J. Physiol. 540(Pt 3), 1111–1124 (2002)CrossRefGoogle Scholar
  27. 27.
    McCollum G., Leen T.K.: Form and exploration of mechanical stability limits in erect stance. J. Motor Behav. 21(3), 225–244 (1989)Google Scholar
  28. 28.
    Mergner T., Maurer C., Peterka R.J. A multisensory posture control model of human upright stance. In: Prablanc, C., Pélisson, D., Rossetti, Y. (eds) Neural Control of Space Coding and Action Production, vol. 142 of Progress in Brain Research, Chap. 12, pp. 189–201. North-Holland Elsevier Science Publishers B.V, Boston (2003)CrossRefGoogle Scholar
  29. 29.
    Morasso P.G., Schieppati M.: Can muscle stiffness alone stabilize upright standing. J. Neurophysiol. 82(3), 1622–1626 (1999)Google Scholar
  30. 30.
    Roth R., Wank V., Müller O., Hochwald H., Günther M.: A simple new device to examine human stance: the totter-slab. Biomedizinische Technik 55(1), 27–38 (2010)CrossRefGoogle Scholar
  31. 31.
    Rozendaal, L.A., van Soest, A.J.K.: Joint stiffness requirements in a multi-segment stance model. In: Proceedings of XXth ISB Conference, Cleveland (2005)Google Scholar
  32. 32.
    Rozendaal, L.A., van Soest, A.J.K.: Multi-segment stance can be stable with zero local ankle stiffness. In: Proceedings of XXIst ISB Conference, Taipei (2007)Google Scholar
  33. 33.
    Rozendaal, L.A., van Soest, A.J.K.: Stabilization of a multi-segment model of bipedal standing by local joint control overestimates the required ankle stiffness. Gait Posture 28(3), 525–527 (2008) (Letter to the Editor)Google Scholar
  34. 34.
    Saffer M., Kiemel T., Jeka J.J.: Coherence analysis of muscle activity during quiet stance. Exp. Brain Res. 185(2), 215–226 (2008)CrossRefGoogle Scholar
  35. 35.
    Sasagawa S., Ushiyama J., Kouzaki M., Kanehisa H.: Effect of the hip motion on the body kinematics in the sagittal plane during human quiet standing. Neurosci. Lett. 450(1), 27–31 (2009)CrossRefGoogle Scholar
  36. 36.
    Scott S.H., Winter D.A.: Biomechanical model of the human foot: kinematics and kinetics during the stance phase of walking. J. Biomech. 26(9), 1091–1104 (1993)CrossRefGoogle Scholar
  37. 37.
    Shampine L.F., Gordon M.K.: Computer Solution of Ordinary Differential Equations: The Initial Value Problem. W.H. Freeman & Co., San Francisco (1975)zbMATHGoogle Scholar
  38. 38.
    van Soest A.J.K., Haenen W.P., Rozendaal L.A.: Stability of bipedal stance: the contribution of cocontraction and spindle feedback. Biol. Cybern. 88(4), 293–301 (2003)zbMATHCrossRefGoogle Scholar
  39. 39.
    van Soest A.J.K., Rozendaal L.A.: The inverted pendulum model of bipedal standing cannot be stabilized through direct feedback of force and contractile element length and velocity at realistic series elastic element stiffness. Biol. Cybern. 99(1), 29–41 (2008)zbMATHCrossRefGoogle Scholar
  40. 40.
    Winter D.A.: Biomechanics and Motor Control of Human Movement. Wiley, New York (1990)Google Scholar
  41. 41.
    Winter D.A., Patla A.E., Prince F., Ishac M., Gielo-Perczak K.: Stiffness control of balance in quiet standing. J. Neurophysiol. 80(3), 1211–1221 (1998)Google Scholar
  42. 42.
    Yang J.F., Winter D.A., Wells R.P.: Postural dynamics in the standing human. Biol. Cybern. 62(4), 309–320 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Michael Günther
    • 1
    • 3
  • Otto Müller
    • 2
  • Reinhard Blickhan
    • 1
  1. 1.Institut für Sportwissenschaft, Lehrstuhl für BewegungswissenschaftFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Dekanat der Medizinschen FakultätEberhard-Karls-Universität TübingenTübingenGermany
  3. 3.Institut für Sport- und BewegungswissenschaftUniversität StuttgartStuttgartGermany

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