Experimental Brain Research

, Volume 157, Issue 4, pp 507–517

Multijoint dynamics and postural stability of the human arm

  • Eric J. Perreault
  • Robert F. Kirsch
  • Patrick E. Crago
Research Article


The goal of this study was to examine how the mechanical properties of the human arm are modulated during isometric force regulation tasks. Specifically, we examined whether the dynamic stability of the limb remained nearly invariant across a range of voluntarily generated endpoint forces and limb postures. Previous single joint studies have demonstrated that dynamic joint stability, as quantified via estimates of the joint damping ratio, is nearly invariant during isometric torque regulation tasks. However, the relevance of these findings to the control of multijoint posture has not been investigated previously. A similar degree of invariance at the multijoint level could suggest a fundamental property of the motor system that could be incorporated into the planning and execution of multijoint tasks. In this work, limb mechanics were quantified using estimates of dynamic endpoint stiffness, which characterizes the relationship between imposed displacements of limb posture and the forces opposing those displacements. Endpoint stiffness was estimated using a two-link robot operating in the horizontal plane at the height of each subject’s glenohumeral joint. The robot was used to apply stochastic position perturbations to the arm and to measure the resulting forces. Endpoint stiffness dynamics were estimated nonparametrically and subsequently summarized using inertial, viscous and elastic parameters. We found that in the tasks studied, there was a differential modulation of endpoint elasticity and endpoint viscosity. Elasticity increased nearly linearly with increases in voluntary force generation while viscosity increased nonlinearly. This differential regulation resulted in limb dynamics that had a remarkably consistent damping ratio across all subjects and all tested conditions. These results emphasize the importance of considering the full dynamic response of a limb when investigating multijoint stability, and suggest that a minimal degree of limb stability is maintained over a wide range of force regulation tasks.


Limb stiffness Multijoint mechanics Impedance Postural stability Biomechanics 


  1. Acosta AM, Kirsch RF, Perreault EJ (2000) A robotic manipulator for the characterization of two-dimensional dynamic stiffness using stochastic displacement perturbations. J Neurosci Methods 102:177–186CrossRefPubMedGoogle Scholar
  2. Agarwal GC, Gottlieb GL (1977) Compliance of the human ankle joint. J Biomech Eng 99:166–170Google Scholar
  3. Bagni MA, Cecchi G, Cecchini E, Colombini B, Colomo F (1998) Force responses to fast ramp stretches in stimulated frog skeletal muscle fibres. J Muscle Res Cell Motil 19:33–42PubMedGoogle Scholar
  4. Bendat JS, Piersol AG (1986) Random data: analysis and measurement procedures. Wiley, New YorkGoogle Scholar
  5. Bennett DJ, Hollerbach JM, Xu Y, Hunter IW (1992) Time-varying stiffness of the human elbow joint during cyclic voluntary movement. Exp Brain Res 88:433–442PubMedGoogle Scholar
  6. Capaday C, Stein RB (1986) Amplitude modulation of the soleus H-reflex in the human during walking and standing. J Neurosci 6:1308–1313PubMedGoogle Scholar
  7. Cecchi G, Bagni MA, Cecchini E, Colombini B, Colomo F (1997) Crossbridge viscosity in activated frog muscle fibres. Biophys Chem 68:1–8CrossRefPubMedGoogle Scholar
  8. Chow JW, Darling WG (1999) The maximum shortening velocity of muscle should be scaled with activation. J Appl Physiol 86:1025–1031PubMedGoogle Scholar
  9. D’Azzo JJ, Houpis CH (1995) Linear control system analysis and design. McGraw-Hill, New YorkGoogle Scholar
  10. Dolan JM, Friedman MB, Nagurka ML (1993) Dynamic and loaded impedance components in the maintenance of human arm posture. IEEE Trans Syst Man Cybern 23:698–709CrossRefGoogle Scholar
  11. Flash T, Gurevich I (1997) Models of motor adaptation and impedance control in human arm movements. In: Morasso P, Sanguineti V (eds) Self-organization, computational maps, and motor control. Elsevier Science, Amsterdam, pp 423–481Google Scholar
  12. Flash T, Mussa-Ivaldi FA (1990) Human arm stiffness characteristics during the maintenance of posture. Exp Brain Res 82:315–326PubMedGoogle Scholar
  13. Franklin DW, Milner TE (2003) Adaptive control of stiffness to stabilize hand position with large loads. Exp Brain Res 152:211–220CrossRefPubMedGoogle Scholar
  14. Gomi H, Osu R (1998) Task-dependent viscoelasticity of human multijoint arm and its spatial characteristics for interaction with environments. J Neurosci 18:8965–8978PubMedGoogle Scholar
  15. Hamming RW (1986) Numerical methods for scientists and engineers. Dover, New YorkGoogle Scholar
  16. Hinrichs RN (1985) Regression equations to predict segmental moments of inertia from anthropometric measurements: an extension of the data of Chandler et al. (1975). J Biomech 18:621–624PubMedGoogle Scholar
  17. Hogan N (1985) The mechanics of multi-joint posture and movement control. Biol Cybern 52:315–331PubMedGoogle Scholar
  18. Huyghues-Despointes CM, Cope TC, Nichols TR (2003) Intrinsic properties and reflex compensation in reinnervated triceps surae muscles of the cat: effect of activation level. J Neurophysiol 90:1537–1546PubMedGoogle Scholar
  19. Joyce GC, Rack PM, Westbury DR (1969) The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J Physiol 204:461–474PubMedGoogle Scholar
  20. Kearney RE, Hunter IW (1990) System identification of human joint dynamics. CRC Crit Rev Biomed Eng 18:55–87Google Scholar
  21. Kearney RE, Stein RB, Parameswaran L (1997) Identification of intrinsic and reflex contributions to human ankle stiffness dynamics. IEEE Trans Biomed Eng 44:493–504PubMedGoogle Scholar
  22. Kirsch RF, Rymer WZ (1992) Neural compensation for fatigue-induced changes in muscle stiffness during perturbations of elbow angle in human. J Neurophysiol 68:449–470PubMedGoogle Scholar
  23. Kirsch RF, Boskov D, Rymer WZ (1994) Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance. IEEE Trans Biomed Eng 41:758–770PubMedGoogle Scholar
  24. Lacquaniti F, Carrozzo M, Borghese NA (1993) Time-varying mechanical behavior of multijointed arm in man. J Neurophysiol 69:1443–1463PubMedGoogle Scholar
  25. Ljung L (1999) System identification theory for the user. Prentice-Hall, Upper Saddle River, NJGoogle Scholar
  26. Mann KA, Werner FW, Palmer AK (1989) Frequency spectrum analysis of wrist motion for activities of daily living. J Orthop Res 7:304–306PubMedGoogle Scholar
  27. Marmarelis PZ, Marmarelis VZ (1978) Analysis of physiological systems. Plenum Press, New YorkGoogle Scholar
  28. McIntyre J, Mussa-Ivaldi FA, Bizzi E (1996) The control of stable arm postures in the multi-joint arm. Exp Brain Res 110:248–264PubMedGoogle Scholar
  29. Milner TE, Cloutier C (1998) Damping of the wrist joint during voluntary movement. Exp Brain Res 122:309–317PubMedGoogle Scholar
  30. Mussa-Ivaldi FA, Hogan N, Bizzi E (1985) Neural, mechanical, and geometric factors subserving arm posture in humans. J Neurosci 5:2732–2743PubMedGoogle Scholar
  31. Nichols TR, Houk JC (1976) Improvement in linearity and regulation of stiffness that results from actions of stretch reflex. J Neurophysiol 39:119–142PubMedGoogle Scholar
  32. Perreault EJ, Kirsch RF, Acosta AM (1999) Multiple-input, multiple-output system identification for the characterization of limb stiffness dynamics. Biol Cybern 80:327–337CrossRefPubMedGoogle Scholar
  33. Perreault EJ, Crago PE, Kirsch RF (2000) Estimation of intrinsic and reflex contributions to muscle dynamics: a modeling study. IEEE Trans Biomed Eng 47:1413–1421PubMedGoogle Scholar
  34. Perreault EJ, Kirsch RF, Crago PE (2001) Effects of voluntary force generation on the elastic components of endpoint stiffness. Exp Brain Res 141:312–323PubMedGoogle Scholar
  35. Perreault EJ, Kirsch RF, Crago PE (2002) Voluntary control of static endpoint stiffness during force regulation tasks. J Neurophysiol 87:2808–2816Google Scholar
  36. Perreault EJ, Day SJ, Hulliger M, Heckman CJ, Sandercock TG (2003) Summation of motor unit forces in cat soleus during experimentally simulated recruitment. J Neurophysiol 89:738PubMedGoogle Scholar
  37. Pierre MC, Kirsch RF (2003) Measurement and reliability of 3D end-point stiffness of the human arm. In: Proc. 25th IEEE/EMBS Conf., Cancun, pp 1433–1436Google Scholar
  38. Politis DN (1998) Computer-intensive methods in statistical analysis. IEEE Signal Process Mag 15:39–55CrossRefGoogle Scholar
  39. Press W, Flannery BP, Teukolsky SA, Vetterling WT (1992) Numerical recipes in C. Cambridge University Press, New YorkGoogle Scholar
  40. Sinkjaer T, Hayashi R (1989) Regulation of wrist stiffness by the stretch reflex. J Biomech 22:1133–1140PubMedGoogle Scholar
  41. Stein RB, Kearney RE (1995) Nonlinear behavior of muscle reflexes at the human ankle joint. J Neurophysiol 73:65–72PubMedGoogle Scholar
  42. Stroeve S (1999) Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control. Biol Cybern 81:475–494Google Scholar
  43. Tsuji T, Morasso PG, Goto K, Ito K (1995) Hand impedance characteristics during maintained posture. Biol Cybern 72:475–485PubMedGoogle Scholar
  44. Weiss PL, Hunter IW, Kearney RE (1988) Human ankle joint stiffness over the full range of muscle activation levels. J Biomech 21:539–544PubMedGoogle Scholar
  45. Winter DA (1990) Biomechanics and motor control of movement. John Wiley, TorontoGoogle Scholar
  46. Zhang L-Q, Rymer WZ (1997) Simultaneous and nonlinear identification of mechanical and reflex properties of human elbow joint muscles. IEEE Trans Biomed Eng 44:1192–1209PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Eric J. Perreault
    • 1
  • Robert F. Kirsch
    • 2
    • 3
  • Patrick E. Crago
    • 2
    • 3
  1. 1.Department of Biomedical Engineering and Department of Physical Medicine and RehabilitationNorthwestern UniversityChicagoUSA
  2. 2.Department of Biomedical EngineeringCase Western Reserve UniversityClevelandUSA
  3. 3.Louis Stokes VA Medical CenterClevelandUSA

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