Biological Cybernetics

, Volume 96, Issue 3, pp 341–350 | Cite as

A model of open-loop control of equilibrium position and stiffness of the human elbow joint

  • Dinant A. Kistemaker
  • Arthur J. (Knoek) Van Soest
  • Maarten F. Bobbert
Original Paper


According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the α-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (K ilf). For this purpose, a model of the upper and lower arm was constructed, equipped with Hill-type muscles. At a constant neural input, the isometric force of the contractile element of the muscles depended on both the myofilamentary overlap and the effect of sarcomere length on the sensitivity of myofilaments to [Ca2+] (LDCS). The musculoskeletal model, for which the parameters were chosen carefully on the basis of physiological literature, captured the salient isometric properties of the muscles spanning the elbow joint. It was found that stable open-loop EPs could be achieved over the whole range of motion of the elbow joint and that K ilf, which ranged from 18 to 42 N m·rad−1, could be independently controlled. In the model, LDCS contributed substantially to K ilf (up to 25 N m·rad−1) and caused K ilf to peak at a sub-maximal level of co-contraction.


Elbow Joint Sarcomere Length Elbow Angle Series Elastic Element Shoulder Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


Intrinsic low-frequency joint stiffness


Mono-articular elbow flexor


Bi-articular elbow extensor


Muscle stimulation


Active state


Elbow angle


Shoulder angle


Contractile element


Series elastic element


Parallel elastic element


Force delivered by CE


Maximum isometric force




Muscle-tendon complex length


CE length


CE optimum length


l CE /l CE_opt


PE length


PE slack length


SE length


SE slack length


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Dinant A. Kistemaker
    • 1
  • Arthur J. (Knoek) Van Soest
    • 1
  • Maarten F. Bobbert
    • 1
  1. 1.Institute for Fundamental and Clinical Human Movement Sciences, IFKBVrije UniversiteitAmsterdamThe Netherlands

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