, Volume 11, Issue 3, pp 123–129 | Cite as

Muscle spindles in muscle control

II. Analysis of muscle servo model
  • Gideon F. Inbar


The muscle spindles (MS) have been proposed by Merton (1953), to be the sensors supplying a feedback signal in the muscle length follow-up servo system. This system is analyzed here, based on the two engineering requirements for man made servo systems, namely the system loop gain and the steady state error (Gille, 1959). In the first part the system's linearized transfer function equations are developed. It is shown that the small loop gain found in the reflex studies indicates a small gain under volitional control of movements, i.e. volitional control is being exercised directly by the alpha or gamma system. For the steady state error no definite conclusions can be drawn from the available data (Rosenthal, 1970; Houk, 1963); however, it is shown to be inversely proportional to the steady state loop gain, and the system is thus of type “0” or “1”.


Engineering Requirement System Loop Muscle Spindle Function Equation Muscle Length 
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  1. Eldred,E., Granit,R., Merton,P.A.: Superspinal control of muscle spindles and its significance. J. Physiol. (Lond.) 122, 498–523 (1953).Google Scholar
  2. Gille,J., Pelegrin,M., Decaulne,P.: Feedback control systems. McGraw-Hill, Book Co. 1959.Google Scholar
  3. Granit,R.: Receptors and sensory perception. New Haven: Yale University Press 1962.Google Scholar
  4. Houk,J.C, Singer,J.J., Goldman,M.R.: An evaluation of length and force feedback to soleus muscles of decerebrate cats. J. Neurophysiol. 33, 784–811 (1970).Google Scholar
  5. —, Henneman,E.: Responses of Golgi tendon organs to active contractions of the soleus muscle of the cat. J. Neurophysiol. 30, 466–481 (1967).Google Scholar
  6. —: A mathematical model of the stretch reflex in Human muscle systems. M. Sc. Dissertation. Cambridge: M.I.T. (1963).Google Scholar
  7. Inbar,G.F., Odom,B., Wagman,I.: Muscle spindles in muscle control: I. Afferent outflow from frog muscle spindles in open and closed loop modes. Kybernetik 11, 119–122 (1972).Google Scholar
  8. Josef,P., Inbar,G.F.: Steady state errors in muscle servo systems. Proc. Fifth Hawaii International Conference on System Sciences Session HH-3 (1972).Google Scholar
  9. Matthews,P.B.C., Stein,R.B.: The sensitivity of muscle spindles afferents to small sinusoidal changes of length. J. Physiol. (Lond.) 200, 723–743 (1969).Google Scholar
  10. —: The reflex excitation of the soleus muscle of the decerebrate cat caused by vibration applied to its tendon. J. Physiol. (Lond) 184, 450–472 (1966).Google Scholar
  11. Merton,P.A.: Speculations on the servo-control of movement. In: The spinal cord, p. 247–260. Malcolm,J.L., Gray,J.A.B., Wolstenholrn (Ed.) Boston: Little, Brown & Co., 1953.Google Scholar
  12. Roberts,T.D.M.: Neurophysiology of postural mechanism, New York: Plenum Press, 1967.Google Scholar
  13. Rosenthal,N.P., Mckean,T.A., Roberts,W.J., Terzuolo,C.A.: Frequency analysis of stretch reflex and its main subsystems in triceps surae muscles of the cat. J. Neurophysiol. 33, 733–749 (1970).Google Scholar
  14. Terzuolo,C.: Personal communication.Google Scholar
  15. Stark,L.: Neurological control systems. New York: Plenum Press 1968.Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Gideon F. Inbar
    • 1
  1. 1.Technion - Israel Institute of TechnologyHaifaIsrael

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