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The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period

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Abstract

Human leg swinging is modeled as the harmonic motion of a hybrid mass-spring pendulum. The cycle period is determined by a gravitational component and an elastic component, which is provided by the attachment of a soft-tissue/muscular spring of variable stiffness. To confirm that the stiffness of the spring changes with alterations in the inertial properties of the oscillator and that stiffness is relevant for the control of cycle period, we conducted this study in which the simple pendulum equivalent length was experimentally manipulated by adding mass to the ankle of a comfortably swinging leg. Twenty-four young, healthy adults were videotaped as they swung their right leg under four conditions: no added mass and with masses of 2.27, 4.55, and 6.82kg added to the ankle. Strong, linear relationships between the acceleration and displacement of the swinging leg within subjects and conditions were found, confirming the motion's harmonic nature. Cycle period significantly increased with the added mass. However, the observed increases were not as large as would be predicted by the induced changes in the gravitational component alone. These differences were interpreted as being due to increases in the active muscular stiffness. Significant linear increases in the elastic component (and hence stiffness) were demonstrated with increases in the simple pendulum equivalent length in 20 of the individual subjects, with r 2 values ranging between 0.89 and 0.99. Significant linear relationships were also demonstrated between the elastic and gravitational components in 22 subjects, with individual r 2 values between 0.90 and 0.99. This finding suggests stiffness is varied concomitantly with alterations in the inertial properties of the leg pendulum in a simplified mechanism of control.

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References

  • Alnaqueeb MA, AlZaid NS, Goldspink G (1984) Connective tissue changes and physical properties of developing and aging skeletal muscle. JAnat 139:203–212

    Google Scholar 

  • Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22:1217–1227

    Article  PubMed  Google Scholar 

  • Bohannon RW (1987) Variability and reliability of the pendulum test for spasticity using a Cybex II isokinetic dynomometer. Phys Ther 67:659–661

    PubMed  Google Scholar 

  • Bohannon RW, Smith MB (1987) Interrater reliability on a modified Ashworth scale of muscle spasticity. Phys Ther 67:206–207

    PubMed  Google Scholar 

  • Cavagna GA, Heglund NC, Taylor CR (1977) Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am J Physiol 233:R243-R261

    PubMed  Google Scholar 

  • Cohen J (1988) Statistical power analysis for the behavioral sciences. Lawrence Erlbaum, Hillsdale

    Google Scholar 

  • Farley CT, Blickhan R, Saito J, Taylor CR (1991) Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits. J Appl Physiol 71:2127–2132

    PubMed  Google Scholar 

  • Fel'dman AG (1966) Functional tuning of the nervous system with control of movement or maintenance of a steady posture. II. Controllable parameters of the muscles. Biophysics 11:565–578

    Google Scholar 

  • Fel'dman AG (1986) Once more on the equilibrium point hypotheiss (λ model) for motor control. J Mot Behav 18:17–54

    PubMed  Google Scholar 

  • Flash T (1987) The control of hand equilibrium trajectories in multijoint arm movements. Biol Cybern 57:257–274

    Article  PubMed  Google Scholar 

  • Gillingham FJ, Walsh EG, Wright GW (1974) Resonance at the wrist in Parkinsonism-changes induced by stereotactic surgery. J Physiol 238:37P

    Google Scholar 

  • Greene PR, McMahon TA (1979) Reflex stiffness of man's anti-gravity muscles during knee bends while carrying extra weights. J Biomech 12:881–891

    Article  PubMed  Google Scholar 

  • Hill AV (1953) The mechanics of active muscle. Proc R Soc Lond 6141:104–117

    Google Scholar 

  • Hogan N (1980) Tuning muscle stiffness can simplify the control of natural movement. In: Mow VC (ed) Advances in Bioengineering. American Society of Mechanical Engineers, New York

    Google Scholar 

  • Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4:2745–2754

    PubMed  Google Scholar 

  • Holt KG, Andres RO, Clarkson P (1989) Biomechanical assessment of induced muscle damage. In: Proceedings 12th International Congress of Biomechanics, Los Angeles

  • Holt KG, Hamill J, Andres RO (1990) The force driven harmonic oscillator as a model for human locomotion. Hum Mov Sci 9:55–68

    Article  Google Scholar 

  • Holt KG, Hamill J, Andres RO (1991) Predicting the minimal energy costs of human walking. Med Sci Sports Exerc 23:491–498

    PubMed  Google Scholar 

  • Katz RT, Rovai GP, Brait C, Rymer WZ (1992) Objective quantification of spastic hypertonia: correlation with clinical findings. Arch Phys Med Rehab 73:339–347

    Article  Google Scholar 

  • Kelso JAS, Holt KG (1980) Exploring a vibratory systems analysis of human movement production. J Neurophysiol 43:1183–1196

    PubMed  Google Scholar 

  • Kugler PN, Turvey MT (1987) Information, natural law and the self assembly of rhythmic movement. Lawrence Erlbaum, Hillsdale

    Google Scholar 

  • Lakie M, Walsh EG, Wright GW (1988) Assessment of human hemiplegic spasticity by a resonant frequency method. Clin Biomech 3:173–178

    Article  Google Scholar 

  • McMohan TA (1984) Muscles, reflexes, and locomotion. Princeton University Press, Princeton

    Google Scholar 

  • McMahon TA, Greene PR (1979) The influence of track compliance on running. J Biomech 12:893–904

    Article  PubMed  Google Scholar 

  • Morawski JM, Wojcieszak I (1978) Miniwalker-a resonant model of human locomotion. In: Proceedings VIth International Congress on Biomechanics, Copenhagen

  • Nichols TR, Houk JC (1976) Improvement in the linearity and regulation of stiffness that results from actions of the stretch reflex. J Neurophysiol 39:119–142

    Google Scholar 

  • Oatis CA (1993) The use of a mechanical model to describe the stiffness and damping characteristics of the knee joint in healthy adults. Phys Ther 73:740–749

    PubMed  Google Scholar 

  • Polit A, Bizzi E (1979) Characteristics of motor programs underlying arm movements in monkeys. J Neurophysiol 42:183–194

    Google Scholar 

  • Tsementzis SA, Gillingham FJ, Gordon A, Lakie M (1980) Two methods of measuring muscle tone applied in patients with decerebrate rigidity. J Neurol Neurosurg Psychiat 43:25–36

    PubMed  Google Scholar 

  • Turvey MT, Schmidt RC, Rosenblum LD, Kugler PN (1988) On the time allometry of co-ordinated rhythmic movements. J Theor Biol 130:285–325

    PubMed  Google Scholar 

  • Vereijken B, Emmerik REA van, Whiting HTA, Newell KM (1992) Free(z)ing degrees of freedom in skill acquisition. J Motor Behav 24:133–142

    Google Scholar 

  • Walsh EG (1973) Motion at the ankle induced by random forcesfrequency analysis. J Physiol 230:44–45P

    Google Scholar 

  • Winter DA (1990) Biomechanics and motor control of human movement. Wiley, New York

    Google Scholar 

  • Winters JM, Stark L (1987) Muscle models: what is gained and what is lost by varying model complexity. Biol Cybern 55:403–420

    Article  PubMed  Google Scholar 

  • Zarrugh MY, Radcliffe CW (1978) Predicting metabolic cost of level walking. Eur J Physiol 38:215–223

    Article  Google Scholar 

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The views expressed in this article are those of the authors and do not reflect the official policy or position of the Department of the Army, Department of Defense, or the US Government

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Obusek, J.P., Holt, K.G. & Rosenstein, R.M. The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period. Biol. Cybern. 73, 139–147 (1995). https://doi.org/10.1007/BF00204052

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