Abstract
An attempt is made to integrate theoretically the mechanical, electromyographic, and psychophysical lines of inquiry into the control of movement by investigating the significance of joint stiffness in the reduction of effort. Attention is focused on single-joint, unperturbed movements of specified duration performed from one specified position to another in the presence of an inertial load. A theoretical measure of the sense of effort is formulated in the light of psychophysical observations and mechanical considerations. This measure is such that it is increased by reciprocal changes in the central drives to opposing sets of muscles, as well as by enhancement of joint stiffness. Mathematical analysis of the interplay of these factors reveals that, in any given condition, the minimization of this measure of effort necessitates a particular value of joint stiffness and a particular trajectory of movement. The predicted stiffness and trajectory are shown to be in quantitative agreement with available observations. In addition, the conditions in which a higher value of stiffness is predicted to be advantageous for reducing the effort are shown to be the conditions that are known to promote greater coactivation of the agonist and antagonist muscles. It is concluded that the seemingly wasteful coactivation may serve to optimize the stiffness. The stiffness, therefore, need not be viewed simply as a means of resisting imposed perturbations, but as a means of reducing the alterations in the central drives necessary for the performance of movement, thereby reducing the effort.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348
Atkeson CG, Saund E (1984) Estimation of equilibrium position, stiffness, and viscosity during human single joint arm movement. Soc Neurosci Abstr 10:335
Bizzi E, Abend W (1983) Posture control and trajectory formation in single- and multi-joint arm movements. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Advances in neurology, vol. 39. Raven Press, New York, pp 31–45
Bizzi E, Accornero N, Chapple W, Hogan N (1982) Arm trajectory formation in monkeys. Exp Brain Res 46:139–143
Bizzi E, Accornero N, Chapple W, Hogan N (1984) Posture control and trajectory formation during arm movement. J Neurosci 4:2738–2744
Cannon SC, Zahalak GI (1982) The mechanical behavior of active human skeletal muscle in small oscillations. J Biomech 15:111–121
Crago PE, Houk JC, Hasan Z (1976) Regulatory actions of human stretch reflex. J Neurophysiol 39:925–935
Elsgolc LE (1962) Calculus of variations. Pergamon, London
Enoka RM (1983) Muscular control of a learned movement: the speed control system hypothesis. Exp Brain Res 51:135–145
Feldman 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 11:498–508
Feldman AG (1980) Superposition of motor programs. I. Rhythmic forearm movements in man. Neurosci 5:81–90
Ghez C (1979) Contributions of central programs to rapid limb movement in the cat. In: Asanuma H, Wilson VJ (eds) Integration in the nervous system. Igaku-Shoin, Tokyo, pp 305–320
Ghez C, Vicario D, Martin JH, Yumiya H (1983) Sensory motor processing of target movements in motor cortex. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Advances in neurology, vol. 39. Raven Press, New York, pp 61–92
Gielen CCAM, Houk JC (1984) Nonlinear viscosity of human wrist. J Neurophysiol 52:553–569
Gottlieb GL, Agarwal GC (1980) Response to sudden torques about ankle in man. III. Suppression of stretch-evoked responses during phasic contraction. J Neurophysiol 44:233–246
Gottlieb GL, Agarwal GC (1983) Muscle-reflex compliance: elasticity and plasticity at the human elbow. Soc Neurosci Abstr 9:632
Hasan Z, Enoka RM (1985) Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis. Exp. Brain Res 59:441–450
Hasan Z, Enoka RM, Stuart DG (1985) The interface between biomechanics and neurophysiology in the study of movement: some recent approaches. Exercise Sport Sci Rev 13:169–234
Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4:2745–2754
Houk JC (1979) Regulation of stiffness by skeletomotor reflexes. Annu Rev Physiol 41:99–114
Houk JC, Rymer WZ (1981) Neural control of muscle length and tension. In: Brooks VB (ed) The nervous system: motor control. American Physiological Society, Bethesda (Handbook of physiology, sect 1, vol II, part 1, pp 257–323)
Humphrey DR, Reed DJ (1983) Separate cortical systems for control of joint movement and joint stiffness: reciprocal activation and coactivation of antagonist muscles. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Advances in neurology, vol 39, Raven Press, New York, pp 347–372
Lestienne F (1979) Effects of intertial load and velocity on the braking process of voluntary limb movements. Exp Brain Res 35:407–418
Lestienne F, Polit A, Bizzi E (1981) Functional organization of the motor process underlying the transition from movement to posture. Brain Res 230:121–132
Marsden CD, Obeso JA, Rothwell JC (1983) The function of the antagonist muscle during fast limb movements in man. J Physiol (London) 335:1–13
Matthews PBC (1982) Where does Sherrington's “muscular sense” originate? Muscles, joints, corollary discharges? Annu Rev Neurosci 5:189–218
McCloskey DI (1981) Corollary discharges: motor commands and perception. In: Brooks VB (ed) The nervous system: motor control. American Physiological Society, Bethesda (Handbook of physiology, sect I, vol II, part 2, pp 1415–1447)
Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227
Nelson WL (1983) Physical principles for economies of skilled movements. Biol Cybern 46:135–147
Person RS (1958) An electromyographic investigation on coordination of the activity of antagonist muscles in man during the development of a motor habit. Pavlov J High Nerv Act 8:13–23
Smith AM (1981) The coactivation of antagonist muscles. Can J Physiol Pharmacol 59:733–747
Soechting JF, Dufresne JR, Lacquaniti F (1981) Time-varying properties of myotatic response in man during some simple motor tasks. J Neurophysiol 46:1226–1243
Vincken MH (1983) Control of limb stiffness. Ph. D. Thesis, Utrecht Rijksuniversiteit
Vincken MH, Gielen CCAM, Denier van der Gon JJ (1983) Intrinsic and afferent components in apparent muscle stiffness in man. Neurosci 9:529–534
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hasan, Z. Optimized movement trajectories and joint stiffness in unperturbed, inertially loaded movements. Biol. Cybern. 53, 373–382 (1986). https://doi.org/10.1007/BF00318203
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00318203