Skip to main content
Log in

Accuracy of planar reaching movements

I. Independence of direction and extent variability

Experimental Brain Research Aims and scope Submit manuscript

Abstract

This study examined the variability in movement end points in a task in which human subjects reached to targets in different locations on a horizontal surface. The primary purpose was to determine whether patterns in the variable errors would reveal the nature and origin of the coordinate system in which the movements were planned. Six subjects moved a hand-held cursor on a digitizing tablet. Target and cursor positions were displayed on a computer screen, and vision of the hand and arm was blocked. The screen cursor was blanked during movement to prevent visual corrections. The paths of the movements were straight and thus directions were largely specified at the onset of movement. The velocity profiles were bell-shaped, and peak velocities and accelerations were scaled to target distance, implying that movement extent was also programmed in advance of the movement. The spatial distributions of movement end points were elliptical in shape. The major axes of these ellipses were systematically oriented in the direction of hand movement with respect to its initial position. This was true for both fast and slow movements, as well as for pointing movements involving rotations of the wrist joint. Using principal components analysis to compute the axes of these ellipses, we found that the eccentricity of the elliptical dispersions was uniformly greater for small than for large movements: variability along the axis of movement, representing extent variability, increased markedly but nonlinearly with distance. Variability perpendicular to the direction of movement, which results from directional errors, was generally smaller than extent variability, but it increased in proportion to the extent of the movement. Therefore, directional variability, in angular terms, was constant and independent of distance. Because the patterns of variability were similar for both slow and fast movements, as well as for movements involving different joints, we conclude that they result largely from errors in the planning process. We also argue that they cannot be simply explained as consequences of the inertial properties of the limb. Rather they provide evidence for an organizing mechanism that moves the limb along a straight path. We further conclude that reaching movements are planned in a hand-centered coordinate system, with direction and extent of hand movement as the planned parameters. Since the factors which influence directional variability are independent of those that influence extent errors, we propose that these two variables can be separately specified by the brain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348

    CAS  PubMed  Google Scholar 

  • Atkeson CG, Hollerbach JM (1985) Kinematic features of unrestrained vertical arm movements. J Neurosci 5:2318–2330

    CAS  PubMed  Google Scholar 

  • Bermejo R, Pullman S, Ghez C (1989) Differences in programming of amplitude and direction in a two dimensional force aiming task. Soc Neurosci Abstr 15:50

    Google Scholar 

  • Bernstein NA (1967) The coordination and regulation of movements. Pergamon, New York

    Google Scholar 

  • Bock O, Arnold K (1992) Motor control prior to movement onset. Exp Brain Res 90:209–216

    Google Scholar 

  • Bonnet M, Requin J, Stelmach GE (1982) Specification of direction and extent in motor programming. Bull Psychon Soc 19:31–34

    Google Scholar 

  • Burnod Y, Grandguillaume P, Otto I, Ferraina S, Johnson PB, Caminiti R (1992) Visuomotor transformations underlying arm movements toward visual targets: a neural network model of cerebral cortical operations. J Neurosci 12:1435–1453

    Google Scholar 

  • Caminiti R, Johnson PB, Urbano A (1990) Making arm movements within different parts of space: dynamic aspects in the primate motor cortex. J Neurosci 10:2039–2058

    Google Scholar 

  • Caminiti R, Johnson PB, Galli C, Ferraina S, Burnod Y (1991) Making arm movements within different parts of space: the premotor and motor cortical representation of a coordinate system for reaching to visual targets. J Neurosci 11:1182–1197

    CAS  PubMed  Google Scholar 

  • Favilla M, Hening W, Ghez C (1989) Trajectory control in targeted force impulses. VI. Independent specification of response amplitude and direction. Exp Brain Res 75:280–294

    Google Scholar 

  • Favilla M, Gordon J, Ghilardi MF, Ghez C (1990a) Discrete and continuous processes in the programming of extent and direction in multijoint arm movements. Soc Neurosci Abstr 16:1089

    Google Scholar 

  • Favilla M, Gordon J, Hening W, Ghez C (1990b) Trajectory control in targeted force impulses. VII. Independent setting of amplitude and direction in response preparation. Exp Brain Res 79:530–538

    Google Scholar 

  • Flanders M, Soechting JF (1990) Parcellation of sensorimotor transformations for arm movements. J Neurosci 10:2420–2427

    Google Scholar 

  • Flanders M, Tillery SIH, Soechting JF (1992) Early stages in a sensorimotor transformation. Behav Brain Sci 15:309–362

    Google Scholar 

  • Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5:1688–1703

    CAS  PubMed  Google Scholar 

  • Georgopoulos AP (1991) Higher order motor control. Annu Rev Neurosci 14:361–378

    Google Scholar 

  • Georgopoulos AP, Massey JT (1988) Cognitive spatial-motor processes. 2. Information transmitted by the direction of two-dimensional arm movements and by neuronal populations in primate motor cortex and area 5. Exp Brain Res 69:315–326

    CAS  PubMed  Google Scholar 

  • Georgopoulos AP, Kalaska JF, Massey JT (1981) Spatial trajectories and reaction times of aimed movements: effects of practice, uncertainty, and change in target location. J Neurophysiol 46:725–743

    Google Scholar 

  • Georgopoulos AP, Kalaska JF, Caminiti R, Massey JT (1982) On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J Neurosci 2:1527–1537

    CAS  PubMed  Google Scholar 

  • Ghez C (1979) Contributions of central programs to rapid limb movements in the cat. In: Asanuma H, Wilson VJ (eds) Integration in the nervous system. Igaku-Shoin, Tokyo, pp 305–320

    Google Scholar 

  • Ghez C, Vicario D, Martin JH, Yumiya H (1983) Sensory motor processing of targeted movements in motor cortex. In: Desmedt JE (eds) Motor control mechanisms in health and disease. Raven, New York, pp 61–92

    Google Scholar 

  • Ghez C, Gordon J, Ghilardi MF, Christakos CN, Cooper SE (1990a) Roles of proprioceptive input in the programming of arm trajectories. Cold Spring Harb Symp Quant Biol 55:837–847

    Google Scholar 

  • Ghez C, Hening W, Favilla M (1990b) Parallel interacting channels in the initiation and specification of motor response features. In: Jeannerod M (eds) Motor representation and control. (Attention and performance, vol XIII) Erlbaum, Hillsdale, NJ, pp 265–293

    Google Scholar 

  • Ghilardi MF, Gordon J, Ghez C (1991) Systematic directional errors in planar arm movements are reduced by vision of the arm. Soc Neurosci Abstr 17:1388

    Google Scholar 

  • Gordon J, Ghez C (1987a) Trajectory control in targeted force impulses. II. Pulse height control. Exp Brain Res 67:241–252

    Google Scholar 

  • Gordon J, Ghez C (1987b) Trajectory control in targeted force impulses. III. Compensatory adjustments for initial errors. Exp Brain Res 67:253–269

    Google Scholar 

  • Gordon J, Ghez C (1989) Independence of direction and amplitude errors in planar arm movements. Soc Neurosci Abstr 15:50

    Google Scholar 

  • Gordon J, Ghilardi MF, Ghez C (1992a) In reaching, the task is to move the hand to a target. Behav Brain Sci 15:337–339

    Google Scholar 

  • Gordon J, Ghilardi MF, Ghez C (1992b) Parallel processing of direction and extent in reaching movements. Eng Med Biol 11:92–93

    Google Scholar 

  • Gordon J, Ghilardi MF, Cooper SE, Ghez C (1994) Accuracy of planar reaching movements. II. Systematic extent errors resulting from inertial anisotropy. Exp Brain Res 99:112–130

    CAS  PubMed  Google Scholar 

  • Gottlieb GL, Corcos DM, Agarwal GC (1989) Strategies for the control of voluntary movements with one mechanical degree of freedom. Behav Brain Sci 12:189–250

    Google Scholar 

  • Hasan Z (1991) Moving a human or robot arm with many degrees of freedom: issues and ideas. In: Nadel E, Stein D (eds) 1990 Eectures in complex systems. (SFI studies in the sciences of complexity, vol III) Addison-Wesley, Redwood City, CA, pp 225–251

    Google Scholar 

  • Hogan N (1985) The mechanics of multi-joint posture and movement control. Biol Cybern 52:315–331

    CAS  PubMed  Google Scholar 

  • Hollerbach JM (1982) Computers, brains and the control of movement. Trends Neurosci 5:189–192

    Article  Google Scholar 

  • Jakobson ES, Goodale MA (1989) Trajectories of reaches to prismatically displaced targets: evidence for “automatic” visuomotor recalibration. Exp Brain Res 78:575–587

    Google Scholar 

  • Kalaska JF, Crammond DJ (1992) Cerebral cortical mechanisms of reaching movements. Science 255:1517–1523

    CAS  PubMed  Google Scholar 

  • Kaminski TR, Gentile AM (1989) A kinematic comparison of single and multijoint pointing movements. Exp Brain Res 78:547–556

    Google Scholar 

  • Karst GM, Hasan Z (1991) Initiation rules for planar, two-joint arm movements: agonist selection for movements throughout the work space. J Neurophysiol 66:1579–1593

    CAS  PubMed  Google Scholar 

  • Keele SW (1968) Movement control in skilled motor performance. Psychol Bull 70:387–403

    Google Scholar 

  • Mel BW (1991) A connectionist model may shed light on neural mechanisms for visually guided reaching. J Cogn Neurosci 3:273–292

    Google Scholar 

  • Meyer DE, Smith JEK, Kornblum S, Abrams RA, Wright CE (1990) Speed-accuracy tradeoffs in aimed movements: toward a theory of rapid voluntary action. In: Jeannerod M (eds) Motor representation and control. (Attention and performance, vol XIII) Erlbaum, Hillsdale, NJ, pp 173–226

    Google Scholar 

  • Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227

    CAS  PubMed  Google Scholar 

  • Newell KM, Carlton EG, Carlton MJ (1982) The relationship of impulse to response timing error. J Mot Behav 14:24–45

    CAS  PubMed  Google Scholar 

  • Poulton EC (1981) Human manual control. In: Brooks VB (eds) Motor control. (Handbook of physiology, sect 1, The nervous system, vol 2, part 2) American Physiological Society, Bethesda, MD, pp 1337–1389

    Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge

    Google Scholar 

  • Riehle A, Requin J (1989) Monkey primary motor and premotor cortex: single-cell activity related to prior information about direction and extent of an intended movement. J Neurophysiol 61:534–549

    Google Scholar 

  • Rosenbaum DA (1980) Human movement initiation: specification of arm, direction, and extent. J Exp Psychol [Gen] 109:444–474

    Google Scholar 

  • Saltzman E (1979) Eevels of sensorimotor representation. J Math Psychol 20:91–163

    Google Scholar 

  • Schmidt RA (1976) A schema theory of discrete skill learning. Psychol Rev 82:225–260

    Google Scholar 

  • Schmidt RA, Zelaznik H, Hawkins B, Frank JS, Quinn JT (1979) Motor-output variability: a theory for the accuracy of rapid motor acts. Psychol Rev 86:415–451

    Google Scholar 

  • Schwartz AB, Kettner RE, Georgopoulos AP (1988) Primate motor cortex and free arm movements to visual targets in three-dimensional space. I. Relations between single cell discharge and direction of movement. J Neurosci 8:2913–2927

    Google Scholar 

  • Shadmehr R, Mussa-Ivaldi FA, Bizzi E (1993) Postural force fields of the human arm and their role in generating multi-joint movements. J Neurosci 13:45–62

    Google Scholar 

  • Smit AC, Van Gisbergen JAM (1990) An analysis of curvature in fast and slow human saccades. Exp Brain Res 81:335–345

    Google Scholar 

  • Soechting JF (1989) Elements of coordinated arm movements in three-dimensional space. In: Wallace SA (eds) Perspectives on the coordination of movement. North-Holland, New York, pp 47–83

    Google Scholar 

  • Soechting JF, Flanders M (1989a) Errors in pointing are due to approximations in sensorimotor transformations. J Neurophysiol 62:595–608

    Google Scholar 

  • Soechting JF, Flanders M (1989b) Sensorimotor representations for pointing to targets in three-dimensional space. J Neurophysiol 62:582–594

    Google Scholar 

  • Soechting JF, Terzuolo CA (1990) Sensorimotor transformations and the kinematics of arm movements in three-dimensional space. In: Jeannerod M (eds) Motor representation and control. (Attention and Performance, vol XIII) Erlbaum, Hillsdale, NJ, pp 479–494

    Google Scholar 

  • Soechting JF, Tillery SIH, Flanders M (1989) Transformation from head- to shoulder-centered representation of target direction in arm movements. J Cogn Neurosci 2:32–43

    Google Scholar 

  • Sokal RR, Rohlf FJ (1981) Biometry: the principles and practice of statistics in biological research, 2nd edn. Freeman, New York

    Google Scholar 

  • Tillery SIH, Flanders M, Soechting JF (1991) A coordinate system for the synthesis of visual and kinesthetic information. J Neurosci 11:770–778

    Google Scholar 

  • Woodworth RS (1899) The accuracy of voluntary movement. Psychol Rev 3 [Suppl whole No. 13]: 1–114

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gordon, J., Ghilardi, M.F. & Ghez, C. Accuracy of planar reaching movements. Exp Brain Res 99, 97–111 (1994). https://doi.org/10.1007/BF00241415

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00241415

Key words

Navigation