Intrinsic joint kinematic planning. II: Hand-path predictions based on a Listing’s plane constraint

  • D. G. LiebermannEmail author
  • A. Biess
  • C. C. A. M. Gielen
  • T. Flash
Research Article


This study was aimed at examining the assumption that three-dimensional (3D) hand movements follow specific paths that are dictated by the operation of a Listing’s law constraint at the intrinsic joint level of the arm. A kinematic model was used to simulate hand paths during 3D point-to-point movements. The model was based on the assumption that the shoulder obeys a 2D Listing’s constraint and that rotations are about fixed single-axes. The elbow rotations were assumed to relate linearly to those of the shoulder. Both joints were assumed to rotate without reversals, and to start and end rotating simultaneously with zero initial and final velocities. Model predictions were compared to experimental observations made on four right-handed individuals that moved toward virtual objects in “extended arm”, “radial”, and “frontal plane” movement types. The results showed that the model was partially successful in accounting for the observed behavior. Best hand-path predictions were obtained for extended arm movements followed by radial ones. Frontal plane movements resulted in the largest discrepancies between the predicted and the observed paths. During such movements, the upper arm rotation vectors did not obey Listing’s law and this may explain the observed discrepancies. For other movement types, small deviations from the predicted paths were observed which could be explained by the fact that single-axis rotations were not followed even though the rotation vectors remained within Listing’s plane. Dynamic factors associated with movement execution, which were not taken into account in our purely kinematic approach, could also explain some of these small discrepancies. In conclusion, a kinematic model based on Listing’s law can describe an intrinsic joint strategy for the control of arm orientation during pointing and reaching movements, but only in conditions in which the movements closely obey the Listing’s plane assumption.


Listing’s law Joint kinematics End-point path model 



The authors wish to thank Jason Friedman for his comments on an earlier version of this manuscript. This research was supported in part by a research grant from the Israeli Ministry of Science and by the Moross laboratory. Tamar Flash is an incumbent of the Hymie Moross Professorial chair.


  1. Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348PubMedCrossRefGoogle Scholar
  2. Admiraal MA, Medendorp WP, Gielen CCAM (2001) Three-dimensional head and upper arm orientations during kinematically redundant movements and at rest. Exp Brain Res 142:181–192PubMedGoogle Scholar
  3. Atkeson CG, Hollerbach JT (1984) Kinematic features of unrestrained arm movements (Technical Report 790). Artificial Intelligence Laboratory, MIT, Boston, MAGoogle Scholar
  4. Biess A, Flash T, Liebermann DG (2001) Multijoint point-to-point arm movements of humans in 3d-space—minimum kinetic energy paths. In: Meulenbroek R, Steenberger B (eds) Proceedings of the Tenth Biennial Conference of the International Graphonomics Society. Institute for Cognition and Information Pub, Nijmegen, pp 142–147Google Scholar
  5. Ceylan M, Henriques DYP, Tweed DB, Crawford JD (2000) Task-dependent constraints in motor control: pinhole goggles make the head move like an eye. J Neurosci 20:2719–2730PubMedGoogle Scholar
  6. Collewijn H, Ferman L, Van den Berg AV (1988) The behavior of human gaze in three-dimensions. In: Cohen B, Henn V (eds) Representation of three-dimensional space in the vestibular oculomotor and visual systems. Ann N Y Acad Sci 545:105–127Google Scholar
  7. Craig JJ (1989) Introduction to robotics. Mechanics and control. Addison-Wesley, Reading, MA, pp 28–59Google Scholar
  8. Crawford JD, Vilis T (1995) How do motor systems deal with the problems of controlling three-dimensional rotations? J Mot Behav 27:89–99Google Scholar
  9. Flanagan JR, Ostry DJ (1989) Trajectories of human multijoint arm movements: evidence of joint level planning. In: Hayward V, Khatib O (eds) Lecture notes in control and information sciences. Experimental robotics I, vol 139. Springer, Berlin Heidelberg New York, pp 594–613Google Scholar
  10. Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 7:1688–1703Google Scholar
  11. Georgopoulos AP, Lurito JT, Petrides M, Schwartz AB, Massey JT (1989) Mental rotation of the neuronal population vector. Science 243:234–236PubMedCrossRefGoogle Scholar
  12. Gielen CCAM, Vrijenhoek EJ, Flash T, Neggers SFW (1997) Arm position constraints during pointing and reaching in 3D. J Neurophysiol 78:1179–1196Google Scholar
  13. Haslwanter T (1995) Mathematics of 3-dimensional eye rotations. Vision Res 35:1727–1739PubMedCrossRefGoogle Scholar
  14. Henriques DYP, Crawford JD (2000) Direction-dependent distortions of retinocentric space in the visuomotor transformation for pointing. Exp Brain Res 132:179–194PubMedCrossRefGoogle Scholar
  15. Henriques DYP, Medendorp WP, Gielen CCAM, Crawford JD (2003) Geometric computations underlying eye-hand coordination: orientation of the two eyes and the head. Exp Brain Res 152:70–78PubMedCrossRefGoogle Scholar
  16. Hepp K (1990) On Listing’s law. Commun Math Phys 132:285–292CrossRefGoogle Scholar
  17. Hermens F, Gielen CCAM (2004) Posture-based or trajectory-based movement planning? A comparison of direct and indirect pointing movements. Exp Brain Res 159:340–348PubMedCrossRefGoogle Scholar
  18. Hollerbach JM, Atkeson CG (1986) Characterization of joint-interpolated arm movements. In: Heuer H, Fromm C (eds) Generation and modulation of action patterns. Exp Brain Res Suppl(15):41–54. Springer, Berlin Heidelberg New YorkGoogle Scholar
  19. Hollerbach JM, Atkeson CG (1987) Deducing planning variables from experimental arm trajectories: pitfalls and possibilities. Biol Cybern 56:279–292PubMedCrossRefGoogle Scholar
  20. Hollerbach JM, Flash T (1982) Dynamic interactions between limb segments during planar arm movement. Biol Cybern 44:67–77PubMedCrossRefGoogle Scholar
  21. Hore J, Watts S, Vilis T (1992) Constraints on arm position when pointing in three dimensions: Donders’ law and the Fick gimbals strategy. J Neurophysiol 68:374–383PubMedGoogle Scholar
  22. Hore J, Watts S, Tweed D (1994) Arm position constraints when throwing in three dimensions. J Neurophysiol 72:1171–1180PubMedGoogle Scholar
  23. Humphrey DR (1979) On the organization of visually directed reaching: contributions by nonprecentral motor areas. In: Talbott RE, Humphrey DR (eds) Posture and movement. Raven Press, New York, NY, pp 51–112Google Scholar
  24. Jeannerod M (1988) The neural and behavioral organization of goal-directed movements. Oxford University Press, OxfordGoogle Scholar
  25. Jeannerod M (1990) The representation of the goal of an action and its role in the control goal-directed movements. In: Schwartz EL (ed) Computational neuroscience. MIT Press, Cambridge, MA, pp 352–368Google Scholar
  26. Kaminski T, Gentile AM (1986) Joint control strategies and hand trajectories in multijoint pointing movements. J Mot Behav 18:261–278PubMedGoogle Scholar
  27. Lee D, Port NL, Georgopoulos AP (1997) Manual interception of moving targets II. On-line control of overlapping submovements. Exp Brain Res 116:421–433PubMedCrossRefGoogle Scholar
  28. Marotta JJ, Medendorp WP, Crawford JD (2003) Kinematic rules for upper and lower arm contributions to grasp orientation. J. Neurophysiol 90:3816–3827PubMedCrossRefGoogle Scholar
  29. Medendorp WP, Crawford JD, Henriques DYP, Van Gisbergen JAM, Gielen CCAM (2000) Kinematic strategies for upper arm-forearm coordination in three dimensions. J Neurophysiol 84:2302–2816PubMedGoogle Scholar
  30. Miller LE, Theeuwen M, Gielen CCAM (1992) The control of arm pointing movements in three dimensions. Exp Brain Res 90:415–426PubMedCrossRefGoogle Scholar
  31. Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227PubMedCrossRefGoogle Scholar
  32. Nakano E, Imamuzu H, Osu R, Uno R, Gomi H, Yoshioka T, Kawato M (1999) Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. J Neurophysiol 81:2140–2155PubMedGoogle Scholar
  33. Nelson WL (1983) Physical principles for economies of skilled movements. Biol Cybern 46:135–147PubMedCrossRefGoogle Scholar
  34. Richardson MJE, Flash T (2002) Comparing smooth arm movements with the two-thirds power law and the related segmented-control hypothesis. J Neurosci 22:8201–8211PubMedGoogle Scholar
  35. Schaal S, Sternad D (2001) Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements. Exp Brain Res 136:60–72PubMedCrossRefGoogle Scholar
  36. Soechting JF, Flanders M (1998) Movement planning: kinematics, dynamics, or both? In: Harris L, Jenkin M (eds) Vision and action. Cambridge University Press, New York, NY, pp 332–349Google Scholar
  37. Soechting JF, Lacquaniti F (1981) Invariant characteristics of a pointing movement in man. J Neurosci 1:710–720PubMedGoogle Scholar
  38. Soechting JF, Terzuolo CA (1988) Sensorimotor transformations underlying the organization of arm movements in three-dimensional space. Can J Physiol Pharmacol 66:502–507PubMedGoogle Scholar
  39. Soechting JF, Buneo CA, Herrmann U, Flanders M (1995) Moving effortlessly on three dimensions: does Donders’ Law apply to arm movements? J Neurosci 15:6271–6280PubMedGoogle Scholar
  40. Straumann D, Haslwanter T, Hepp-Reymond MC, Hepp K (1991) Listing’s law for the eye, head and arm movements and their synergistic control. Exp Brain Res 86:209–215PubMedCrossRefGoogle Scholar
  41. Todorov E, Jordan MI (1998) Smoothness maximization along a predefined path accurately predicts speed profiles of complex arm movements. J Neurophysiol 80:696–714PubMedGoogle Scholar
  42. Torres EB, Zipser D (2002) Reaching to grasp with a multi-jointed arm. I. Computational model. J Neurophysiol 88:2355–2367PubMedCrossRefGoogle Scholar
  43. Tweed D, Vilis T (1987) Implications of rotational kinematics for the oculomotor systems in three dimensions. J Neurophysiol 58:832–849PubMedGoogle Scholar
  44. Tweed D, Vilis T (1990) Geometric relations of eye position and velocity vectors during saccades. Vision Res 30:111–127PubMedCrossRefGoogle Scholar
  45. Uno Y, Kawato M, Suzuki R (1989) Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model. Biol Cybern 61:89–101PubMedCrossRefGoogle Scholar
  46. Van Beers RJ, Wolpert DM, Haggard P (2002) When feeling is more important than seeing in sensorimotor adaptation. Curr Biol 12:834–837PubMedCrossRefGoogle Scholar
  47. Vilis T, Tweed D (1991) What can rotational kinematics tell us about the neural control of eye movements? In: Humphrey DR, Freund H-J (eds) Motor control: concepts and issues. Wiley, New York, NYGoogle Scholar
  48. Viviani P, Flash F (1995) Minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning. J Exp Psychol Hum Percept Perform 17:32–53Google Scholar
  49. Viviani P, Terzuolo C (1982) Trajectory determines movement dynamics. J Neurosci 7:431–437Google Scholar
  50. Wang X (1998) Three-dimensional kinematic analysis of influence of hand orientation and joint limits on the control of arm postures and movements. Biol Cybern 80:449–463CrossRefGoogle Scholar
  51. Wang X, Verriest JP (1998) A geometric algorithm to predict the arm reach posture for computer-aided ergonomic evaluation. J Vis Comput Anim 9:33–47CrossRefGoogle Scholar
  52. Westheimer G (1957) Kinematics of the eye. J Optic Soc Am 47:967–974CrossRefGoogle Scholar
  53. Wolpert DM, Ghahramani Z, Jordan MI (1995) Are arm trajectories planned in kinematic or dynamic coordinates? An adaptation study. Exp Brain Res 103:460–470PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • D. G. Liebermann
    • 1
    • 2
    Email author
  • A. Biess
    • 2
  • C. C. A. M. Gielen
    • 3
  • T. Flash
    • 2
  1. 1.Department of Physical Therapy, Sackler Faculty of MedicineTel-Aviv UniversityRamat AvivIsrael
  2. 2.Department of Applied Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  3. 3.Department of Medical Physics and BiophysicsUniversity of NijmegenEZ NijmegenThe Netherlands

Personalised recommendations