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Author Biess, A.; Flash, T.; Liebermann, D.G. url  openurl
  Title Riemannian geometric approach to human arm dynamics, movement optimization, and invariance Type Journal Article
  Year 2011 Publication Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Abbreviated Journal Phys Rev E Stat Nonlin Soft Matter Phys  
  Volume 83 Issue 3 Pt 1 Pages 031927  
  Keywords Arm/*physiology; Biomechanics; Computer Simulation; Humans; Kinetics; Male; Models, Biological; Models, Statistical; Models, Theoretical; *Movement; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Torque  
  Abstract We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparameterized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system.  
  Address Bernstein Center for Computational Neuroscience, DE-37073 Gottingen, Germany. armin@nld.ds.mpg.de  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume (down) Series Issue Edition  
  ISSN 1539-3755 ISBN Medium  
  Area Expedition Conference  
  Notes PMID:21517543 Approved no  
  Call Number Serial 29  
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Author Liebermann, D.G.; Krasovsky, T.; Berman, S. url  doi
openurl 
  Title Planning maximally smooth hand movements constrained to nonplanar workspaces Type Journal Article
  Year 2008 Publication Journal of Motor Behavior Abbreviated Journal J Mot Behav  
  Volume 40 Issue 6 Pages 516-531  
  Keywords Adaptation, Physiological; Adult; Algorithms; Female; Hand/*physiology; Humans; *Intention; Kinesthesis/*physiology; Male; Models, Statistical; Movement/*physiology; Psychomotor Performance/*physiology; Reference Values; Writing  
  Abstract The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.  
  Address Department of Physical Therapy, The Stanley Steyer School of Health Professions, Sackler Faculty of Medicine, Tel Aviv University, Israel. dlieberm@post.tau.ac.il  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume (down) Series Issue Edition  
  ISSN 0022-2895 ISBN Medium  
  Area Expedition Conference  
  Notes PMID:18980905 Approved no  
  Call Number Serial 33  
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