Experimental Brain Research

, Volume 196, Issue 3, pp 439–451 | Cite as

Joint-level kinetic redundancy is exploited to control limb-level forces during human hopping

  • Jasper T. Yen
  • Arick G. Auyang
  • Young-Hui ChangEmail author
Research Article


Compensatory mechanisms can take advantage of neuromechanical redundancy to meet global task goals in spite of local injuries or perturbations. We hypothesized that joint-level kinetic redundancy is also exploited during intact, unperturbed human locomotion to accomplish limb-level force goals. The limb-level force goals of hopping in place at a constant frequency are minimizing cycle-to-cycle variance of vertical ground reaction force and varying horizontal (fore-aft) ground reaction force to make backward and forward corrections in position from cycle to cycle. Uncontrolled Manifold analysis of joint torque variance showed that hoppers exploited redundancy to minimize vertical force variance at landing, mid-stance, and takeoff, and to vary horizontal force at landing and takeoff. Timing fluctuations, however, increased vertical force variance. We conclude that joint torque variance is not random noise, but has functional relevance and is purposefully structured to meet specific locomotor goals.


Biomechanics Neuromechanics UCM Locomotion Spring-mass model 



The authors thank Dr. Lena Ting and members of the Neuromechanics Laboratory. We also thank Dr. T. Richard Nichols and the members of the Comparative Neuromechanics Laboratory for helpful comments in preparing the manuscript. This work was funded by National Science Foundation IGERT DGE-0333411 and National Science Foundation GRFP fellowship awarded to JTY.

Supplementary material

Supplementary video Animation 1 A representative subject’s joint torque variability at each 1% time slice during stance phase of hopping in place. a Each dot represents the torque vector (combination of ankle, knee, and hip torque) in 3-D joint torque space from one hop at one instant in time (t = %stance phase). The camera view is orientated such that the UCMV plane (i.e. the manifold of vertical force-equivalent joint torque combinations) spans across the horizon and into the page. The camera view is rotating and translating as the animation advances through each time slice to keep the data cloud centered and the UCMV plane oriented horizontally. The radii defining the principle axes of the red ellipse are calculated as two standard deviations of all joint torque combinations shown for that time slice. This ellipse is aligned along the UCMV plane at landing, mid-stance, and takeoff. b Sagittal plane stick figure representing the subject’s leg (black) and ground reaction force (green) at each corresponding time slice. c Joint torque variance component that stabilizes vertical force (GEV) and destabilizes vertical force (NGEV). d Index of Motor Abundance for vertical force calculated as the difference between GEV and NGEV divided by their sum. The vertical lines in c and d correspond to the current time slices represented in a and b (MPG 1442 kb)


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Jasper T. Yen
    • 1
  • Arick G. Auyang
    • 2
  • Young-Hui Chang
    • 1
    • 2
    Email author
  1. 1.Department of Biomedical EngineeringGeorgia Institute of Technology, Emory UniversityAtlantaUSA
  2. 2.Comparative Neuromechanics Laboratory, School of Applied PhysiologyGeorgia Institute of TechnologyAtlantaUSA

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