Multivariable static ankle mechanical impedance with active muscles

Hyunglae Lee, Patrick Ho, Mohammad Rastgaar, Hermano Igo Krebs, Neville Hogan

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


This paper reports quantification of multivariable static ankle mechanical impedance when muscles were active. Repetitive measurements using a highly backdrivable therapeutic robot combined with robust function approximation methods enabled reliable characterization of the nonlinear torque-angle relation at the ankle in two coupled degrees of freedom simultaneously, a combination of dorsiflexion-plantarflexion and inversion-eversion, and how it varied with muscle activation. Measurements on 10 young healthy seated subjects quantified the behavior of the human ankle when muscles were active at 10% of maximum voluntary contraction. Stiffness, a linear approximation to static ankle mechanical impedance, was estimated from the continuous vector field. As with previous measurements when muscles were maximally relaxed, we found that ankle stiffness was highly direction-dependent, being weakest in inversion/eversion. Predominantly activating a single muscle or co-contracting antagonistic muscles significantly increased ankle stiffness in all directions but it increased more in the sagittal plane than in the frontal plane, accentuating the relative weakness of the ankle in the inversion-eversion direction. Remarkably, the observed increase was not consistent with simple superposition of muscle-generated stiffness, which may be due to the contribution of unmonitored deep ankle muscles. Implications for the assessment of neuro-mechanical disorders are discussed.

Original languageEnglish (US)
Article number12
Pages (from-to)44-52
Number of pages9
JournalIEEE Transactions on Neural Systems and Rehabilitation Engineering
Issue number1
StatePublished - Jan 2014
Externally publishedYes


  • Ankle joint
  • Ankle joint stiffness
  • Ankle stiffness
  • Human ankle
  • Impedance structure
  • Multivariable impedance
  • Multivariable stiffness
  • Stiffness anisotropy

ASJC Scopus subject areas

  • Internal Medicine
  • Neuroscience(all)
  • Biomedical Engineering


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