Multivariable static ankle mechanical impedance with relaxed muscles

Hyunglae Lee, Patrick Ho, Mohammad A. Rastgaar, Hermano I. Krebs, Neville Hogan

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


Quantitative characterization of ankle mechanical impedance is important to understand how the ankle supports lower-extremity functions during interaction with the environment. This paper reports a novel procedure to characterize static multivariable ankle mechanical impedance. An experimental protocol using a wearable therapeutic robot, Anklebot, enabled reliable measurement of torque and angle data in multiple degrees of freedom simultaneously, a combination of inversion-eversion and dorsiflexion-plantarflexion. The measured multivariable torque-angle relation was represented as a vector field, and approximated using a method based on thin-plate spline smoothing with generalized cross validation. The vector field enabled assessment of several important characteristics of static ankle mechanical impedance, which are not available from prior single degree of freedom studies: the directional variation of ankle mechanical impedance, the extent to which the ankle behaves as a spring, and evidence of uniquely neural contributions. The method was validated by testing a simple physical "mock-up" consisting of passive elements. Experiments with young unimpaired subjects quantified the behavior of the maximally relaxed human ankle, showing that ankle mechanical impedance is spring-like but strongly direction-dependent, being weakest in inversion. Remarkably, the analysis was sufficiently sensitive to detect a subtle but statistically significant deviation from spring-like behavior if subjects were not fully relaxed. This method may provide new insight about the function of the ankle, both unimpaired and after biomechanical or neurological injury.

Original languageEnglish (US)
Pages (from-to)1901-1908
Number of pages8
JournalJournal of Biomechanics
Issue number10
StatePublished - Jul 7 2011
Externally publishedYes


  • Ankle joint
  • Ankle joint stiffness
  • Ankle mechanical impedance
  • Human ankle
  • Multivariable stiffness

ASJC Scopus subject areas

  • Biophysics
  • Biomedical Engineering
  • Orthopedics and Sports Medicine
  • Rehabilitation


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