The difference between stiffness and quasi-stiffness in the context of biomechanical modeling

Elliott J. Rouse*, Robert D. Gregg, Levi J. Hargrove, Jonathon W. Sensinger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

84 Scopus citations


The ankle contributes the majority of mechanical power during walking and is a frequently studied joint in biomechanics. Specifically, researchers have extensively investigated the torque-angle relationship for the ankle during dynamic tasks, such as walking and running. The slope of this relationship has been termed the 'quasi-stiffness.' However, over time, researchers have begun to interchange the concepts of quasi-stiffness and stiffness. This is an especially important distinction as researchers currently begin to investigate the appropriate control systems for recently developed powered prosthetic legs. The quasi-stiffness and stiffness are distinct concepts in the context of powered joints, and are equivalent in the context of passive joints. The purpose of this paper is to demonstrate the difference between the stiffness and quasi-stiffness using a simple impedance-controlled inverted pendulum model and a more sophisticated biped walking model, each with the ability to modify the trajectory of an impedance controller's equilibrium angle position. In both cases, stiffness values are specified by the controller and the quasi-stiffness are shown during a single step. Both models have widely varying quasi-stiffness but each have a single stiffness value. Therefore, from this simple modeling approach, the differences and similarities between these two concepts are elucidated.

Original languageEnglish (US)
Article number6365248
Pages (from-to)562-568
Number of pages7
JournalIEEE Transactions on Biomedical Engineering
Issue number2
StatePublished - 2013


  • Ankle impedance
  • biped model
  • inverted pendulum
  • prosthetics
  • quasi-stiffness
  • stiffness

ASJC Scopus subject areas

  • Biomedical Engineering


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