Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 222-230).Ankle mechanical impedance, which is a dynamic relationship between angular displacement and the corresponding torque at the ankle joint, plays a key role in natural interaction of the lower-extremity with the environment. The human ankle is a biomechanically complex joint consisting of three bones with non-intersecting anatomical axes, and its motions under normal motor control and function are predominantly in multiple degrees-of-freedom (DOF). This thesis provides a quantitative characterization of multivariable ankle mechanical impedance of young healthy subjects in two DOF, both in the sagittal and the frontal planes. Multi-variable studies provide several important characteristics of the human ankle, unavailable from single DOF studies, which have mostly been in the sagittal plane. Three characterization methods were developed to study ankle mechanical impedance in different conditions: 1) steady-state static, 2) steady-state dynamic, and 3) transient dynamic. First, steady-state static ankle mechanical impedance, which is a non-linear torque and angle relationship at the ankle, was characterized in two coupled DOFs over the normal range of motion. Robust vector field approximation methods based on thin-plate spline smoothing with generalized cross validation showed that static ankle impedance is highly direction dependent, being weak in the inversion-eversion direction. Activating a single muscle or co-contracting antagonistic muscles significantly increased static ankle impedance in all directions but more in the dorsiflexion-plantarflexion direction than the inversion-eversion. Static ankle behavior in both relaxed and active muscles was close to that of a passive elastic system. Second, steady-state dynamic ankle mechanical impedance was characterized based on linear time-invariant multi-input multi-output stochastic system identification methods. A highly linear relationship between muscle activation and ankle impedance was identified in all movement directions in the sagittal and frontal planes. Furthermore, small coupling between 2 DOF and energetic passivity were observed at different levels of muscle activation and over a wide frequency range. Third, transient dynamic ankle mechanical impedance was characterized during walking on a treadmill, across the gait cycle from the end of stance phase through swing and to early stance phase. Modified linear time-varying ensemble based system identification methods enabled reliable identification of transient behavior of the ankle. In both DOF, damping and stiffness decreased at the end of stance phase before the toe-off, remained relatively constant during the whole swing phase, and substantially increased around the heel-strike. Quantitative characterization of multi-variable ankle mechanical impedance of young healthy subjects will shed light on its roles in lower-extremity motor function. It will serve as a baseline for clinical studies in patients, especially those with neurological disorders, as well as studies of elderly subjects, whose biomechanical and neurological properties may be altered due to impairments and/or aging. Finally, the methods presented in this thesis are intended to be sufficiently general to be applicable to any multi-joint system or single joint having multiple DOF.by Hyunglae Lee.Ph.D
