Page 256 - Handbook of Biomechatronics

Lower-Limb Prosthetics 251

The vertical excursion of the center of mass is not decreased by pelvic
obliquity or stance-phase knee flexion, which we believe provide shock
absorption to the system (Fig. 4B) (Gard and Childress, 1997a,b, 2000;
Childress & Gard, 1999). Most of the above theoretical results have been
confirmed by empirical data (Miff, 2000).
Thus, a shock-absorbing element must be added to the above model
(Fig. 4A) in order to stand for the natural shock absorption function pro-
vided by the knee flexion, pelvic obliquity, ankle plantar flexion, and the
viscoelastic properties of the tissues.
For the above purpose, Bertos (2006) and Bertos et al. (2005) proposed a
shock absorption model of walking (Eq. 2, Fig. 5):

B k
s +
y m sðÞ M e M e
¼ (2)
y b sðÞ 2 B k
s + s +
M e M e
where y m is the subject’s vertical BCOM trajectory, y b the vertical trajectory
of the rocker-based inverted pendulum model, k the stiffness, B the viscous
damping, and M e the effective mass of the body during the stance phase of
walking.

y m
M e

k B
V

y b
Fig. 5 Shock-absorption model for able-bodied human walking. Able-bodied human
walking was modeled with a second-order mechanical vibration system. y b is the trajec-
tory that a rocker-based inverted pendulum walking with no shock absorption would
follow. y m is the trajectory of the BCOM of one able-bodied walker (which includes
any shock absorption effect), M e the effective mass of the subject during the stance
phase of walking, k is the stiffness, B the viscous damping, and v the average forward
speed of walking. (From Bertos, G.A., Childress, D.S., Gard, S.A., 2005. The vertical mechan-
ical impedance of the locomotor system during human walking with applications in reha-
bilitation. In: IEEE 9th International Conference on Rehabilitation Robotics. IEEE, New York,
pp. 380–383.)