Page 255 - Handbook of Biomechatronics

250 Georgios A. Bertos and Evangelos G. Papadopoulos

mechanisms provided by pelvic obliquity and stance-phase knee flexion into
the prosthesis design. We might be able to functionally simulate the shock
absorption action with devices, which will provide close to normal walking
shock absorption effect. We hope that by incorporating the right shock
absorption into the prosthesis, the gait will be closer to normal, safer, and
more comfortable to the amputee.
Gard and Childress (1997a,b) have introduced an inverted pendulum
model with rockers (Fig. 4A). The vertical excursion of the BCOM, h,
can be calculated by the constraints imposed by the legs and the “roll-over
shape”:

S 2
h ¼ l (1)
8Lρ

where S l is the step length, L is the anatomical leg length, and ρ is a dimen-
sionless constant approximately equal to 1.7.

200 Rocker-based inverted pendulum model
Theoretical h
Vertical displacement (mm) Trunk trajectory without knee flexion and pelvic obliquity
trunk trajectory 100
L
L v 0
r 200
Walking
surface 100 Measured trunk trajectory

0
Virtual 0 200 400 600 800 1000 1200 1400
walking surface Fore-Aft displacement (mm)
(A) (B)
Fig. 4 The rocker-based inverted pendulum of walking. (A) The rocker-based inverted
pendulum model of walking. L is the anatomical leg length, r is the foot rocker radius, L v
is the virtual leg length (approximately the height of the subject), S l is the step length,
and h is the vertical excursion of the body center of mass. (B) The model predicts a ver-
tical excursion (dotted line) comparable with what we measured for able-bodied
ambulators (solid line). The inverted pendulum with rockers model predicts the peak-
to-peak vertical excursion of the BCOM. The pelvic obliquity and stance-phase knee flex-
ion introduce a phase shift and provide shock absorption to the system. ((A) Gard, S.A.,
Childress, D.S., 2001. What determines the vertical displacement of the body during normal
walking? J. Prosthet. Orthot. 13(3), 64–67; (B) From Gard, S.A., Childress, D.S., 2000. What
determines vertical motion of the body during normal gait. Paper Presented at the 5th
Annual Meeting of the Gait and Clinical Movement Analysis Society (GCMAS), Rochester,
MN, April 12–15.)