ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

second derivatives ( ) of .
Joint torques ( ) were computed by a top-bottom process based on iterative Newton-
Euler equations (Luh et al, 1980) in which inertial parameters were provided by tables
from de Leva (1996). Numerical optimizations were computed during the knee flexion
phase of the movement. We specified fifty-one connecting points to compute the
quantic splines.
4. RESULTS
Horizontal and vertical measured ground reaction forces were compared with those
computed by classical top-down inverse dynamics and optimal inverse dynamic
approaches (see Fig. 2). Large differences were observed between measured forces and
forces computed using classical inverse dynamic equations. The maximal plot deviation
was larger than 50N. In contrast, forces computed using dynamic optimization showed
similar patterns for each of the fifty-one connecting points compared with the measured
forces. The unknown joint accelerations were perfectly adjusted to match the discrete
force plate measurements. As a result, the residual force was not observed while using
our dynamic optimization approach.
Fig. 2: Horizontal (left) and vertical (right) ground reaction forces measured by the force plate (continuous
black lines) and computed using classical top-bottom inverse dynamics (red dotted lines) and optimal inverse
dynamics (black dots) approaches.
Optimal joint accelerations and joint torques showed smoother patterns compared with
those computed with the classical method (see Fig. 3). Joint acceleration values were
underestimated by the classical method. As an example, the knee acceleration amplitude
was 60% larger while it was computed using our optimization approach (see Tab. 1).
Table 1: Amplitude of the joint accelerations and joint torques computed using classical top-bottom inverse
dynamics and optimal inverse dynamics approaches.
Classical approach Optimal approach
Joint acceleration amplitude (rad.s -2 )
Hip 4.56 4.9
Knee 5.6 9.16
Ankle
Joint torques amplitude (N.m)
7.6 8.4
Hip 110 98
Knee 115 110
Ankle 93 47