INTRODUCTION - Injury Biomechanics and Control: Optimal Protection from Impact - page 3

J 2

0 J 1

FIGURE 1.1 Trade-off curve.

criteria can be reduced against this design. Designs with the values of the
performance criteria represented by points below the trade-off curve are
unfeasible. Any point on the trade-off curve corresponds to a design which
is optimal with respect to one of the criteria, provided that the other cri-
terion is constrained. It is impossible to improve the design of the isolator
with respect to both criteria J 1 and J 2 against any design represented by a
point on the trade-off curve.
During the design process, limiting performance analysis may be fol-
lowed by the parametric synthesis of the isolation system. At this stage, a
particular design configuration of the isolation system replaces the generic
control force used in the limiting performance analysis and the design
parameters are determined by minimizing the performance index. If the
minimum value of the performance index is close to the value that character-
izes the limiting performance, this design can be recommended for practical
implementation because it is near optimal. If the discrepancy between the
limiting performance characteristic and the minimal value of the perfor-
mance index for the isolator with the selected design configuration is large,
the design configuration should be changed and the parametric optimization
repeated.
The problems in this topic are formulated using simple mathematical
models intended to simulate the mechanical response of a human body to
impact loads. Using the response characteristics of these models, quantita-
tive measures of the injury risk are defined. Of course, simple mathematical
models with only a few degrees of freedom cannot fully simulate the com-
plex response of a body to impact. At the first stage of the analysis, use of
these simple models is justified because the solutions can be obtained ana-
lytically or numerically with a minimum of effort and the findings are easy
to interpret. The control strategy obtained by using a simplified model can
then be verified and adjusted by using multibody or finite-element mathe-
matical models that may have a large number of degrees of freedom and
parameters. The more complicated the model, the more difficult it is to find
an optimal solution.