KINETICS: FORCES AND MOMENTS OF FORCE - Biomechanics and Motor Control of Human Movement - page 131

corner of the closed-link parallelogram consisting of the two lower limbs
and the pelvis. The hip abductor/adductor moments have been shown to be
totally dominant in side-by-side standing (Winter et al., 1996), while the ankle
invertor/evertor moments play a negligible role in balance control.
The validity of the inverted pendulum model is evident in the validity
of Equations (5.9) and (5.10). As COP and COM are totally independent
measures, then the correlation of (COP - COM) with C OM will be a measure
of the validity of this simplified model. Recent validations of the model
during quiet standing (Gage et al., 2004) showed a correlation of r =− 0 . 954

in the anterior/posterior (A/P) direction and r 0 . 85 in the medial/lateral

(M/L) direction. The lower correlation in the M/L direction was due to the
fact that the M/L COM displacement was about 45% of that in the A/P
direction. Similar validations have been made to justify the inverted pendulum
model during initiation and termination of gait (Jian et al., 1993); correlations
averaged - 0.94 in both A/P and M/L directions.

=−

5.3 BONE-ON-BONE FORCES DURING DYNAMIC CONDITIONS

Link-segment models assume that each joint is a hinge joint and that the
moment of force is generated by a torque motor. In such a model, the reaction
force calculated at each joint would be the same as the force across the sur-
face of the hinge joint (i.e., the bone-on-bone forces). However, our muscles
are not torque motors; rather, they are linear motors that produce additional
compressive and shear forces across the joint surfaces. Thus, we must over-
lay on the free-body diagram these additional muscle-induced forces. In the
extreme range of joint movement, we would also have to consider the forces
from the ligaments and anatomical constraints. However, for the purposes of
this text, we will limit the analyses to estimated muscle forces.

5.3.1 Indeterminacy in Muscle Force Estimates
Estimating muscle force is a major problem, even if we have good estimates of
the moment of force at each joint. The solution is indeterminate, as initially
described in Section 1.3.5. Figure 5.18 demonstrates the number of major
muscles responsible for the sagittal plane joint moments of force in the lower
limb. At the knee, for example, there are nine muscles whose forces create
the net moment from our inverse solution. The line of action of each of these
muscles is different and continuously changes with time. Thus, the moment
arms are also dynamic variables. Therefore, the extensor moment is a net
algebraic sum of the cross product of all force vectors and moment arm
vectors,

Nf

N e

M j (t ) = F ei (t ) × d ei (t ) − F fi (t ) × d fi (t ) (5.11)

= =

i 1 i 1