ANTHROPOMETRY - Biomechanics and Motor Control of Human Movement - page 100

can be calculated. Care must be taken when ω z approaches 0 or reverses its
polarity, because R , as calculated by Equation (4.16 a ), becomes indeterminate
or falsely approaches very large values. In practice, we have found errors
become significant when ω z falls below 0.5 r/s.

4.3 MUSCLE ANTHROPOMETRY

Before we can calculate the forces produced by individual muscles during
normal movement, we usually need some dimensions from the muscles them-
selves. If muscles of the same group share the load, they probably do so
proportionally to their relative cross-sectional areas. Also, the mechanical
advantage of each muscle can be different, depending on the moment arm
length at its origin and insertion, and on other structures beneath the muscle
or tendon that alter the angle of pull of the tendon.

4.3.1 Cross-Sectional Area of Muscles
The functional or physiologic cross-sectional area (PCA) of a muscle is a
measure of the number of sarcomeres in parallel with the angle of pull of the
muscles. In pennate muscles, the fibers act at an angle from the long axis and,
therefore, are not as effective as fibers in a parallel-fibered muscle. The angle
between the long axis of the muscle and the fiber angle is called pennation
angle . In parallel-fibered muscle, the PCA is:

m
dl

cm 2 PCA = (4.17)

where m = mass of muscle fibers, grams

density of muscle, g / cm 3 , 1 . 056 g / cm 3

d = =

l = length of muscle fibers, centimeters

In pennate muscles, the physiological cross-sectional area becomes:

m cos θ
dl

cm 2 PCA = (4.18)

where: θ is the pennation angle, which increases as the muscle shortens.
Wickiewicz et al. (1983), using data from three cadavers, measured muscle
mass, fiber lengths, and pennation angle for 27 muscles of the lower extremity.
Representative values are given in Table 4.3. The PCA as a percentage of the
total cross-sectional area of all muscles crossing a given joint is presented in
Table 4.4. In this way, the relative potential contribution of a group of agonist
muscles can be determined, assuming that each is generating the same stress.
Note that a double-joint muscle, such as the gastrocnemius, may represent
different percentages at different joints because of the different total PCA of
all muscles crossing each joint.