KINETICS: FORCES AND MOMENTS OF FORCE - Biomechanics and Motor Control of Human Movement - page 133

Figure 5.19 Anatomical drawing of foot and ankle during the pushoff phase of a
runner. The tendons for the major plantarflexors as they cross the ankle joint are shown,
along with ankle and ground reaction forces.

as follows for the five major muscles of the extensor group acting at the
ankle:

5

M a (t ) = PCA i × S ei (t ) × d ei (t ) (5.12)

i = 1

Since the PCA for each muscle is known and d ei can be calculated for
each point in time, the stress, S ei (t ) can be estimated.
For this model, the ankle joint center is assumed to remain fixed and
is located as shown in Figure 5.20. The location of each muscle origin and
insertion is defined from the anatomical markers on each segment, using polar
coordinates. The attachment point of the i th muscle is defined by a distance
R i from the joint center and an angle θ mi between the segment's neutral
axis and the line joining the joint center to the attachment point. Thus, the
coordinates of any origin or insertion at any instant in time are given by:

X mi (t ) = X i (t ) + R i cos[ θ mi (t ) + θ s (t ) ] (5.13 a )

Y mi (t ) = Y i (t ) + R i sin[ θ mi (t ) + θ s (t ) ]

(5.13 b )