Fundamentals of Biomechanics

144 FUNDAMENTALS OF BIOMECHANICS
Figure 6.9. Right-angle trigonometry is used to find the components of a vector like the iliopsoas muscle force illustrated.
Notice the muscle force is resolved into components along the longitudinal axis of the femur and at right
angles to the femur. The right angle component is the force that creates rotation (F R ).
understand where the largest changes occur
and what angles of force application are
best. Let's look at a horizontal component
of a force in two dimensions. This is analogous
to our iliopsoas example, or how any
force applied to an object will favor the horizontal
over the vertical component. A cosine
function is not a linear function like
our spring example in chapter 2. Figure 6.10
plots the size of the cosine function as a percentage
of the resultant for angles of pull
from 0 to 90º.
A 0º (horizontal) angle of pull has no
vertical component, so all the force is in the
horizontal direction. Note that, as the angle
of pull begins to rise (0 to 30º), the cosine or
horizontal component drops very slowly,
so most of the resultant force is directed
horizontally. Now the cosine function begins
to change more rapidly, and from 30 to
60º the horizontal component has dropped
from 87 to 50% the size of the resultant
force. For angles of pull greater than 60º, the
cosine drops off very fast, so there is a dra-