MUSCLE MECHANICS - Biomechanics and Motor Control of Human Movement - page 240

The resultant curve is actually a surface, which here is represented only for
the maximum contraction condition. The more normal contractions are at a
fraction of this maximum, so that surface plots would be required for each
level of muscle activation, say at 75%, 50%, and 25%.
9.2.4 Combining Muscle Characteristics with Load
Characteristics: Equilibrium
Muscles are the only motors in the human system, and when they are active,
they must be in equilibrium with their load. The load can be static, for
example, when holding a weight against gravity or applying a static force
against a fixed object (e.g., a wall, the floor), or in an isometric cocontrac-
tion, where one muscle provides the load of the other. Or the load may be
dynamic and the muscles are accelerating or decelerating an inertial load or
overcoming the friction of a viscous load. In the vast majority of voluntary
movements, there is a mixture of static and dynamic load. The one condition
that is satisfied during the entire movement is that of equilibrium: at any
given point in time the operating point will be the intersection of the muscle
and load characteristics. In a dynamic movement, this operating or equilib-
rium point will be continuously changing. In Chapter 5, an equilibrium was
recognized every time the equations of motion were written: Equations (5.3)
and subsequent Examples 5.1, 5.2, 5.3, and 5.4. However, such equations
recognized the net effect of all muscles acting at each joint and represented
them as a torque motor without any concern about the internal characteristics
of the muscles themselves. These are now examined.
Consider a muscle that is contracting against a springlike load that can
have a linear or a nonlinear force-length characteristic. Figure 9.14 a plots
the force-length characteristics of a muscle at four different levels of activa-
tion, along with the linear and nonlinear characteristics of the spring loads.
Assume that the muscle is at a length l 1 longer than the resting length,
l 0 when the spring is at rest. The linear spring is compressed with a 50%
muscle contraction, the equilibrium point a is reached, and the muscle will
shorten from l 1 to l 2 . When the nonlinear spring is compressed with a 50%
contraction, the muscle shortens from l 1 to l 3 and the equilibrium point b
is reached. If a gravitational load is lifted by the elbow flexors, the flexor
muscles have the characteristics shown in Figure 9.14 b . Starting with the
forearm lowered to the side so that it is vertical, the initial equilibrium point
is a . Then, as the flexors contract and shorten, equilibrium points b through
e are reached. Finally, as the muscles are activated 100%, the equilibrium
point, e , is reached. During the transient conditions en route from a to e ,
the equilibrium point will also move about on the force-velocity characteris-
tics, tracing a three-dimensional locus. The concept of dynamic equilibrium
is now addressed.
We use the data from a typical walking stride to plot the time course
of the contractions of the muscles about the ankle. Because the angular