Fundamentals of Biomechanics

156 FUNDAMENTALS OF BIOMECHANICS
Figure 6.18. The mechanical work done on a weight in this rowing exercise is the product of the force and the
displacement.
load is constant over the duration of the
movement. Calculus is necessary to calculate
the work of the true time-varying
forces applied to weights in exercises. This
example also assumes that the energy losses
in the pulleys are negligible as they
change the direction of the force created by
the patient.
Note that mechanical work can only be
done on an object when it is moved relative
to the line of action of the force. A more
complete algebraic definition of mechanical
work in the horizontal (x) direction that
takes into account the component of motion
in the direction of the force on an object
would be W = (F cos ) • d x . For example, a
person pulling a load horizontally on a dolly
given the data in Figure 6.19 would do
435 Nm or Joules of work. Only the horizontal
component of the force times the displacement
of object determines the work
done. Note also that the angle of pull in this
example is like the muscle angle of pull analyzed
earlier. The smaller the angle of pull,
the greater the horizontal component of the
force that does work to move the load.
The vertical component of pull does
not do any mechanical work, although it
may decrease the weight of the dolly or
load and, thereby decrease the rolling friction
to be overcome. What is the best angle
to pull in this situation depends on many
factors. Factoring in rolling friction and the
strength (force) ability in various pulling
postures might indicate that a higher angle
of pull that doesn't maximize the horizontal
force component may be “biomechanically”
effective for this person. The inertia of
the load, the friction under the person's
feet, and the biomechanical factors of
pulling from different postures all interact
to determine the optimal angle for pulling
an object. In fact, in some closed kinematic
chain movements (like cycling) the optimal
direction of force application does not always
maximize the effectiveness or the
component of force in the direction of motion
(Doorenbosch et al., 1997).
Mechanical work does not directly correspond
to people's sense of muscular effort.
Isometric actions, while taking considerable
effort, do not perform mechanical