The Muscular System 47is called the mechanical advantage (EA/RA). If the
effort arm and resistance arm were of equal length,
then this would yield a mechanical advantage of 1
and would mean that if you wanted to hold a 15-
pound (6.8-kilogram) weight, it would take about 15
pounds of muscle force to counterbalance this weight.
However, throughout most human limbs, third-class
levers predominate, where EA is much smaller than
RA as shown in figure 2.11A. Since in third-class levers
the effort is located between the axis and resistance,
RA always must be greater than EA and the mechani-
cal advantage must always be less than 1 (figure
2.11B). Furthermore, muscle attachments are usually
very close to the joint (axis), making EA very small
relative to RA with mechanical advantages often 0.1 or
even lower (Smith, Weiss, and Lehmkuhl, 1996).
This gives the limbs very low mechanical advan-
tage where very large forces have to be generated to
overcome relatively small resistances. For example,
as shown in figure 2.11C, about 79 pounds (351 N)
of force must be exerted by the biceps brachii to
counterbalance holding a 10-pound (4.5-kilogram)
weight in the hand. This calculation, in contrast to
the calculation shown in figure 2.11A, takes into
account the contribution of the weight of the fore-
arm, as well as the weight of the dumbbell. When
doing a calculation where the external weight is
large (e.g., lifting another dancer), the weight of
the arm may be excluded for purposes of simplicity
and because its contribution to the torque produced
by the resistance is relatively small. However, in
other instances, such as when lifting a lower limb in
dance class (e.g., side extension), consideration of
the weight of this limb is vital, and it is primarily the
torque produced by the weight of the leg that must
be overcome by the muscles of the hip in order to
effect the desired movement.
However, whether the weight of the limb is key
or not, the point remains that large forces have to
be generated by muscles to overcome much smaller
resistances, and the triceps brachii must exert about
222 pounds (987 N) of force in order for the hand
to press down with 20 pounds (89 N) of force on a
scale. In cases in which the elbow is extended and
the resistance arm is greater, the torque produced
by a 10-pound weight would be approximately 20
foot-pounds at shoulder height as shown in figure
2.12A, and about 300 pounds (1,335 N) of tension in
the deltoid may be necessary to raise the arm to this
height (Rasch and Burke, 1978). So, in human limbs
this prevalence of third-class levers represents a grave
disadvantage in terms of mechanical advantage and
has important implications for injury predisposition.
However, this arrangement does foster a large rangeFIGURE 2.11 Levers and torque. (A) Biceps force
required to counter dumbbell torque; (B) mechanical
advantage; (C) biceps force required to counter forearm
and dumbbell torque.