Biomedical Engineering Reference
In-Depth Information
Fig. 5.8
Representation of
a combination of a fixed
pulley with a movable
pulley used to lift a load
with a force of action
F
A
¼ W
/2
fixed pulley
F
A
F
A
movable pulley
F
A
W = F
R
A fixed pulley behaves as a first class lever with equal arms
r
which is the radius
of the wheel. If the system is in equilibrium, the torques caused by the forces must
be equal:
F
A
r
¼
F
R
r
:
F
R
. In this case, the mechanical
advantage is 1 because the magnitude of the action force is the same as the
magnitude of the resistance force.
Figure
5.7b
shows a movable pulley. It behaves as a second class lever, in which
the arm of the action force is 2
r
and that of the resistance,
r
, taking as the axis the
point where the force
F
A
is applied on the rope at the left. Therefore, if the system is
in equilibrium we can write:
From this equation, we can conclude that
F
A
¼
F
A
2
r
¼
F
R
r
:
F
R
/2. Thus, the mechanical advantage in
a movable pulley is 2. As can be seen, movable pulleys allow us to exert a force of
magnitude smaller than would be required without it. It is worthwhile to note that,
in our analysis, the weight of the pulley was not considered.
From this equation, we find that
F
A
¼
5.6.1 Combination of Pulleys
It is possible to project systems of complex pulleys that involve many pulleys and
that certainly lead to a significant mechanical advantage.
Figure
5.8
shows a combination of a fixed with a movable pulley. As can be seen,
in this case, the force of action is reduced to half of the resistance which is the
