Biomedical Engineering Reference
In-Depth Information
5.6 Pulleys
Up to here we have discussed the action of muscles on bones to perform any
movement or even to sustain a certain structure in its place, when it is submitted
to external loads. However, we should not forget situations in which external forces,
such as traction that gives rise to torques and lever effects, are exerted by equipment
in hospitals or even in fitness gyms. Usually these forces have a magnitude
determined by the system of pulleys, which will be discussed next.
A pulley is a disc or a wheel with a groove around it where a rope, a cord, a cable
or a chain passes whose function is to change the direction of the force. The disc has
a central axis about which it rotates. The pulleys can be fixed or movable. The axis
of a fixed pulley is attached to some support, while in a movable pulley one of the
extremities of the rope is fastened to a support.
Several structures of the human body have properties of simple fixed pulleys.
Tendons have the role of ropes and bone prominences, of discs (fixed pulleys). The
lubricant fluids reduce the friction between the tendon and the bone to almost zero.
A fixed pulley allows you to change the direction of a force without, however,
changing its magnitude. At one extremity of the rope, a resistance force
F
R
(load
W
)
is applied and at the other, the action force
F
A
, as can be seen in Fig.
5.7a
. If the
object with weight
W
is in equilibrium, the sum of all the forces applied to it must
be equal to zero. Hence, a force
F
A
of the same intensity as the weight
W
, with
opposite direction, must also be applied to the object. As the rope changes the
direction of the force, the force
F
A
to the right that will be applied by a person has
the same magnitude as the force
F
A
to the left. Let us now demonstrate that
F
A
¼
F
R
.
a
b
F
A
F
A
rr
fixed pulley
movable pulley
r
r
F
A
F
A
= F
r
/ 2
F
A
W = F
R
W = F
R
Fig. 5.7
(
a
) Representation of a fixed pulley attached to a structure. This type of pulley changes
the direction of the applied force
F
A
, but not its magnitude,
F
A
F
R
.(
b
) Representation of a
movable pulley. Here, the condition of equilibrium imposes that the magnitude of force
F
A
be half
that of
W
¼
W
¼
¼
F
R
, that is,
F
A
¼
W
/2