Torques - Biomechanics of the Human Body - page 29

2.3 Binary or Couple

Binary or couple is a system formed by two forces of the same magnitude and
opposite direction applied on a body, whose lines of action are separated by a
nonzero distance called the binary arm. The forces applied to the tap wrench or to a
round doorknob constitute a couple. Figure 2.7 shows a sketch of a couple.
We can find the torque of a couple ( 2.3 ) by calculating the torque of each force
about the axis of rotation separately and then summing them:

M ¼ Fd ⊥ 1 þ Fd ⊥ 2 ¼ Fd ⊥ 1 þ ð d ⊥ 2 Þ ¼ Fx : (2.3)

Both forces tend to rotate the bar counterclockwise about an axis through O.

Exercise 2.4 To remove the lug nut that fixes the wheel of a car, a man applies
forces with a magnitude of 40 N with each hand on a tire iron, maintaining the
hands 50 cm apart. Draw a diagram representing this situation and calculate the
torque of the couple of forces exerted by the man.

The axis of rotation through O can be at any place between the couple of forces,
as can be seen in Fig. 2.8 . Even in such cases, the resultant torque is the same as
in ( 2.3 ):

M ¼ Fd ⊥ 1 þ Fd ⊥ 2 ¼ Fd ⊥ 1 þ ð d ⊥ 2 Þ ¼ Fx :

It is important now to analyze the situation in which the forces that constitute
the couple have lines of action not perpendicular to the bar, as illustrated in
Fig. 2.9 . Note that d is the distance between the points of application of the forces

x

F

Fig. 2.7 Two forces
of equal magnitude but
opposite direction are
applied at the ends of a bar.
The system rotates about the
axis through O
(perpendicular to this page)
at the center of the bar.
The binary arm is
represented by x

d 1 d 2

F