Couple

A pair of two equal and unlike parallel forces (i.e. forces equal in magnitude, with lines of action parallel to each other and acting in opposite directions) is known as a couple.

A couple is unable to produce any translatory motion (i.e., motion in a straight line). But it produces a motion of rotation in the body on which it acts. The simplest example of a couple is the forces applied to the key of a lock, while locking or unlocking it.

Arm of a Couple

The perpendicular distance (a), between the lines of action of the two equal and opposite parallel forces is known as arm of the couple as shown in Fig.1.

Fig. 1

Moment of a Couple

The moment of a couple is the product of the force (i.e., one of the forces of the two equal and opposite parallel forces) and the arm of the couple.

Mathematically,

                  Moment of a couple = P × a

Where,

     P = Magnitude of the force

     a = Arm of the couple

Classification of Couple

The couple may be classified into the following two categories, depending upon their direction, in which the couple tends to rotate the body, on which it acts.

1) Clockwise Couple

A couple, whose tendency is to rotate the body, on which it acts, in a clockwise direction, is known as a clockwise couple as shown in Fig. 2 (a). Such a couple is also called positive couple.

Fig. 2

2) Anticlockwise Couple

A couple, whose tendency is to rotate the body, on which it acts, in an anticlockwise direction, is known as an anticlockwise couple as shown in Fig. 2 (b). Such a couple is also called a negative couple.

Characteristics of a Couple

A couple (whether clockwise or anticlockwise) has the following characteristics.

1. The algebraic sum of the forces constituting the couple is zero.
2. The algebraic sum of the moments of the forces constituting the couple about any point is the same and equal to the moment of the couple itself.
3. A couple cannot be balanced by a single force. But it can be balanced only by a couple of opposite sense.
4. Any no. of coplanar couples can be reduced to a single couple, whose magnitude will be equal to the algebraic sum of the moments of all the couples.