A couple is defined as a pair of forces having equal magnitude and opposite direction with different but parallel lines of action. Since the total force in any direction is zero, the net effect of a couple is a pure moment, or torque. The magnitude of this moment is the magnitude of one of the forces times the perpendicular distance between the forces,

M = F d

The moment vector is perpendicular to the plane containing the lines
of action of the two forces.

Using a vector approach, the moment of a couple is defined as

M = r ×
F

Here r is the position vector from one force to the other, and
F is the force to which r is directed.

Equivalent Systems

Two systems are equivalent if and only if the sum of forces for the two systems is equal and the sum of moments about an arbitrary point in both systems is equal:

Using the concept of equivalent systems, any system
of forces and moments can be replaced by a single force and couple at an arbitrary point
P. Applying the conditions for equivalent systems gives