The couple

• A couple is the system of two equal, opposite and parallel forces whose lines of action do not coincide.
• Its resultant force is zero, so it produces pure rotation; its moment is M = F × d, where d is the perpendicular distance between the two lines of action.
• The moment of a couple is the same about every point in the plane — this is what distinguishes it from an ordinary force system.
• A couple can only be balanced by another couple of equal moment and opposite sense; a single force can never equilibrium a couple.

Worked example

Two forces of 12 N act along parallel lines 0.4 m apart in opposite senses: M = 12 × 0.4 = 4.8 N·m. The same value is obtained about any point, including a point outside the strip between the lines.

Resultant of a system with a couple

A force F together with a couple of moment M in the same plane is equivalent to a single force F displaced perpendicular to itself by d = M/F, because moving the force off the original line creates exactly the couple M.