Mechanical engineering involves the study of motion, energy, and force, and is concerned with designing, manufacturing, and maintaining mechanical systems. One important concept in this field is the couple moment, produced by two equal and opposite forces acting at two points in a rigid body separated by a certain distance.

When the rigid body undergoes a differential displacement due to a couple, its motion can be divided into two parts: equal translation of the two points to their final positions and rotation about one of them. During the translation, the two forces undergo the same amount of displacement, but in opposite directions. Therefore, the work done by the forces, being opposite in sign but equal in magnitude, results in zero work.

However, during the rotation, the force causes an angular displacement, which leads to non-zero work. The work done during rotation can be calculated as the product of the magnitude of the couple moment and the angle of rotation.

If the couple moment and angle of rotation have the same sense, the work done by the couple moment is positive. Conversely, if the couple moment and rotation angle have opposite senses, the work done will be negative.

The work done by a couple moment is an essential factor to consider in designing mechanical systems. Engineers take into account the amount of work that will be done during rotation, as well as the magnitude and direction of the couple moment, to ensure that the system will function properly.