The point O selected as the point of concurrency for the forces is arbitrary, and the magnitude and direction of M depend on the particular point O selected. The magnitude and direction of R , however, are the same no matter which point is selected.

In general, any system of forces may be replaced by its resultant force R and the resultant couple M. In dynamics we usually select the mass center as the reference point. The change in the linear motion of the body is determined by the resultant force, and the change in the angular motion of the body is determined by the resultant couple. In statics, the body is in complete equilibrium when the resultant force R is zero and the resultant couple M is also zero. Thus, the determination of resultants is essential in both statics and dynamics.

Wrench Resultant. When the resultant couple vector M is parallel to the resultant forces R, as shown in Fig.1.9, the resultant is called a wrench . By definition a wrench is positive if the couple and force vectors point in the same direction and negative if they point in opposite directions. A common example of a positive wrench is found with the application of a screwdriver , to drive a right-handed screw. Any general force system may be represented by a wrench applied along a unique line of action.