The Resolution of a Force into a Force and a Couple

The action of a single force can always be duplicated by an equal parallel force plus a couple. Suppose that it is desired to resolve the force of Fig. 1a, whose point of action is , into a parallel force passing through the point , plus a couple. We introduce into the system the two equal and opposite forces and acting at the point . Since these two forces form a system in equilibrium they can be added without altering the motional effects of the original upon the system. The circled forces in Fig. 1b can now be treated as a couple , and the original single force has been resolved into an equal parallel force and a couple.