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In our everyday life, we deal with couples constantly, however, encountering one in a statics and especially a dynamics problem, many are foiled – completely lost.
The formal definition of a couple is that it is composed of two forces, equal in magnitude but opposite in direction, and most importantly, the two forces do not have the same line of action. If the forces had the same line of action, this definition would represent a statement of Newton’s 3rd Law.
Using this definition of a couple means that in driving your car you are applying a couple to the steering wheel constantly. To go left, you drop your left arm and raise your right arm. To go right, you do the opposite. It’s just that simple.
The confusion usually first appears because of the various symbologies representing a couple in a problem. To me, the most straightforward symbol of a couple is a partial circle with an arrow at one end indicating clockwise or counterclockwise rotation. The magnitude of the couple is placed near this symbol. Other symbols try to show graphically the formal definition of a couple, showing two equal forces separated by some distance. You are given the magnitude of the forces and the distance between them. You are then required to calculate the magnitude of the couple. Not difficult, but not obvious either.
The greatest confusion comes when in the process of applying equilibrium, you choose to take moments at the location of the couple and the couple stays in the equation. This in contrast to when you take moments at a point where a force is located and it does not appear in the equilibrium equation. This is because a couple is a “free” vector, meaning it has the same moment no matter where the moment is taken.
Again, couples are everywhere. Applying these properties should reduce confusion to a minimum. – Dr. Tom
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