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A system of two parallel forces of equal magnitude and opposite sense. Under a couple's action a rigid body tends only to rotate about a line normal to the couple's plane. This tendency reflects the vector properties of a couple.
The total force of a couple is zero. The total moment C of a couple is identical about any point. Accordingly, C is the moment of either force about a point on the other and is perpendicular to the couple's plane. See Resultant of forces, Statics
The moment of a couple about a directed line is the component of its total moment in the line's direction. Couples are equivalent whose total moments are equal.
a system of two forces P and P’ acting on a rigid body that are equal to each other in absolute value, are parallel, and are opposite in direction—that is, P’ = – P (see Figure 1). A couple has no resultant. In other words, its action on a body cannot be mechanically equivalent to the action of any single force; accordingly, a couple cannot be balanced by a single force.
The distance l between the lines of action of the two forces is called the arm of the couple. The effect of a couple’s action on a body is described by the couple’s moment, which is represented by a vector M equal in absolute value to the quantity Pl and perpendicular to the couple’s plane on the side where the rotation
caused by the couple appears to be counterclockwise in a right-handed coordinate system. A basic property of a couple is that the effect of its action on a given body is not changed if the couple is shifted anywhere in its plane or in a plane parallel to its plane. In addition, if the absolute value of the forces of the couple and the length of the arm are changed while the moment of the couple is kept fixed, the effect on the body is not changed. Thus the moment of a couple can be regarded as applied to any point of the body. If two couples have identical moments M and are applied to the same body, they are mechanically equivalent to each other. Any system of couples that are applied to a given body is mechanically equivalent to a single couple having a moment equal to the geometric sum of the moment vectors of the couples. If the geometric sum of the moment vectors of a system of couples is equal to zero, the system is balanced.
S. M. TARG [19–4–85–3]