STATICS. 



[128. 



IV. Theory of Couples. 



128. The combination of two equal forces of opposite sensed, 

 F, acting along parallel lines, is called a couple of forces ; or 

 simply a couple (Art. 112). 



The perpendicular distance AB=p (Fig. 30) of the forces of 

 the couple is called the arm, and the product Fp of the force F 

 into the arm / is called the moment of the couple. 



If we imagine the couple (F, p) to act upon an invariable 

 plane figure in its plane, and if the middle point of its arm be 



a fixed point of, this figure, 

 the couple will evidently tend 

 to turn the figure about this 

 middle point. (It is to be 

 observed that it is not true, 

 in general, that a couple act- 

 ing on a rigid body produces 

 rotation about an axis at right 

 angles to its plane.) A couple 

 of the type \F, p) or (F' t p') 

 (see Fig. 30) will tend to rotate counter-clockwise, while a couple 

 of the type (F u ,p n ) tends to turn clockwise. Couples in the 

 same plane, or in parallel planes, are therefore distinguished as 

 to their sense ; and this sense is expressed by the algebraic sign 

 attributed to the moment. Thus, the moment of the couple 

 (F,p) in Fig. 30, is + Fp, that of the couple (F",p rf ) is -F"p". 



129. The effect of a couple is not changed by translation. 



Let AB=p (Fig. 31) be the arm of the couple (F, p) in its 

 original position, and A'B 1 the same arm in a new position par- 

 allel to the original one in the same plane, or in any parallel 

 plane. By introducing at each end of the new arm A'B f two 

 opposite forces F, F, each equal and parallel to the original 

 forces F, the given system is not changed (Art. 80). 'But the 



Fig. 30. 



