I33-] 



THEORY OF. COUPLES. 



79 



drawing the vector toward that side of the plane from which 

 the couple is seen to rotate counter-clockwise. 



Fig. 34. 



We shall call this geometrical representative AB of the 

 couple simply the vector of the couple. It is sometimes called 

 its moment, or its axis, or its axial moment. 



133. As was pointed out in Art. 1 1 2, a couple is equivalent 

 to a single force acting along a line at infinity. Couples are, 

 therefore, used in statics to avoid the introduction of such 

 forces whose line of action is at an infinite distance, just as in 

 kinematics a rotation about an axis at infinity receives the 

 special name of translation, and an angular velocity about an 

 axis at infinity is called a velocity of translation. 



It has been shown in Kinematics, Arts. 64, 65, that two equal 

 and opposite rotations about parallel axes produce a translation, 

 and in Kinematics, Art. 256, that two equal and opposite angular 

 velocities about parallel axes produce a velocity of translation ; 

 similarly, two equal and opposite forces along parallel lines form 

 a new kind of quantity called a couple of forces, or simply a couple. 



While rotations, angular velocities, and forces are represented 

 by rotors, i.e. by vectors confined to definite lines, translations, 

 velocities of translation, and couples have for their geometrical 

 representatives vectors not confined to particular lines. 



Just as in the case of couples of infinitesimal rotations and of 

 couples of angular velocities, the vector representing a couple 



