8o 



STATICS. 



[134. 



of forces has for its magnitude and sense those of the moment 

 of the couple, and for its direction that perpendicular to the 

 plane of the couple. 



It is due to this analogy between the two fundamental con- 

 ceptions that a certain dualism exists between the theories of 

 statics and kinematics, so that a large portion of the theory of 

 kinematics of a rigid body might be made directly available for 

 statics by simply substituting for angular velocity and velocity 

 of translation the corresponding ideas of force and couple. 



134. When any number of couples act on a rigid body their 

 resultant can readily be found. Representing each couple by 

 its vector, we have only to combine these vectors by geometrical 

 addition. In the particular case when the couples all lie in 

 parallel planes, or in the same plane, their vectors may be taken 

 in the same line, and add, therefore, algebraically. 



Hence, the resultant of any number of couples is a single cotiple 

 whose vector is the geometric sum of the vectors of the given couples. 



Conversely, a couple can be resolved into components by 

 resolving its vector into components. 



135. To combine a single force P with a couple (F, p) lying 



in the same plane it is only nec- 

 essary to place the couple in its 

 plane into such a position (Fig. 

 35) that one of its forces, say 

 F, shall lie in the same line 

 and in opposite sense with the 

 single force P, and to transform 

 the couple (F, /) into a couple 

 (P, p'), by Art. 131, so that Fp 

 = Pp'. The original single force 

 P and the force P of the trans- 

 formed couple destroying each 

 other at A, there remains only 

 the other force P, at A', of the transformed couple which is par- 



-P 



-F 



Fig. 35. 



! 



