GENERAL PRINCIPLES 



23 



to the plane of the couple ; thus AM F 1 / X d ; this being the 

 axis of the couple. 



The resolution of a force into two parallel forces and the 

 composition of three or more forces are very simple propositions ; 

 they are explained by the above. 



As the forces applied to a solid have a general resultant R. and 

 a resultant moment, M, and -as that moment becomes a couple, 

 it follows that : 



The forces of a system unite into a single force and into a 

 couple, or into a force and a moment. 



In taking into consideration the displacements compatible 

 with the restraints of a solid, it also follows that there must be six 

 equations to express the equilibrium of a solid, namely the com- 

 ponents of its translation (X, Y, and Z), and those of its moment 

 or of its rotation (L, M and N) which must be separately zero. 

 In effect, an entirely free solid body has six degrees of liberty. 

 Thus, a moving point on a surface can only move in the 

 direction of X and Y, that is, two degrees of liberty ; a bicycle 

 has three degrees of liberty. 



17. Applications (1) RESOLUTION OF FORCES. Given a vertical 

 force, F, that of gravity, for example, it can be subdivided into 

 two equal forces applied to the points A and B, and the points 

 A and B must be equi-distant from M (see 20) (fig. 43). If a 



force F is subdivided between three 

 . points, A, B, and C, a triangle ABC is 



, constructed, and, joking AM, F is 



first resolved into Fj and F 2 ; and then 

 i F 2 into F 3 and F 4 , thus giving a final 

 subdivision into three forces, F lf F 8 , 

 F 4 (fig. 41). Those three forces will 

 be equal if the triangle ABC is equi- 

 7 10 43 lateral. The first case is that of a 



bicycle, for example : the second that 



of the majority of three-legged supports for physical instruments. 

 The subdivision into four points like 

 the four legs of a table is theoretically 

 unstable, seeing that, on ground where A, 

 the resistance varies from one point to 

 another, two legs would alone support 

 all the weight. In practice, the legs and 

 the ground give somewhat, which results 

 in stability being reached. 



2. DEGREES OF LIBERTY. The re- 

 straints of solid bodies or their degree of 

 liberty, enable their movements to be 

 recorded. Numerous examples of this 



will be found when considering the articulations of the human 

 body. 



B 



M 



