APPLICATION OF GRAPHIC METHODS 307 



diagram is completed by drawing link 1. The forces which 

 keep the pulley b in equilibrium are shown in position and 

 direction at the joint B. Similarly, the forces which balance c 

 are shown at C, but the driving and resisting links, as well as 

 link 6, appear as if under compression. Before proceeding to 

 draw the frame with friction, it may be well to show how the 

 stiffness of the belt may be taken into account. In Fig. 26 the 

 arrows show the direction of the motion of the belt. The pulley 

 b at the lower side has to exert a force P in the direction of the 

 arrow on the belt, and also a right-handed couple m to bend the 

 belt ; the resultant of this force and couple is an equal force 



4H 



shifted to the left or downwards by a distance ; we might, 



therefore, represent the actual belt by a perfectly flexible belt 

 placed as shown by the dotted line d l d. 2 . The effect of the 

 stiffness of the belt at the other places where it is bent and un- 

 bent, is also to shift the line of application of the force as shown 

 by the dotted lines c? 3 , d v rf 5 , d 6 , d 7 d s . Thus the resultants of 

 the forces due to the tension of the belt on each pulley will not 

 be opposite each other ; the resultant will be shifted outwards on 

 the driving pulley, and inwards on follower, or disadvantage- 

 ously in both places. The actual amount of shifting cannot be 

 ascertained until P and P,, the tensions on the belt, are known ; 

 but the nature of the change is easily apprehended, and is 

 therefore included in the dynamic frame, Fig. 266. This frame 

 is drawn as for the case without friction. 



23. Compound Machines. It is evident that the resisting 

 link of one complete simple machine may be used as the driving 

 link of another simple machine. This combination gives rise to 

 what may be called a compound machine. If the two machines 

 have no element in common, they must be connected by two 

 joints in the manner of which Fig. 27 gives a typical example. 

 In this figure the lines may be considered to represent either 

 the links of a dynamic frame, or the axes of a series of material 

 elements, jointed without friction. The contraction of element 

 e would cause an expansion of the line joining the joint be with 

 da. This line would indicate the position of the resisting link 

 of the machine abcde, if this machine were a simple one. This 

 same line lies between the joints b t a l and d l c l in the position 



x ?. 



