APPLICATION OF GRAPHIC METHODS 289 



do not abut at the intersection of the two adjacent links 1 need 

 not represent bearing pressures at working joints, as will be seen 

 by considering an actual machine corresponding to the dynamic 

 frame, as, for instance, that of Fig. 11, p. 292 ; the three elements 

 corresponding in this case to links 2, 5, and 6 will then simply 

 constitute a stiff system or frame, which might be replaced by a 

 single rigid element. When this is the case the machine will 

 belong to class 2, the dynamic frame of which is that of Fig. 10, 

 p. 281, in which a bar is substituted for links 2, 5, and 6. When 

 treating of compound machines, we shall find reason to consider 

 machines of class 2 rather as half machines than complete simple 

 machines. When couples are admitted in place of driving and 

 resisting links, the dynamic frame necessarily includes two stiff 

 bars, between which the couple or couples act. We then have 

 three cases: 1. The resisting and driving couples may act 

 between the same pair of stiff bars. This gives a dynamic frame of 

 merely two bars, with the two pairs of links by which the couples 

 are exerted. 2. A driving or resisting couple between two bars 

 may be combined with a resisting or driving link between the 

 same bars. 3. A resisting couple or a driving couple may, in 

 the quadrilateral of Figs. 8 and 9, be substituted for any link, 

 the couple being exerted between two bars replacing two links, 

 which, together with the link removed, form a triangle. When 

 we examine the usual combinations of elementary parts forming 

 actual machines, we shall in all cases find that these combinations 

 may be represented by a dynamic frame of one of the classes 

 described. 



12. Efficiency of Elements. The relation between the energy 

 exerted and the useful work done in a machine is affected by a 

 loss of energy in transmission through the elements, as well as 

 by a loss in transmission past the joints. At each joint we may 

 say that only a certain fraction of the energy received is trans- 

 mitted, the remainder being wasted in overcoming useless 



1 In the frame of the machine shown in Fig. 45, p. 323, links 1 and 6 

 might be drawn so as to appear adjacent, by placing link 4 so as to join the 

 intersection of 1 and 6 with that of 2 and 5. The links 2, 3, 5* do not, however, 

 in this example, form a stiff frame, and the machine belongs to class 1. This 

 is obvious when link i is placed so as to join the intersection of 1 and 5 with 

 that of 2 and 6. Machines of class 2 have only 5 working joints. 



VOL. II. n 



