APPLICATION OF GRAPHIC METHODS 311 



should have, if the first machine had been completed by a 

 single resisting link ; the circuit must in either case be com- 

 pleted, so that the resisting link may abut against the common 

 element (?, against which the first driving link also abuts. The 

 driving link of the second machine gJid is in the line of the 

 resisting link of dbcde. The direction of this link is for both 

 machines determined by the transmitting joint eg i.e., by the 

 form of the teeth of the wheels. The driving link of the machine 

 J. is in the line of the resultant tension due to the band /, 

 which is here a transmitting element. The driving or resisting 

 link of each successive machine, if taken by itself, would abut 

 against the common element d. The first driving and last trans- 

 mitting element do abut against this common element. In any 

 machine it will be found easy to analyse the series of parts so as 

 to divide the whole structure into a series of complete machines, 

 each joined to its neighbour by a transmitting joint or link. 

 Each machine can then be treated as a separate whole. We see 

 in the example given that the dynamic frame consists of three 

 distinct quadrilaterals with diagonals. The connecting links 

 may be considered as double links in each case. Thus we may 

 consider the joint C, Fig. 29a, as connected by one link with the 

 joint G which it drives, while at the same time the joint D t is 

 connected by a link with D u . Thus, when the reciprocal figure 

 for the whole frame is drawn, as in Fig. 29ft, it forms one con- 

 nected whole. The stress corresponding to each connecting 

 link is used twice as in all reciprocal figures. In Fig. 296 each 

 link is numbered from 1 to 6 for each successive machine. The 

 length of the first line 1 corresponds to the driving effort. The 

 length of the last small line 6 corresponds to the resistance 

 which that effort can overcome at od. The diagram is drawn 

 without taking friction or stiffness into account, so that the 

 frame shown is kinematically equivalent to the machine. It 

 would be easy in a drawing on a large scale to show the complete 

 effect of friction and stiffness., for \ve have already learnt to take 

 these into account for each component simple machine. We 

 see, therefore, that in any simple train of machinery there can 

 be little difficulty in estimating the true relation between effort 

 and resistance (neglecting weight and mass) ; this difficulty 



