312 APPLIED SCIENCE 



never exceeds that met with in analysing a simple machine, and 

 all simple machines are of one type. 



25. Half Machines Compounded. In certain cases two suc- 

 cessive machines have two elements in common, as well as the 

 driving or resisting link. In this case we may consider the 

 addition as in reality only half a machine. The typical example 

 of this arrangement is given in Fig. 30, where links b and c are 

 common to two complete machines 1st, abcde, with its resisting 

 link ; and 2nd, bchgi, with its driving link. It will be seen that 

 the half machine hig has a certain analogy with the machines of 

 class 2, only it is here the stiff bar which acts as a driving 

 element by an alteration in its length ; h, i, or g might repre- 

 sent the final resisting element. We are never driven to adopt 

 this subdivision of a machine, except at one or other end of a 

 train of machines which may not be divisible into a series of 

 complete machines with joints or elements of transmission. 

 Thus, if we (Fig. 31) have a steam-engine with a spur-wheel on 

 its crank shaft, driving a single pinion from the shaft of which 

 a weight is hanging, we cannot divide the train into two distinct 

 complete machines, each having a quadrilateral with diagonals 

 as its dynamic frame. We may, however, draw two distinct 

 dynamic frames, as shown in Fig. 31a, where 7, 8, 9, 10, 11, and 

 12 are the links of a complete spur-wheel machine, similar to 

 that of Fig. 22a, driven by a link 7, but link 7 is in the same 

 line as link 2 of the well-known engine frame. Links 8 and 3, 

 6 and 11, are also common to the two frames. The diagram 

 shows that we might analyse the machine in two ways, calling, 

 for instance, the steam-engine a complete machine, and the 

 extra spur-wheel, with its weight, a half machine ; or we might 

 call the two spur-wheels a complete machine, and the piston, 

 steam, and connecting rod a half machine. 



It is a matter of no consequence how we subdivide a train. 

 The relative stresses in the first and last links will be the same, 

 whether we use half machines with two common elements, or 

 successive machines with one common element. This example 

 shows us that the machines of class 2 may very properly be 

 regarded as only half machines. This view is supported by the 

 observation that when one machine of class 2 drives another of 

 the same class, we get for the system a single complete dynamic 



