THE KINEMATICS OF MACHINERY. 101 



80). The axis of the prism pair is normal to the axis of the 

 three cylinder pairs, and we may therefore use the symbol 

 ((7s P^-) for the chain in its new form. There are here 

 again four links, and therefore four inversions, and we shall 

 find that all four mechanisms are now different. 



We have first the mechanism shown in Fig. 8, and familiar 

 by its continual use in direct-acting engines (pi P- 1 -) 4 . Next, 

 following the same order as before, we may fix the link 6, 

 the connecting rod of Fig. 8. The mechanism thus obtained, 

 (C" P^-f, is quite different from the former, but equally 



FIG. 15. ' , , ' . 1 



* > ' 



familiar (Fig. 15). To make it more recognisable, the prism 

 pair 4 is reversed in the figure, that is the link c is made to 

 carry the open prism and d the full one. The motion is 

 obviously unaffected by the change. The mechanism can be 

 easily seen to be that of the oscillating engine. The link c 

 corresponds to the cylinder, swinging on fixed trunnions at 3, 

 and the link d to the piston-rod and piston of the steam-engine. 

 We see then that the relation between the mechanisms 

 which are familiar to us as the driving-trains of the direct- 

 acting and oscillating engines, is simply that they are differ- 

 ent inversions of one and the same chain. 



Let us now suppose the chain fixed upon the link which 

 was the crank in the last two mechanisms (Fig. 16). This 

 gives us a third mechanism which entirely differs from either 

 of the two former ones. It is quite familiar as a " quick- 

 return " motion in some machine tools, for which purpose 

 also the mechanism last mentioned has sometimes been 

 used. 



Fixing, lastly, the link c, we get the less familiar mechanism 

 shown in Fig. 17 (C" z P-L) . The link b swings about 3, and 

 the crank a rotates in space somewhat as in the mechanism 



