286 APPLIED SCIENCE 



an ideal joint, but in cases like that of link 5 this ideal joint is any 

 point in a given straight line. When the dynamic joints are at 

 an infinite distance owing to the parallelism of certain links 

 it is convenient to substitute ideal stiff frames, bars, or plates 

 joining the parallel links and acting as the actual rigid elements 

 or stiff frames would do, with the exception that the joints be- 

 tween the ideal bars and links are frictionless ; this substitution 

 may also be made when the links are nearly parallel. It is clear 

 that, by the ordinary method of statics, we might calculate the 

 relative stresses in all the links of the frame in Fig. 5, if 

 we were to imagine links 1, 2, 5, and 4 joined by a stiff 

 bar or triangular frame to which they were jointed without fric- 

 tion ; this gives a modified dynamic frame, as shown in Fig. 5d. 

 The position of this stiff bar is unimportant, but when used to 

 connect parallel links, it is conveniently drawn perpendicular to 

 these. When the links are not all in one plane, these bars 

 become imaginary rigid plates or stiff frames. The rigid bars 

 will be shown in the diagram by thicker lines than the links. 



A couple in an actual machine can only be exerted between 

 two elements which are acted upon in opposite directions. 

 There is no such thing as ' a solitary couple ' in nature ; 

 we always find a pair of equal and opposite couples, as we find 

 a pair of equal and opposite forces. Two equal and opposite 

 couples require two rigid elements between which they are 

 exerted, and these elements appear in the modified dynamic 

 frame as two rigid bars, perpendicular to the forces producing 

 the couples. Fig. 7 shows a simple machine in which the 

 driving link of Fig. 6 is replaced by a driving couple between the 

 elements a and b. The driving couple is indicated by the two 

 springs e and e } , which it is assumed are producing exactly equal 

 and opposite stresses between a and b in two parallel directions. 

 Fig. 7 a shows the dynamic frame for this machine with friction. 

 First we draw the links 1 and la tangent to the friction circles 

 for the joints ea, eb, e { a, e } b. The distance between the links 1 

 and la shows the arm of the driving couple as diminished by 

 friction ; next we draw links 4 and 5 by the rules already given, 

 then, remembering that the force in link 5 at joint ad must pro- 

 duce an equal and parallel bearing pressure on the pin at the 

 joint /, we draw this bearing pressure tangent to the friction 



