APPLICATION OF GRAPHIC METHODS 287 



circle, so as to make the stated angle with the surface of the 

 joint ; we also draw the bearing pressure due to element b, on 

 another part of the same pin. The intersection of these lines of 

 pressure gives the dynamic joint through which the pull of link 

 6 must be exerted ; this link is now drawn, and the diagram 

 completed by the two bars drawn perpendicular to links 4 and 5 

 respectively. Let Pj be the force of the original couple, and D the 

 distance between links 1 and la. Let A be the distance between 

 the lines of bearing pressure on element a- then P 5 , the 



P D 



stress in link 5, is given by the expression P. = L- . Similarly 



A. 



P D 



P 4 = _L_. The stresses in links 4 and 5 being known give the 

 B 



stress in link 6 by the simple composition of forces. The 

 portion of Fig. 7 referring to the material means of producing 

 the two couples does not necessarily belong to the diagram ; the 

 couple between a and b may in certain cases be produced by 

 some other machine, being, in fact, the resisting couple of that 

 other machine, and in that case the efficiency of the means of 

 producing the couple must be determined by an examination of 

 the first or driving machine. This case is, in fact, one case of 

 compound machinery, and will be treated hereafter. In what 

 follows, a driving couple may be occasionally described as ex- 

 isting between two elements, without reference to the mode 

 in which it is applied ; a resisting couple may be spoken of in 

 the same manner. 



10. Assumption that the Links of Frame lie in one Plan*. One 

 object of our investigation is to find a means of ascertaining the 

 efficiency of any mechanical arrangement the word ' efficiency * 

 being understood in the sense given it by EAXKTXE as the 

 ratio of the useful work done in a machine to the whole work 

 or energy expended. Now RAXKTXE (' Millwork,' 371 A) has 

 pointed out certain conditions which must be fulfilled to give 

 the highest efficiency in any design, viz. : First, that the useful 

 resistance to the motion of any element, the effort to move it 

 and the force due to the weight of the part must lie nearlv in 

 one plane, or else act in directions parallel to one another ; and 

 secondly, that the acting parts must not overhang the bearings. 

 Injurious couples are introduced if these conditions are not 



