271 



ON THE APPLICATION OF GRAPHIC METHODS TO 

 THE DETERMINATION OF THE EFFICIENCY OF 

 MACHINERY. 1 



PART I. 



1. THE object of the present paper is to show how, by 

 graphic methods, we may find the relation between the effort 

 exerted at one part of a machine in motion, and the resistance 

 overcome at another part ; the solution found is rigorous for all 

 motions in one plane, and takes count of the friction, weight, 

 and inertia of the parts. It also takes into account the stiff- 

 ness of ropes or belts. 



The paper shows that we may represent any machine, at 

 any given instant, by a frame of links, the stresses in which are 

 identical with the pressures at the joints of the machine. This 

 self- strained frame is called the dynamic frame of the machine, 

 and may be so drawn as to represent the machine either rigor- 

 ously, taking into account friction, weight, inertia, and rigidity, 

 or approximately, omitting some of the conditions under which 

 the machine works. 



Moreover, it is shown that for all machines (in which the 

 motions can be represented as in one plane) the dynamic frame 

 is of one type, either simple or compounded. The dynamic 

 analysis of machinery into parts represented by this simple 

 frame is believed by the author to be novel. It is consistent 

 with the kinematic analysis of REULEAUX. 



The driving effort and the resistance are in the frame repre- 

 sented by stresses in links, and reciprocal figures afford an easy 

 method of determining the relation between those stresses so 

 soon as the frame has been drawn. Incidentally, the method 

 also gives the resultant pressure at every joint in the machine, a 



1 From Transaction* of the Royal Society of Edinburgh, vol. xxviii., 1877 



