TRANSACTIONS. 

I.—On the Application of Graphic Methods to the Determination of the Efficiency 
_ of Machinery. By Professor FLEEMING JENKIN. (Plates I.-XII.) 
(Read 2d April 1877.) 
§ 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 stiffness 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 
rigorously, 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 represented 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 result of considerable practical value. When the relation between 
the stresses due to effort and resistance has been found, it is easy to caleu- 
VOL. XXVIII. PART I. . A 
