TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. aly: 
§ 9. Modification of the Dynamic Frame—Couples.—When any element of 
a machine is in equilibrium under the forces applied at two joints the dynamic link 
will in direction and position correspond more or less closely with the direction 
in which the element of the machine lies between the joints. Thus, when the 
machine constitutes a material frame in one plane, as in fig. 6, the dynamic 
frame, fig. 6a, will have a general resemblance to the machine. The similarity 
between the actual frame composed of material links and the ideal dynamic 
frame in this case must not lead the reader to expect that he will always be 
able to identify a link in the dynamic frame as corresponding to an element in . 
the actual machine. Half a dynamic link corresponds to each joint of the 
machine, and there may be dynamic links which, like link 3 of fig. 5, have no 
_ corresponding joint in the machine, but the dynamic link will only correspond 
with an actual element when the number of joints in the latter is limited to two. 
Since a two-jointed element has a link resembling it, we may sometimes name 
this link by the letter of the element ; thus, all the links of 6a might be called 
indifferently by the letter of the element or the number assigned to the link ; but 
in fig. 50 or 5c, we can name only the link 5 by the letter of an element. In fact, 
the capital letter always signifies 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 between 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 bya stiff bar or 
triangular frame to which they were jointed without friction; 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’. The 
driving couple is indicated by the two springs e and ¢,, which it is assumed are 
