TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 13 
take place in one plane parallel to the plane of action in the machine, and this 
hypothesis will be adopted in all that follows when the contrary is not stated. 
§11. Simple and Compound Dynamic Frames.—The dynamic frame of a 
complete machine mustcontain a driving link or couple and a resisting link or 
couple, together with the links necessary to connect the driving and resisting 
links or couples in such a way as to form a self-strained frame. <A 
complete machine may be either simple or compound. Simple machines are 
those having dynamic frames which cannot be decomposed into two or more 
self-strained frames, such that the resisting link or couple of the one becomes 
the driving link or couple of the other. Compound machines have dynamic 
frames so formed that they can be decomposed into the frames of simple 
machines so connected that the resisting link of one becomes the driving link 
of the next. If we exclude rigid bars as members, there is only one frame 
which can be self-strained, and which is yet incapable of analysis into two 
distinct self-strained frames. This frame has been already described, and 
consists of a quadrilateral, with two diagonals, as shown in figures 8 
and 9. There is no essential difference between those two figures, which each 
consist of a quadrilateral figure 2, 3, 4, 5, having opposed angles joined by the 
two links 1 and 6. This simplest self-strained frame will be shown to be the 
dynamic frame of many elementary combinations in machinery. The driving 
and resisting links may in this frame be arranged in two ways. 1. They may, 
as in the examples hitherto given, be represented by two links, such as 1 and 6, 
2 and 4, or 3 and 5, which are not jointed together ; any one of these pairs may 
be considered as diagonals of a quadrilateral joined by the four remaining links, 
and each pair may be called conjugate links. For the convenience of descrip- 
tion, when these links are placed as 2 and 4, or 1 and 6, fig. 8, they may be 
called opposite links. 2. The driving and resisting links may be adjacent, that 
is to say, they may, as in the case of 1 and 4, or 2 and 6, have a common inter- 
section or joint. When the driving and resisting links are adjacent, as 1 and 
4, those links which do not abut at the intersection of the two adjacent links* 
need not represent bearing pressures at working joints, as will be seen by con- 
sidering an actual machine corresponding to the dynamic frame, as for instance 
that of fig. 11; the three elements corresponding in this case to links 2, 5, and 
6 will then simply constitute a stiff system or frame, which might be replaced 
by a single rigid element. When this is the case the machine will belong to 
class 2, the dynamic frame of which is that of fig. 10, in which a bar is 
substituted for links 2, 5, and 6. When treating of compound machines, 
* In the frame of the machine shown in fig. 45, Plate XII., links 1 and 6 might be drawn so as to 
appear adjacent, by placing link 4 so as to join the intersection of 1 and 6 with that of 2 and 5. The 
links 2, 3, 5, do not, however, in this example, form a stiff frame, and the machine belongs to class 1. 
This is obvious when link 4 is placed so as to join the intersection of 1 and 5 with that of 2 and 6. 
Machines of class 2 have only 5 working joints. 
VOL. XXVIII, PART I. D 
