TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 19 
Asteam engine with an oscillating cylinder, steam-piston, and piston rod, to repre- 
sent element ¢, and a pump to represent element /, as sketched in fig. 15, affords 
an example closely approximating to a simple machine of class 1 ; the typical 
dynamic frame of this engine has already been shown in fig. 6, and is here 
repeated with the slight variation that the pins are supposed to be fastened to 
b and d instead of eand It must be observed that the stress cannot be axial 
either in the driving or resisting elements ; indeed, these parts are not true 
elements, for there is a joint between two elements in each of them. They, in 
fact, with the links of the quadrilateral, constitute a machine working a machine 
- such as will be discussed when treating of compound machines ; similarly, when 
we represent the driving and resisting element by springs, as in the foregoing 
cases, we might have observed that in an actual spring the stress would not be 
strictly axial. In most practical cases, however, the stress will be so nearly 
axial that for the present we may neglect these considerations, and assume that 
we know the stress in the driving or resisting link.* We then have the frame 
shown in fig. 15a. : 
If the same engine, fig. 16, were employed to overcome or transmit a couple 
substituted for link 6 or element /, the dynamic frame would become that shown . 
in fig. 16a. The engine is shown with the piston rod in tension; links 2 and 5 
must be first drawn tangent to their friction circles, then the bearing pressures 
parallel respectively to 2 and 5, and tangent to the friction circles for eb and ec. 
The line of pull in the element ¢ is given by the line joining the intersection 
of the bearing pressures with that of 2 and 5; the diagram is completed by 
the bar perpendicular to 5 and that perpendicular to 2; these bars are mere 
indications of the arms of the equal and opposite couples exerted on elements 
e and b. These elements must be stiff, and their rotation relatively to one 
another, is, by hypothesis, resisted by a couple such as would be produced by 
friction exerted on a wheel forming part of b revolving between clips or rubbers 
forming part of c. The diagram supposes that the frictional resistance thus 
obtained is so exactly equal at opposite ends of a diameter of the friction wheel 
as to constitute a couple which does not directly affect the pressures on the 
joints ¢6, ec. ay 
§18. Ordinary Direct acting Steam Engine.—The ordinary direct act- 
ing steam engine with a single cylinder gives another example of a simple 
complete machine. Fig. 17 shows a sketch of an engine of this type 
with the resistance exerted as if by a link between the periphery of a fly- 
wheel and the fixed element or bed plate. We will assume that the position 
* The steam, piston, and cylinder constitute, with the resisting link, a simple inclined plane 
machine, vide § 15, and this machine drives the second machine, constituted by the piston rod, connect- 
ing rod, crank, bed plate, and resisting link; the piston rod and bed plate are common to the two 
machines, wide § 24, 25. 
