TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 21 
sented by the stresses in the four half links, 1, 5, 6, and 3, joined as in the 
diagram by a link 4, in which the stress will be that due to the resultant of 1 
and 3, or 5and 6. - The frame, if drawn on the hypothesis of no friction, will be 
_ kinematically equivalent to the actual engine; that is to say, the infinitesimal 
compression of link 6, resulting from a given infinitesimal expansion of link 1, 
will be equal in length to the actual travel of the fly-wheel at its rim past the 
friction-block, when the piston advances by an amount equal to the given expan- 
sion of link 1. The diagram,-independently of its value as a means of estimat- 
ing the relation between effort and resistance, is of use in showing clearly the 
direction and magnitude of the stresses to which the bed plate is subject. As 
the revolution of the crank continues the dynamic frame changes, Figs. 17 to 20a 
show four positions of the engine with four dynamic frames; the bearing-points 
are marked in each case by dots on the circles representing sections of the pins. 
The changes in the direction of the stress in the connecting-rod, relatively to its 
axis, should be observed, as well as the sudden changes which take place in the 
points of bearing pressure as the crank shaft revolves. It is these sudden 
changes which give rise to “knocks” in the engine when the shafts or pins 
and bearings or eyes do not fit. At joint ab four sudden changes occur—two | 
due to changes of relative motion between the pin and eye, and two to changes 
in the direction of the stress in the link; at joimts be and cd there are 
only two changes. It must be understood that the whole dynamic frame is 
modified by any change in the direction or position of the resisting link. It 
will be found easy to construct diagrams showing the modifications—resulting 
from a change of this kind or from the substitution of a couple—between c and 
d for the resisting link ; this latter case corresponds to the arrangement of an 
engine employed to drive a long shaft with separate bearings co-axial with the 
crank shaft. 
§ 19. Wedge.—When a wedge is employed to form a complete machine we 
find a dynamic frame of class 1, similar to that given by the direct-acting 
steam-engine. Fig. 21 shows a complete wedge machine. The letters on the 
parts indicate the elements, where ¢ is the driving, and / the resisting element. 
Dotted: les on the same figure show the simple dynamic frame without 
friction. The dynamic frame with friction is given in fig. 21a; links 1 and 6 are 
determined by being made tangent to the friction circles for joints ec, ea, fb, and 
Jc. Links 2 and 5 must intersect link 1 at the same point. If the wedge has - 
- plane joints, the position of this point is indeterminate, but with fair fitting it 
may be expected to lie at or near the centre of the joint. The direction of 
the links 2 and 5 is fixed by the condition that they shall make the stated 
angle with the joint, and their position is without influence on the relative pro- 
portions of the links of the frame. The intersection of links 6 and 5 gives the 
joint B; the intersection of link 6 with 2 determines the joint C. Link 4 is 
VOL. XXVIII. PART I. F 
