PISTON VELOCITY AND ACCELERATION DIAGRAMS 307 
, ain 8 
BD sin (90-6) cos 0 . * 
ST ” BC © sin (90-4) cos ~ but sin PM 
and cos p= 1 — S00. Therefore 
BD_ mee eet ga SOL BD) __ cos 9 V 
BC »/n® — sin® 0 r 
268. Angular Acceleration of Connecting-rod.—Referring to Fig. 
470, p. 301, just as DH or CL represents the rate of increase of CD, so 
DF or KL represents the rate of increase of BD, or the rate of increase 
of BD’ (Fig. 476), and therefore KL/AB represents the angular accelera- 
tion of the connecting-rod. The figure CBKL (Fig. 470) is a linear 
_ acceleration diagram, the scale of which was shown (Art. 264) to be such 
that BC represents V*/r, the linear acceleration of B in the direction BC, 
Hence if KL and BC be measured in inches, and r and mr are the true 
lengths in feet of the crank and connecting-rod respectively, angular 
acceleration of connecting-rod = a = KL Vener = kL." and since KL 
BC r- BC nr?’ 
is the only variable in the expression for a, KL will represent a4 on a 
certain scale. Let this scale be 1 inch to z radians per second per second, 
and let the linear scale of the drawing be 1 inch to y feet, then 
: 2 2 
o=KL-2=———~ ._,-KL-y-—., ande= Sn, 
Referring to Fig. 467 
SE ee a 
. ‘ re 
: 
The angular acceleration of the connecting-rod may be plotted in a 
— similar to that described for the angular velocity in the preceding 
ticle. 
269. Case where Line of Stroke does not Intersect Axis of 
Crank Shaft.—The illustrations of the direct-acting engine mechanism 
which have been given in preceding Articles have shown the line of stroke 
passing through the axis of the crank shaft, and this is the usual arrange- 
ment, but in a single-acting engine, that is, an engine in which all the 
work is done on one side of the piston, there are advantages in arranging 
the mechanism as shown in Fig. 478, where pq, the line of stroke, when 
produced, does not pass 
through C, the axis of 
the crank shaft. 
One result of alter- 
ing the position of the 
ine of stroke, as shown Mie, 
in Fig. 478, is that ree 8 rD 
during the forward or Pp 
working stroke the ob- Stroh 
liquity of the connect- 
nad is diminished, Q 
and in consequence of . 
this the ae e on ds i 
the cross-head guide is diminished, and the turning moment on the 
crank is slightly more uniform. The diminished pressure on the guide 
means of course less work lost in friction at that part. During the 
return stroke the obliquity of the connecting-rod is increased by this 
