306 APPLIED MECHANICS 
on the connecting-rod, as shown to the right in Fig. 477. The cross-head 
end of the connecting-rod is placed at C, and assumed to be at rest. The 
fe hy Ao ate 3 
Angular Velocity — = Seg = -S 5 Zz 
Time Curve. ry 
atta el es 
4.24% o 610’ 
AER pao iC \6__ Polar Curves. 
Time— \ BD=Cd=Ce =FE=BE 
is ate BD =Angular — 
=b----- == | of Gnnecting- rod. 
Fig. 477. 
different values of 4 corresponding to different values of @ are readily 
obtained by the construction shown, and which may be briefly described 
as follows. With C as centre, and radius equal to the length of the 
connecting-rod, measured on the linear scale, describe the are 03’. Let 
CB be one position of the crank. Draw BB’ parallel to C0’ to meet 
0'3’ at B’. Join CB’, then angle B’CO’=¢. Draw BD parallel to B’C 
to meet the perpendicular to C0’ from C at D, Then BD represents 
the angular velocity of the connecting-rod when the crank is at CB. 
Make, on B’C, B’-E=BD. Then Eis a point on a polar curve of angular 
velocity of connecting-rod. If Cd=BD be marked off on B/C from C 
as a pole, then d is a point on another polar curve of angular velocity of 
connecting-rod, Observe that when BD is positive B’E is measured from 
the arc 0'3’ on the side opposite to C, and when negative it is measured 
from the are 0’3’ towards C. Also for the other polar diagram, when BD 
is positive Cd is measured from C towards the are 0’3’, and when negative 
it is measured from C in the opposite direction. 
The construction for the angular velocity curve on a time base is 
obvious, and clearly shown in the figure. 
The scale on which BD will measure the angular velocity of the 
connecting-rod is found as follows. Let BC, BD, and AB denote the 
lengths of these lines on the drawing, measured in inches on the full size 
scale. Let the scale for angular velocity be 1 inch to a radians per 
second, and let the linear scale of the drawing be 1 inch to y feet. Also 
let 7 be the true radius of the crank in feet, and let V be in feet per 
second. Then 
Angular velocity of connecting-rod BD+AB_ BD 
_ Angular velocity of crank ~BC+BC AB’ 
But angular velocity of crank= Ly therefore angular® velocity of 
; BD V 
connecting-rod = w = Sere: | 
But AB=n-BC=nr/y, therefore w= = 3 i= BD -«, and there- 
fore x= yV ; 
ny? 
