a cam rotating about the axis C, the cam 
"A MISCELLANEOUS MECHANISMS 413 
of its stroke while the cam turns through anangle of 90°. In its lowest position 
the sole of the foot of the bar is 3 inches above the axis of the cam, and the stroke 
of the bar is 5 inches. Draw the outline of the cam, 
10. The arm EF (Fig. 675) swings about the axis O through an angle of 30°, 
In its lowest position the under surface of 
EF is inclined at 20° to the horizontal. 
The swinging motion of EF is controlled by 
always in contact with the under sur- 
face of EF. The cam has uniform angular 
velocity, and the arm has simple harmonic 
motion during its upward and downward 
swings. The time of each swing is one-third 
of a revolution of the cam, and the arm has 
ods of rest’ in its top and bottom 
positions. Design the cam. 
11. Design a cam to give reciprocating 
motion to a frame carrying a bobbin to be 
filled with yarn to the barrel shape shown in 
Fig. 676. The yarn is fed on to the bobbin at a fixed level A. There are 
two cases to be considered, namely, (a) the bobbin revolves at constant speed, 
-and (b) the yarn is delivered at a constant rate. 
[Hints.—Divide the bobbin into zones 1, 2, 3, etc., 
of equal height. Let r,, rg, 73, etc., be the mean 
external radii of these zones respectively. The 
e through which the cam turns while the zones 
1, 2, 3, etc., are passing the level A are proportional 
to(r,-1), (r2-7), (73-7), etc., respectively in case 
(a), and to (r?-7*), (r3-—r?), (73-17), etc., respec- 
tively in case (b)}. 
12. In the case shown in Fig. 643, Pp. 401, 
where a cam works against a flat-footed follower, 4 
show that, if the displacement of the follower is AP 
proportional to the displacement of the cam, the 
curve of the latter is the involute of a circle. 
13. Referring to the Hooke’s joint shown in a 
Fig. 657, p. 406, @=30°, and the shaft ¢ has a 
uniform speed of 200 revolutions per minute. 
Construct the angular velocity curve and also the polar angular acceleration 
curve! for the shaft d. 
14. In a single Hooke’s joint @ is the acute angle between the axes of the 
shafts. One of the shafts has a uniform speed. Express the fluctuation of the 
speed of the other shaft as a percentage of the speed of the first for values of 6 
from 0° to 50°, and plot the results. 
15. In a double Hooke’s joint (Fig. 660, 
p. 407) the axes of the joints in the forks of 
the intermediate shaft B are wrongly placed, 
being at right angles to one another instead 
of parallel. The shaft A has a uniform speed. 
Express the fluctuation of the speed of the 
shaft C as a percentage of the speed of A for 
a number of values of @ from 0° to 50°, and Fiq. 677. 
plot the results. 
16. Hooke’s joint is frequently made with the axes of the cross not inter- 
secting, as shown in Fig. 677. Examine this arrangement, and discuss its 
defects. 
dw, dw, da_ cos @ sin? @ sin 2a 
1 Angular acceleration=~ Ja di (aint boot a 
