diameters of the crank shaft journal, the crank pin, and the cross-head pin are 
F a it: and 54 inches respectively. Find the velocity of the piston and the 
: ity of rubbing of each journal in feet per minute in the position of the 
| mechanism, for which the crank arm has turned through an angle of 30° from 
the inner dead centre. {U.L.] 
13. Taking the same cases and the same particulars as in Exercise 11, con- 
struct the connecting-rod acceleration diagrams, and construct the acceleration 
scale, showing radians per second per second. Take from the diagrams the values 
of a in radians per second per second when @=75", and state the results, 
14. In a direct-acting engine the line of stroke is at a perpendicular 
distance of 4 inches from the axis of the crank shaft If the radius of the 
crank is 8 inches, and the length of the connecting-rod is 30 inches, find the 
length of the piston stroke, On the stroke of the piston as base, construct the 
piston velocity and piston acceleration curves for both the forward and return 
strokes. The speed of the engine being 200 revolutions per minute, construct 
the velocity and acceleration scales. 
15. The table of a small planing machine is driven from a crank through a 
connecting-rod, which is 9 inches long. The axis of the crank shaft is 3 inches 
below the line of stroke. If the stroke of the table is 
6 inches, find the radius of the crank. Construct the 
velo curves for both the cutting and return strokes 
of the table, on a stroke base, the crank rotating uniformly 
at 20 revolutions per minute. What are the velocities of 
the table, in feet per minute, at mid-stroke (a) when cut- 
ting, (b) when returning? Also, what is the time ratio of 
the cutting and return strokes, a 
S 
16. In an oscillating engine the piston has a stroke of 
6 feet, and the distance between the axis of the trunnions 
and the axis of the shaft is 10 feet 6 inches. The shaft 
makes 35 revolutions per minute. Find (a) the maximum 
velocity of the cylinder in radians per second, 
(5) the piston speed in feet per minute at mid-stroke, and ~ 
(c) the mean piston speed in feet per minute. ‘\5 
17. Fig. 483 shows the swinging-block slider-crank chain : 
as applied to a shaping machine. The pinion E drives the \ 
wheel F', which rotates on the fixed pin B, and carries the -Z C 
m 
5 
. a 
a \ 42:5 +e - -8= > 
pin ©. The pin C carries the block b, which works in the F° a 
slot of the lever dd, which oscillates about the fixed pin be 
A. The upper end of the lever dd carries a pin H, from 
which a connecting-rod transmits motion to the ram carry- Fiq. 483. 
ing the cutting tool. The stroke of the ram is varied by 
altering the distance of the pin C from B. For the given dimensions find the 
length of the stroke of the ram. Construct on a stroke base the velocity curves 
for the cutting and return strokes, The wheel F makes 20 revolutions per minute. 
What is the time ratio of the cutting and return strokes ? 
18. Referring to the Whitworth quick return motion, shown in Fig. 481, 
p. 308, BC=1} inches, AB=5 inches, CP=5 inches, and the connecting-rod to the 
ram is16 inches long. The line of stroke passes through C, and is perpendicular 
to BC. The driving wheel makes 15 revolutions per minute. Construct ona 
stroke base the tool velocity curves for the cutting and return strokes. What 
is the time ratio of the cutting and return strokes ? 
19. A and B (Fig. 484) are fixed centres. The crank BC revolves uniformly 
with an angular velocity of 10 radians per second about the centre B. The end 
© is pivoted to a block, which can slide along AD. AD revolves about the 
centre A. The point E moves along EA. Determine the velocity of sliding at 
both C and E when BC is at right angles to AB, and find also the maximum 
velocity of E. Show how the mechanism can be applied as a quick return 
motion for a shaping machine, and determine the ratio between the times of 
cutting and return. fU.L.] 
20. The crank AB (Fig. 485) rotates uniformly at 150 revolutions per minute. 
The end D of the rod BD is constrained to move in the straight line GH. The 
end E of the rod CE moves on the straight line EK. Determine the velocity of 
the point E for the given position of the mechanism. Indicate how you would 
determine the acceleration of the point E. [U.L.] 
