PISTON VELOCITY AND ACCELERATION DIAGRAMS 309 
return motion or turning-block slider-crank chain, and is obtained by 
_ making a the fixed link. ¢ becomes a crank, the rotary motion of which 
_ is communicated to }, but the angular velocities of b and ¢ are unequal, 
4 oo a two points during a revolution, This mechanism is used for 
driving the ram of a shaping machine or the ram of a slotting machine. 
The link or crank ¢ is really a spur-wheel rotating about an axis at B, 
_ and carrying a pin A projecting from one side, on which fits the block d, 
which in turn fits in a slot formed in 6. The link 4 rotates about an axis 
at C, and carries a pin P, the position of which may be varied to suit the 
required stroke of the ram, which carries the cutting tool at one end. 
The reciprocating motion of the ram is obtained from 
the pin P through a connecting-rod. The line of 
stroke of the ram is shown passing through C, and 
cutting the circle described by the pin A at E and F. 
The pin A has uniform velocity, and the times of the 
Steam 
~~ = om 
St 
yy 
SS 
Ne 
pe, i Rabo oe 
° 
forward or cutting stroke, and the return or idle : 
stroke of the ram, are to one another as the arc Cc . 
EHF is to the are FKE. iar ’ 
: The only other possible inversion of the slider- a 
__ erank chain is that obtained by fixing the block d. 
This inversion, called the swinging slider-crank, is ry 
| not very important, but one interesting application of aa If ii ° 
it is found in the pendulum pump, shown in Fig. 482. a 
The block d has become the steam cylinder, pump SA 2 d. 
barrel, and frame. The link } has become the piston, s § gis 
___ piston-rod, and plunger. The connecting-rod ¢ swings t- 
___pabout a pin A fixed on the side of the steam cylinder. Fic. 489 
The crank a has become a fly-wheel, which rotates 
: about a pin B attached to the lower end of the swinging link ¢, and it 
also rotates about a pin C, which is attached to the sliding link 4. The 
| stroke of the piston and plunger is evidently twice the radius of the 
4 crank a. 
Exercises XVIII. 
1. Construct the piston velocity diagrams, as shown in Fig. 467, p. 300, for 
the following cases :—(1) l/r=«, (2) l/r=4°5, (3) l/r=2, where /=length of con- 
necting-rod, and r=radius of crank. The three sets of diagrams to be drawn 
on the same corresponding bases, or, in the case of the polar diagrams, from the 
same pole, in order to show the differences due to variations in the value 
of //r. Take r=10 inches, yelocity of crank pin 10 feet per second, and linear 
scale . Construct on the diagrams the velocity scale, showing feet per second. 
Take from the diagrams the values of vin feet per second when @=45°, and 
state the results, 
2. In a direct-acting engine mechanism the radius of the crank is 10 inches, 
and the velocity of the crank pin 10 feet per second, find, by calculation, the 
answers to the queries in the following table :— 
Z (inches) ri ok) co 45 | 45 | 45 | 45 20 | 20 | 20 | 20 
@ (degrees). ./| 30/ ... | 30 | 150]... | ... | 30 | 150 Pe 
i, a (inches) . a) ae: 18 ? 2 2 |] 18 ? ? 2 18 
v (feet per second) ? | 2 2 ? 2 2 2 ? ? 2 
where / is the length of the connecting-rod, @ the angle between the crank and 
