Engineering Mechanics

(^462) „„„„„ A Textbook of Engineering Mechanics
22.6.GRAPHICAL METHOD FOR THE VELOCITY OF PISTON OF A
RECIPROCATING PUMP
Consider the mechanism of a reciprocating pump in which AB be the crank, BC the connecting
rod and C the piston. Now let us locate the position of instantaneous centre O as shown in Fig. 22.9
and as discussed below :
Fig. 22.9. Velocity of piston of a reciprocating pump.

1. First of all, select some suitable point A, and draw a circle with radius equal to AB (i.e.
   crank length of the mechanism).


2. Through A, draw a horizontal line meeting the circle at D, which represents the inner dead
   centre. Extend this line.


3. Now draw AB at an angle θ through which the crank has turned at the instant, the velocity
   of piston is required to be found out.


4. Cut off BC equal to the length of the connecting rod.


5. Now extend the line AB and through C draw a line at right angles to AC meeting at O,
   which represents the instantaneous centre of the connecting rod BC.


6. Measure the lengths OB and OC and use them in the usual relations of instantaneous
   centre as discussed below :
   Let ω 1 = Angular velocity of the crank AB in radians/sec.
   ω 2 = Angular velocity of connecting rod BC about O, in radians/sec,
   r= Radius of the crank AB.
   ∴ Velocity of B, vB=ω 2 × OB ...(i)
   We also know that the velocity of B,
   vB=ω 1 × AB ...(ii)
   Equating equation, (i) and (ii),

ω 2 × OB=ω 1 × AB or 2 1 AB

OB

ω×

ω= ...(iii)

Similarly, velocity of piston C,

vC= ω 2 × OC

Now by substituting the value of ω 2 in the above equation,

11

C

ABOC rOC

v

OB OB

ω× × ω× ×

===vOCB

OB

× ...(Q AB = r)

Thus by measuring the lengths of OB and OC to the scale, we can find out the velocity of

piston (i.e.vC).