Chapter 22 : Combined Motion of Rotation and Translation 467
First of all, draw the space diagram for the reciprocating pump machanism as shown in Fig.
22.14 (a). Now draw the velocity diagram as shown in Fig. 22.14 (b) and as discussed below :
- Take some suitable point a and draw a horizontal line representing the direction of motion
of the piston (i.e. vC). - Through a, draw another line ab representing the direction of motion of B (i.e. vB) which
is at 40° with the horizontal. - Now cut off ab equal to 11 m/s to some suitable scale.
- Through b, draw bc perpendicular to the connecting rod BC of the space diagram.
- Now ac gives the velocity of piston to the scale. By measurement, we find that velocity of
piston,
vC = ac = 8.3 m/s Ans.
Example 22.6. The crank AB in the mechanism shown in Fig. 22.15 rotates at 5 rev/s is
300 mm long.
Fig. 22.15.
The link CB is 600 mm long, and the piston C moves in horizontal guides. Find for the position
shown (i) velocity of piston C, (ii) angular velocity of the connecting rod BC and (iii) velocity of a
point D at the centre AB.
Solution. Given : Angular rotation of crank (N) = 5 rev/s ; Length of the crank (r) = 300
mm = 0.3 m and length of the link CB (l) = 600 mm = 0.6 m
We know that angular velocity of crank,
ω = 2πN = 2π × 5 = 10π rad/s
and velocity of B, vB = ωr = 10π × 0.3 = 9.4 m/s
Fig. 22.16.
First of all, draw the space diagram for the mechanism as shown in Fig. 22.16 (a). Now draw
the velocity diagram as shown in Fig. 22.16 (b) and as discussed below :
- Take some suitable point a, and draw a horizontal line representing the direction of motion
of the piston (i.e. vC). - Through a, draw a line ab representing the direction of motion B (i.e. vB) which is at 45°
with the horizontal. - Now cut off ab equal to 9.4 m/s representing velocity of B to some suitable scale.
- Through b, draw bc perpendicular to the connecting rod (which is vertical).
- Now ac gives the velocity of piston to the scale.
By measurement, we find that the velocity of piston
vC = ac = 6.65 m/s Ans.
By measurement, we also find that bc = 6.65 m/s