Chapter 22 : Combined Motion of Rotation and Translation 469
Since these two velocities are equal, opposite and collinear, therefore their resultant is
zero. Or in other words, the particle A will be momentarily at rest.- Similarly, it can be proved the particle B (i.e. highest point of the wheel ) will be subjected
to a resultant velocity of 2v and acts perpendicular to OB. - The lowest point (A) is the instantaneous centre of the motion of the wheel.
EXERCISE 22.2
- In a crank and connecting rod mechanism, the crank is 300 mm long and the connecting
rod 1500 mm long. If the crank rotates uniformly at 300 r.p.m., find the velocity of the
cross head when the crank is inclined at 30° with the inner dead centre. (Ans. 5.39 m/s) - The lengths of connecting rod and crank in a reciprocating engine are 1000 mm and 225
mm respectively. The crank is rotating at 360 r.p.m. Find the velocity of cross head, when
the crank has turned through 30° with the line joining the centres. (Ans. 5.19 m/s) - The crank and connecting rod of a steam engine are 0.5 m and 2 m respectively. The crank
makes 180 r.p.m. in the clockwise direction. When the crank has turned 45° from the inner
dead centre, determine (i) velocity of piston, and (ii) angular velocity of connecting rod.
(Ans. 8.15 m/s ; 32.5 r.p.m.)
QUESTIONS
- Describe the phenomenon of combined motion of rotation and translation. Give few
examples. - Explain the term ‘instantaneous centre’.
- How would you locate the instantaneous centre of a rigid link moving with combined
motion of rotation and translation? - What are the various methods for finding out the velocity of piston of a reciprocating
pump? Explain one of them. - Derive a relation for the velocity of piston in a crank and connecting rod mechanism.
OBJECTIVE TYPE QUESTIONS
- In a combined motion of rotation and translation
(a) the motion of roation takes place before the motion of translation
(b) the motion of translation takes place before the motion of rotation
(c) both the motions take place simultaneously - The instantaneous centre is a point which is always fixed.
(a) yes (b)No - The velocity of piston in a reciprocating pump mechanism depends upon
(a) angular velocity of the crank (b) radius of the crank
(c) length of the connecting rod (d) both (a) and (b)
(e) all the above - The velocity of a piston in a reciprocating pump mechanism is maximum when the
obliquity is
(a) zero (b) maximum (c) average (d) minimum
ANSWERS
1.(c) 2. (b) 3.(e) 4.(b)Top