Machine Kinematics Questions and Answers – Inversion of Mechanism

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This set of Machine Kinematics Multiple Choice Questions & Answers (MCQs) focuses on “Inversion of Mechanism”.

1. The number of degrees of freedom of a planer linkage with 8 links and 9 simple revolute joints is
a) 1
b) 2
c) 3
d) 4

Explanation: No. of links, I = 8
No. of revolute joints, J = 9
No. of higher pair, h = 0

Number of degree of freedom, n = 3(I -1) – 2j – h
= 3(8 – 1) – 2×9 – 0 = 3.

2. A palnar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Grubler’s criterion, is
a) 0
b) 1
c) 2
d) 3

Explanation: Whatever may be the number of links and joints Grubler’s criterion applies to mechanism with only single degree freedom. Subject to the condition 3I – 2J – 4 = 0 and it satisfy this condition.
Degree of freedom is given by = 3(I – 1) – 2j = 3(8 -1) – (2×10) = 1.
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3. Match the approaches given below to perform stated kinematics/dynamics analysis of machine.
Analysis Approach
P. Continuous relative rotation 1. D’Alembert’s principle
Q. Velocity and acceleration 2. Grubler’s criterion
R. Mobility 3. Grashof’s law
S. Dynamic-static analysis 4. Kennedy’s theorem
a) P-1,Q-2,R-3,S-4
b) P-3,Q-4,R-2,S-1
c) P-2,Q-3,R-4,S-1
d) P-4,Q-2,R-1,S-3

Explanation:
1. D’Alembert’s principle – Dynamic-static analysis
2. Grubler’s criterion – Mobility(for a plane mechanism)
3. Grashof’s law – Continuous relative rotation
4. Kennedy’s theorem – Velocity and acceleration.

4. Which of the following statements is incorrect
a) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.
b) Inversions of a mechanism are created by fixing different links one at a time.
c) Geneva mechanism is an intermittent motion device.
d) Gruebler’s criterion assumes mobality of a planar mechanism to be one.

Explanation: According to Grashof’s rule for complete relative rotation r/w links L + S < p + q.

5. In a four bar linkage, s denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 360° if
a) S + L < P + Q
b) S + L > P + Q
c) S + P < L + Q
d) S + P > L + Q

Explanation: According to Grashof’s law for four bar mechanism, the sum of shortest and longest link lengths should not be greater than the sum of remaining two link length.
i.e. S + L < P + Q.

6. The number of inversions for a slider crank mechanism is
a) 6
b) 5
c) 4
d) 3

Explanation: No. of links of a slider crank mechanism = 4
So there are four inversion of slider crank mechanism.

7. The mechanism used in a shaping machine is
a) A closed 4bar chain having 4 revolute pairs
b) A closed 6bar chain having 6 revolute pairs
c) A closed 4bar chain having 2 revolute and 2 sliding pairs
d) An inversion of single slider crank chain

Explanation: Quick return mechanism.

8. Match the following
Types of mechanism Motion achieved
P. Scott Russel mechanism 1. Intermittent motion
Q. Geneva mechanism 2. Quick return motion
R. Off set slider crank mechanism 3. Simple harmonic motion
S. scotch Yoke mechanism 4. Straight line motion
a) P-2,Q-3,R-1,S-4
b) P-3,Q-2,R-4,S-1
c) P-4,Q-1,R-2,S-3
d) P-4,Q-3,R-1,S-2

Explanation:
1. Intermittent motion – Geneva mechanism
2. Quick return motion – Off set slider crank mechanism
3. Simple harmonic motion – scotch Yoke mechanism
4. Straight line motion – Scott Russel mechanism.

9. In a kinematic chain, a quaternary joint is equivalent to
a) one binary joint
b) two binary joint
c) three binary joint
d) four binary joint

Explanation: When ‘l’ number of links are joined at the same connection, the joint is equivalent to (l – 1) binary joints.

10. When supported on three points, out of 12 degrees of freedom the number of degrees of freedom arrested in a body is
a) 3
b) 4
c) 5
d) 6