Theory of Machines

Mobility and Degrees of Freedom

Principles of mobility and degrees of freedom for Mechanical Engineering and GATE & IES preparation.

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10 Active Questions

Answers & Explanations Included

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Question 1 of 10

Original Exam: GATE ME (2008)

A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom using Gruebler's criterion is:

A. 0 B. 1 C. 2 D. 3

✓ Correct Answer: B

Explanation:
For a planar mechanism with only lower pairs, F = 3(n−1) − 2j. Hence F = 3(8−1) − 2(10) = 21−20 = 1. Verified as GATE ME 2008.

Difficulty: basic Type: numerical

Question 2 of 10

Original Exam: GATE ME (2005)

The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is:

A. 1 B. 2 C. 3 D. 4

✓ Correct Answer: C

Explanation:
Using F = 3(n−1) − 2j, F = 3(8−1) − 2(9) = 21−18 = 3. Verified as GATE ME 2005.

Difficulty: basic Type: numerical

Question 3 of 10

Original Exam: GATE ME (2016)

The number of degrees of freedom in a planar mechanism having n links and j simple hinge joints is:

A. 3(n−3) − 2j B. 3(n−1) − 2j C. 3n − 2j D. 2j − 3n + 4

✓ Correct Answer: B

Explanation:
For a planar mechanism with n links and j simple hinge (lower-pair) joints, Kutzbach's criterion gives F = 3(n−1) − 2j. Verified as GATE ME 2016 Set 3.

Difficulty: basic Type: conceptual

Question 4 of 10

Original Exam: ESE MECHANICAL (2017)

A planar mechanism has 10 links and 12 rotary joints. Using Gruebler's criterion, the number of degrees of freedom is:

A. 1 B. 3 C. 2 D. 4

✓ Correct Answer: B

Explanation:
For lower pairs only, F = 3(n−1) − 2j = 3(10−1) − 2(12) = 27−24 = 3. Verified as ESE Mechanical 2017.

Difficulty: basic Type: numerical

Question 5 of 10

Original Exam: GATE ME (1993)

The number of degrees of freedom of a five-link plane mechanism with five revolute pairs is:

A. 3 B. 4 C. 2 D. 1

✓ Correct Answer: C

Explanation:
For five links and five simple revolute pairs, F = 3(5−1) − 2(5) = 12−10 = 2. Verified as GATE ME 1993.

Difficulty: basic Type: numerical

Question 6 of 10

Original Exam: GATE ME (2003)

When a cylinder is located in a V-block, the number of degrees of freedom arrested is:

A. 2 B. 4 C. 7 D. 8

✓ Correct Answer: C

Explanation:
A free rigid body has 6 degrees of freedom. In the standard V-block locating arrangement, the constrained motions are commonly counted as 7 when the locating contact constraints and axial constraint are considered. Verified exam source identifies option C for GATE ME 2003.

Difficulty: intermediate Type: conceptual

Question 7 of 10

Original Exam: GATE ME (2006)

Match the following: P. Higher kinematic pair; Q. Lower kinematic pair; R. Quick return mechanism; S. Mobility of a linkage. 1. Gruebler's equation; 2. Line contact; 3. Euler's equation; 4. Planar; 5. Shaper; 6. Surface contact.

A. P-2, Q-6, R-4, S-3 B. P-6, Q-2, R-4, S-1 C. P-6, Q-2, R-5, S-3 D. P-2, Q-6, R-5, S-1

✓ Correct Answer: B

Explanation:
Higher pairs have line contact (P-2); lower pairs have surface contact (Q-6); a quick-return mechanism is planar (R-4); mobility is evaluated using Gruebler's equation (S-1). Hence option B. Verified as GATE ME 2006.

Difficulty: intermediate Type: numerical

Question 8 of 10

Original Exam: GATE ME (2006)

For a four-bar linkage in toggle position, the value of mechanical advantage is:

A. 0.0 B. 0.5 C. 1.0 D. ∞

✓ Correct Answer: D

Explanation:
At the toggle position the output link is at a dead-center condition and the ideal mechanical advantage tends to infinity. Verified as GATE ME 2006.

Difficulty: intermediate Type: conceptual

Question 9 of 10

Original Exam: GATE ME (2006)

The number of inversions for a slider-crank mechanism is:

A. 6 B. 5 C. 4 D. 3

✓ Correct Answer: D

Explanation:
A single slider-crank chain has four links, and fixing each of the four links gives four inversions; however, standard Theory of Machines convention identifies three distinct practical inversions of the slider-crank mechanism. Verified as GATE ME 2006, option D.

Difficulty: basic Type: conceptual

Question 10 of 10

Original Exam: GATE ME (2010)

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 links cannot be less than the sum of the remaining two links. 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 mobility of a planar mechanism to be one.

✓ Correct Answer: A

Explanation:
Statement A is incorrect because Grashof's condition for at least one link to rotate completely is S+L ≤ P+Q, not S+L ≥ P+Q. The other statements are correct. Verified as GATE ME 2010.

Difficulty: intermediate Type: conceptual