1. Mobility is different than the number of degrees of freedom. True or false?

a) True

b) False

### View Answer

2. According to Kutzbach criterion, the mobility of a rigid body is given by the formula:

a) 3(n+1)-2j_{1}-j_{2}

b) 3(n+1)+2j_{1}+j_{2}

c) 3(n-1)+2j_{1}+j_{2}

d) 3(n-1)-2j_{1}-j_{2}

### View Answer

_{1}-j

_{2}; where n = number of links, j

_{1}= number of lower pairs, j

_{2}= number of higher pairs.

3. What is the equation for Grubler’s criterion for plane mechanisms with constrained motion?

a) 3n-2j_{1}-4=0

b) 3n-3j_{1}-4=0

c) 3n+2j_{1}+4=0

d) 3n+3j_{1}+4=0

### View Answer

_{2}= 0 in the equation of mobility according to Kutzbach criterion. 1 = 3(n-1)-2j

_{1}-0 Therefore, 3n-2j

_{1}-4=0

4. State the three dimensional form of Kutzbach criterion.

a) 6(n-1)+5j_{1}+4j_{2}+3j_{3}+2j_{4}+j_{5}

b) 6(n-1)-5j_{1}-4j_{2}-3j_{3}-2j_{4}-j_{5}

c) 6(n+1)+5j_{1}+4j_{2}+3j_{3}+2j_{4}+j_{5}

d) 6(n+1)-5j_{1}-4j_{2}-3j_{3}-2j_{4}-j_{5}

### View Answer

_{1}-4j

_{2}-3j

_{3}-2j

_{4}-j

_{5}. It is also called as Kutzbach criterion to determine the degree of freedom of a spatial mechanism.

5. Find the mobility of the following three bar mechanism.

a) 3

b) 2

c) 0

d) 1

### View Answer

_{1}= 3, j

_{2}= 0. Hence, m = 3(3-1)-(2×3)-0 = 0 As the degree of freedom is 0, there is no relative motion between the links and the mechanism forms a structure.

6. Find the mobility of the given mechanism.

a) 0

b) 1

c) 2

d) 3

### View Answer

_{1}= 4, j

_{2}= 0. Hence, m = 3(4-1)-(2×4)-0 = 1 As the degree of freedom is 1, the mechanism can be brought into motion by a single input motion.

7. Find the mobility of the given mechanism.

a) 0

b) 1

c) 2

d) 3

### View Answer

_{1}= 5, j

_{2}= 0. Hence, m = 3(5-1)-(2×5)-0 = 2 As the degree of freedom is 2, two separate input motions are required to produce constrained motion for the mechanism.

8. If there are redundant constraints in the chain and it forms a statically indeterminate structure, what is the degree of freedom or the mobility of this structure?

a) 0

b) 1

c) 2

d) Less than 0

### View Answer

9. Find the mobility of the given mechanism

a) -2

b) 2

c) -1

d) 1

### View Answer

_{1}= 8, j

_{2}= 0. Hence, m = 3(6-1)-(2×8)-0 = -1 The degree of freedom is -1, thus there are redundant constraints in the chain and a statically indeterminate structure is formed.

10. Find the mobility of the following mechanism with a higher pair.

a) 3

b) -1

c) 1

d) 2

### View Answer

_{1}= 3, j

_{2}= 1. Hence, m = 3(4-1)-(2×3)-1 = 2 The degree of freedom or mobility is 2.

11. Find the mobility of the given mechanism

a) 1

b) 3

c) 2

d) 0

### View Answer

_{1}= 7, j

_{2}= 0. Hence, m = 3(6-1)-(2×7)-0 = 1 The degree of freedom or mobility is 1.

12. State the equation for the three dimensional form of Grubler’s criterion.

a) 6n-5j_{1}-7=0

b) 6n-6j_{1}-6=0

c) 6n+5j_{1}+7=0

d) 6n+6j_{1}+6=0

### View Answer

_{2}= j

_{3}= j

_{4}= j

_{5}= 0 in the equation of mobility according to three dimensional form of Kutzbach criterion. 1 = 6(n-1)-5j

_{1}-(4×0)-(3×0)-(2×0)-0 Therefore,6n-5j

_{1}-7=0.

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