1. In the given diagram identify the path of contact.

a) CD

b) AB

c) FE

d) BP

### View Answer

2. The formula to calculate path of contact is ______________________

a) (R_{a}^{2} + R^{2}cos^{2} φ)^{0.5} + (r_{a}^{2} + r^{2}cos^{2} φ)^{0.5} – (R+r)sin φ

b) (R_{a}^{2} – R^{2}cos^{2} φ)^{0.5} + (r_{a}^{2} – r^{2}cos^{2} φ)^{0.5} + (R+r)sin φ

c) (R_{a}^{2} – R^{2}cos^{2} φ)^{0.5} + (r_{a}^{2} – r^{2}cos^{2} φ)^{0.5} – (R+r)sin φ

d) (R_{a}^{2} – R^{2}cos^{2} φ)^{0.5} + (r_{a}^{2} – r^{2}cos^{2} φ)^{0.5} – (R-r)sin φ

### View Answer

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}+ (r

_{a}

^{2}– r

^{2}cos

^{2}φ)

^{0.5}– (R+r)sin φ.

3. The condition which must be fulfilled by two gear tooth profiles to maintain a constant angular velocity ratio between them is called __________________

a) arc of contact

b) path of contact

c) law of gearing

d) interference

### View Answer

4. Find the path of contact if r = 20 mm, r_{a}= 25 mm, R = 50 mm, R_{a} = 55 mm and φ = 20°.

a) 11.836 mm

b) 21.135 mm

c) 69.018 mm

d) 36.046 mm

### View Answer

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}+ (r

_{a}

^{2}– r

^{2}cos

^{2}φ)

^{0.5}– (R+r)sin φ = 21.135 mm.

5. What is the formula for the path of approach?

a) (R_{a}^{2} – R^{2}cos^{2} φ)^{0.5} – Rsinφ

b) (R_{a}^{2} + R^{2}cos^{2} φ)^{0.5} + Rcosφ

c) (R_{a}^{2} + R^{2}cos^{2} φ)^{0.5} + Rsinφ

d) (R_{a}^{2} + R^{2}cos^{2} φ)^{0.5} – Rcosφ

### View Answer

_{a}

^{2}+ R

^{2}cos

^{2}φ)

^{0.5}– Rsinφ; where R

_{a}= The addendum radius of the larger gear, R = The radius of the larger gear and φ is the pressure angle. Path of approach is the portion of path of contact from the beginning of contact to the pitch point. Similarly, the formula for the path of recess is (R

_{a}

^{2}+ R

^{2}cos

^{2}φ)

^{0.5}– rsinφ.

6. To avoid interference what is the maximum length of the path of approach?

a) Rsinφ

b) rsinφ

c) Rcosφ

d) rcosφ

### View Answer

7. Two gears in a mesh have 45 teeth each and the module is 5 mm. The pressure angle is given to be φ = 15°. The addendum is equal to 1 module. Find the path of contact.

a) 31.159 mm

b) 48.201 mm

c) 34. 356 mm

d) 42.543 mm

### View Answer

_{a}= r

_{a}= 112.5 + 5 = 117.5 mm Path of contact = (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}+ (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}– (R+r)sin φ= 31.159 mm.

8. The pressure angle of two gears in a mesh is φ = 20°. The gear ratio is 3 and the number of teeth on the pinion is 20. The module is given to be 8 mm. The addendum is one module. Find the path of contact of these two gears.

a) 21.324 mm

b) 12.543 mm

c) 56.343 mm

d) 39.458 mm

### View Answer

_{a}= r + a = 88 mm, R

_{a}= r + a = 248 mm Path of contact = (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}+ (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}– (R+r)sin φ = 39.458 mm.

9. The pressure angle of two gears in a mesh is φ = 25°. The number of teeth on the pinion is 25 and the number of teeth on the gear is 70. The module is given to be 10 mm. The addendum is 1.1 times the module. Find the path of approach and path of contact of these gears.

a) 24.421 mm, 22.417 mm

b) 22.417 mm, 24.421 mm

c) 26.407 mm, 20.431 mm

d) 20.431 mm, 26.407 mm

### View Answer

_{a}= r + a = 136 mm, R

_{a}= R + a = 361 mm Path of approach = (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}– Rsinφ = 24.421 mm Path of recess = (r

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}– rsinφ = 22.417 mm.

10. The pressure angle of two gears in a mesh is φ = 15°. The number of teeth on the larger gear is 50. The module is 4 mm. The addendum is equal to be 1.25 module. Find the path of approach of these gears.

a) 39.211 mm

b) 15.287 mm

c) 31.092 mm

d) 21.122 mm

### View Answer

_{a}= R + a = 105 mm Path of approach = (R

_{a}

^{2}– R

^{2}cos

^{2}φ)

^{0.5}– Rsinφ = 15.287 mm.

11. The pressure angle of two gears in a mesh is φ = 35°. The number of teeth on the pinion is 20. The module is 10 mm and the addendum is 1 module. Find the path of recess of these gears.

a) 34.213 mm

b) 23.328 mm

c) 16.058 mm

d) 32.091 mm

### View Answer

_{a}= r + a = 110 mm Path of recess = (r

_{a}

^{2}– r

^{2}cos

^{2}φ)

^{0.5}– rsinφ= 16.058 mm.

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