1. The distance travelled by a point on either pitch circle of the two wheels during the period of contact of a pair of teeth is called ____________________

a) path of contact

b) arc of contact

c) contact ratio

d) angle of action

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2. The contact ratio is the ratio of arc of contact to the ____________

a) circular pitch

b) dedendum

c) circular pitch

d) module

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3. If the contact ratio is 2.7, two pairs of teeth are always in contact and three pairs of teeth are in contact for _________ % of the time.

a) 100

b) 50

c) 45

d) 70

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4. For continuous transmission of motion, the contact ratio i.e. n must always be _______

a) equal to 1

b) equal to 0

c) more than unity

d) less than unity

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5. Two involute gears have path of contact 40 mm and the pressure angle is 50°. Find the arc of contact.

a) 62.23 mm

b) 25.71 mm

c) 30.64 mm

d) 52.21 mm

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6. Two gears in a mesh have the arc of contact = 27 mm. The pressure angle is 15°. Find the path of contact.

a) 104.32 mm

b) 6.98 mm

c) 27.95 mm

d) 26.08 mm

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7. Two involute gears in a mesh have a circular pitch of 25 mm. The arc of contact is 55 mm. Find the number of pairs of teeth in contact.

a) 2.2

b) 0.45

c) 13.75

d) 1.3

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8. Two involute gear have a module of 5 mm, the arc of contact is 25 mm. Find the contact ratio of these two gears.

a) 5

b) 1.59

c) 0.2

d) 3

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9. The path of contact of two gears in a mesh is 50 mm and the pressure angle is 45°. The module is 8 mm. Find the contact ratio of these two gears.

a) 4.2

b) 1.9

c) 3.7

d) 2.8

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10. The path of approach = 13.92 mm and path of recess = 11.56 mm. The pressure angle is 22.5°. The module is 4 mm. Find the contact ratio of these two gears.

a) 2.19

b) 3.54

c) 3.12

d) 2.53

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11. Two involute gears in a mesh have a module of 10 mm and the pressure angle is 35°. The larger gear has 45 teeth whereas the pinion has 15 teeth. The addendum is equal to one module. Find the arc of contact.

a) 36. 832 mm

b) 32.460 mm

c) 39.626 mm

d) 27.239 mm

### View Answer

_{a}= r + a = 85 mm, R

_{a}= R + a = 235 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)sinφ = 32.46 mm Arc of contact = Path of contact/cos φ = 32.46/cos 35° = 39.626 mm.

12. The pressure angle of two gears in a mesh is φ = 22.5°. The number of teeth on the pinion is 25 and the gear ratio is 2. The module is 7 mm and addendum = 1 module. Find the angle of action of these two gears.

a) 32.056°

b) 34.697°

c) 22.72°

d) 28.531°

### View Answer

_{a}= r + a = 94.5 mm R = mT/2 = 175 mm and R

_{a}= R + a = 182 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)sinφ = 32.056 mm Arc of contact = Path of contact/cos φ = 32.056/cos 22.5° = 34.697 mm. Angle of action = Arc of contact / r = 0.3965 rad = 22.72°.

13. The pressure angle of two gears in a mesh is φ = 25°. The number of teeth on the pinion is 45 and the gear ratio is 2. The module is 6 mm and addendum = 1.1 module. Find the contact ratio of these two gears.

a) 1.7

b) 2.3

c) 4.2

d) 3.5

### View Answer

_{a}= r + a = 141.6 mm R = mT/2 = 270 mm and R

_{a}= R + a = 276.6 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)sinφ = 29.068 mm Arc of contact = Path of contact/cos φ = 29.068/cos 25° = 32.073 mm. Contact ratio = Arc of contact / Circular pitch = 32.073 / πm = 32.073 / (πx6) = 1.7.

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