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# Machine Kinematics MCQ – Toothed Gearing – 2

The condition of correct gearing is

a) pitch line velocities of teeth be same

b) radius of curvature of two profiles be same

c) common normal to the pitch surface cuts the line of centres at a fixed point

d) none of the mentioned

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Answer: c

Explanation: The fundamental condition of correct gearing is the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

Law of gearing is satisfied if

a) two surfaces slide smoothly

b) common normal at the point of contact passes through the pitch point on the line joining the centres of rotation

c) number of teeth = P.C.D. / module

d) addendum is greater than dedendum

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Answer: b

Explanation: Law of gearing says that the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

Involute profile is preferred to cyloidal because

a) the profile is easy to cut

b) only one curve is required to cut

c) the rack has straight line profile and hence can be cut accurately

d) none of the mentioned

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Answer: b

Explanation: The face and flank of involute teeth are generated by a single curve where as in cycloidal

gears, double curves (i.e. epi-cycloid and hypo-cycloid) are required for the face and flank respectively.

Thus the involute teeth are easy to manufacture than cycloidal teeth. In involute system, the basic rack has straight teeth and the same can be cut with simple tools.

The contact ratio for gears is

a) zero

b) less than one

c) greater than one

d) none of the mentioned

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Answer: c

Explanation: The theoretical minimum value for the contact ratio is one, that is there must always be at least one pair of teeth in contact for continuous action.

The maximum length of arc of contact for two mating gears, in order to avoid interference, is

a) (r + R) sin φ

b) (r + R) cos φ

c) (r + R) tan φ

d) none of the mentioned

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Answer: c

Explanation: Interference may only be prevented, if the addendum circles of the two mating gears cut the

common tangent to the base circles between the points of tangency.

maximum length of arc of contact = (r + R) tan φ

where r = Pitch circle radius of pinion,

R = Pitch circle radius of driver, and

φ = Pressure angle.

When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

a) (r + R) sin φ/2

b) (r + R) cos φ/2

c) (r + R) tan φ/2

d) (r + R) cot φ/2

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Answer: a

Explanation: In case the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then

Path of approach, KP = 1/2 MP.

Interference can be avoided in involute gears with 20° pressure angle by

a) cutting involute correctly

b) using as small number of teeth as possible

c) using more than 20 teeth

d) using more than 8 teeth

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Answer: c

Explanation: None.

The ratio of face width to transverse pitch of a helical gear with α as the helix angle is normally

a) more than 1.15/tan α

b) more than 1.05/tan α

c) more than 1/tan α

d) none of the mentioned

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Answer: a

Explanation: None.

The maximum efficiency for spiral gears is

a) sin (θ + φ ) + 1/ cos (θ − φ ) + 1

b) cos (θ − φ) + 1/sin (θ + φ ) + 1

c) cos (θ + φ ) + 1/ cos (θ − φ ) + 1

d) cos (θ − φ) + 1/cos (θ + φ ) + 1

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Answer: c

Explanation: ηmax = cos (θ + φ ) + 1/ cos (θ − φ ) + 1

where θ = Shaft angle, and φ = Friction angle.

For a speed ratio of 100, smallest gear box is obtained by using

a) a pair of spur gears

b) a pair of helical and a pair of spur gear compounded

c) a pair of bevel and a pair of spur gear compounded

d) a pair of helical and a pair of worm gear compounded

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Answer: d

Explanation: None.