Machine Kinematics Problems on “Minimum Number of Teeth on a Pinion for Involute Rack in Order to Avoid Interference”.
1. The minimum number of teeth on the pinion which will mesh with any gear without interference for 200 full depth involute teeth will be
a) 12
b) 14
c) 18
d) 24
Answer: c
Clarification: The minimum number of teeth on the pinion in order to avoid interference for 14.50 full depth involute are 32 and for 200 full depth involute teeth are 18.
2. In gears, interference takes place when
a) the tip of a tooth of a mating gear digs into the portion between base and root circles
b) gears do not move smoothly in the absence of lubrication
c) pitch of the gears is not same
d) gear teeth are undercut
Answer: a
Clarification: Interference occurs when the number of teeth on the smaller of the two meshing gears is less than a required minimum.
3. An involute pinion and gear are in mesh. If both have the same size of addendum, then there will be an interference between the
a) tip of the gear tooth and flank of pinion
b) tip of the pinion and flank of gear
c) flanks of both gear and pinion
d) tip of both gear and pinion
Answer: a
Clarification: The phenomenon when the tip of a tooth under cuts the root on its mating gear, is known as interference.
4. Which of the following statement is correct for involute gears?
a) The interference is inherently absent
b) The variation in centre distance of shafts increases radial force
c) A convex flank is always in contact with concave flank
d) The pressure angle is constant throughout the teeth engagement
Answer: d
Clarification: None.
5. The interference may only be avoided if the addendum circles of the two mating gears cut the common tangent to the base circles between the points of tangency.
a) True
b) False
Answer: a
Clarification: None.
6. 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) (r2 + R2) cosɸ/2
b) (r2 + R2) sinɸ/2
c) (r + R) cosɸ/2
d) (r + R) sinɸ/2
Answer: d
Clarification: None.
7. The maximum efficiency of spiral gears is
a) sin (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1
b) cos(ϴ – ɸ) +1/sin (ϴ + ɸ) + 1
c) cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1
d) cos(ϴ – ɸ) +1/cos (ϴ + ɸ) + 1
Answer: c
Clarification: The maximum efficiency of spiral gears is
cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1
where, ϴ = Shaft angle
and ɸ = Friction angle.
8. The contact ratio for gears is
a) zero
b) less than one
c) greater than one
d) infinity
Answer: c
Clarification: 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.
9. In a simple train of wheels, if the number of intermediate wheels is odd, the motion of the follower will be same as that of the driver.
a) True
b) False
Answer: a
Clarification: The speed ratio (or velocity ratio) of gear train is the ratio of the speed of the driver to
the speed of the driven or follower. But if the number of intermediate gears are even, the motion of the driven or follower will be in the opposite direction of the driver.
10. In a simple train of wheels, the velocity ratio _____________ the intermediate wheels.
a) depends upon
b) is independent of
c) is equal to
d) none of the mentioned
Answer: b
Clarification: The speed ratio (or velocity ratio) of gear train is the ratio of the speed of the driver to
the speed of the driven or follower and ratio of speeds of any pair of gears in mesh is the inverse of
their number of teeth.
11. The train value of a gear train is
a) equal to velocity ratio of a gear train
b) reciprocal of velocity ratio of a gear train
c) always greater than unity
d) always less than unity
Answer: b
Clarification: The train value is the reciprocal of speed ratio.
12. When the axes of the first and the last wheels are co-axial, then the train is known as
a) simple train of wheels
b) compound train of wheels
c) reverted gear train
d) epicyclic gear train
Answer: c
Clarification: When there is only one gear on each shaft, it is known as simple gear train.
When there are more than one gear on a shaft, it is called a compound train of gear.
When the axes of the first gear (i.e. first driver) and the last gear (i.e. last driven or follower) are co-axial, then the gear train is known as reverted gear train.
13. When the axes of the shafts, over which the gears are mounted, move relative to a fixed axis, then the train is known as reverted gear train.
a) True
b) False
Answer: b
Clarification: When the axes of the first gear (i.e. first driver) and the last gear (i.e. last driven or follower) are co-axial, then the gear train is known as reverted gear train.
14. The gear train usually employed in clocks is a
a) simple gear train
b) reverted gear train
c) sun and planet gear
d) differential gear
Answer: b
Clarification: The reverted gear trains are used in automotive transmissions, lathe back gears, industrial speed reducers, and in clocks (where the minute and hour hand shafts are co-axial).
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