Machine Kinematics Puzzles on “Path of Contact”.
1. Which of the following is a commonly used pressure angle in gears?
a) 20
b) 10
c) 12
d) 17
Answer: a
Clarification: The pressure angle is the angle between the tangent to the pitch circles and the line drawn normal (perpendicular) to the surface of the gear teeth. It has a set of standard values which is accepted globally, 20° is one of them.
2. Addendum circle of the gear wheel has the shortest radius.
a) True
b) False
Answer: b
Clarification: Addendum circle of the gear wheel has the largest radius, the base circle has the smallest radius. Addendum of the gear plays a vital role in determining whether interference will take place or not.
3. Which of the following is true for Length of arc of contact?
a) Sum of Arc of recess and Arc of approach
b) Difference of arc of approach and arc of recess
c) Twice the arc of approach
d) Twice the arc of recess
Answer: a
Clarification: The arc of contact is given by the sum of Length of arc of approach and length of arc of recess. Numerically it is the ratio of length of path of contact and the cosine of the pressure angle.
4. Which of the following is true for Length of path of contact?
a) Sum of path of recess and path of approach
b) Difference of path of approach and path of recess
c) Twice the arc of approach
d) Twice the path of recess
Answer: a
Clarification: The path of contact is given by the sum of Length of path of approach and length of path of recess. Numerically it is dependent on pitch radius, addendum radius and the sine of pressure angle.
5. From the following data, find the addendum in mm:
Teeth on each wheel: 40
Pressure angle: 20°
Module: 6mm
Arc of contact/ pitch: 1.75
a) 6.12
b) 6.51
c) 6.61
d) 6.81
Answer: a
Clarification: Pc = πm = 18.85mm
Arc of contact = 1.75xp = 33mm
Length of path of contact = cosΦx Arc of contact
From another relation of length of path of contact we get
Ra = 126.12 mm
R = 120mm
Therefore addendum = 6.12mm.
6. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the length of path of contact in mm.
a) 52.3
b) 55.4
c) 53.2
d) 54.5
Answer: a
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm.
7. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the length of arc of contact in mm.
a) 52.333
b) 55.66
c) 53.22
d) 54.55
Answer: b
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm
Length of arc of contact = length of path of contact / cosΦ
= 55.66mm.
8. Maximum sliding velocity is the sum of angular velocities and its product with the length of path of contact.
a) True
b) False
Answer: b
Clarification: Maximum sliding velocity is the sum of angular velocities and its product with the length of path of appraoch.
Vs = (ω2 + ω1)x(length of path of approach).
9. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the contact ratio.
a) 1.5
b) 1.75
c) 2
d) 1,33
Answer: b
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm
Length of arc of contact = length of path of contact / cosΦ
Contact ratio = Length of arc of contact/Pc
=1.75.
10. Find maximum sliding velocity in cm/s from the given data
addendum = 1 module = 5mm
Pitch line speed = 1.2m/s
Pressure angle of involute profile: 20 degrees
Tp = 20
Gear ratio = 2
a) 45.5
b) 46.8
c) 45.1
d) 47.2
Answer: a
Clarification: We know that
V = ω1r = ω2R
120/(mt/2) = ω1
ω1 = 24 rad/s
similarly
ω2 = 12 rad/s
Now maximum sliding velocity = (ω2 + ω1)x(length of path of approach)
= 455.4 mm/s
= 45.5 cm/s.
To practice all Puzzles on Machine Kinematics,