Ghh

23. 3.Reverted Gear Train

26. Epicyclic gear train

27. Epicyclic gear train

28. Epicyclic gear train

29. Epicyclic gear train

31. Epicyclic or Planetary Gear Trains
The conventional gear trains described in the previous sections are all one-degree-of-freedom (DOF)
devices. Another class of gear train has wide application, the epicyclic or planetary train. This is a
two-DOF device. Two inputs are needed to obtain a predictable output.The epicyclic gear trains are
useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser
space. They are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley
blocks, wrist watches etc.

45. EXAMPLE 1
[Dec 2010, Dec 2012, Jan 2015]

51. EXAMPLE 1
[Dec 2010, Dec 2012, Jan 2015]

58. In an epicyclic gear train an arm ‘C’ carries
two gears ‘A’ and ‘B’ Having number of
teeth Ta and Tb respectively. If arm ‘C’
rotates One revolution clockwise, how
many times gear ‘B’ will rotate When gear
‘A’ is fixed. Derive the relation by tabular
method, And relative velocity method
and if Ta = 200, Tb = 25. find the
Revolution of ‘B’
[June 2016]
ANS : NB = 9 rpm ( Anti-clock wise)

62. In an epicyclic gear train an arm ‘C’ carries
two gears ‘A’ and ‘B’ Having number of
teeth Ta and Tb respectively. If arm ‘C’
rotates One revolution clockwise, how
many times gear ‘B’ will rotate When gear
‘A’ is fixed. Derive the relation by tabular
method, And relative velocity method
and if Ta = 200, Tb = 25. find the
Revolution of ‘B’
[June 2016]
ANS : NB = 9 rpm ( Anti-clock wise)

66. In a reverted epicyclic gear train arm F, carries two
wheels A and D and a compound wheel B-C. All four
gears have equal module. Wheel A meshes externally
with wheel B. Wheel D meshes externally with wheel C.
Number of teeth on gear A is 40. Number of teeth on
gear D is 24. Number of teeth on gear C is 36. Wheel A is
fixed. Arm F rotates at 300 rpm clockwise.
Find (a) number of teeth on gear B
(b) develop table to determine speed of all gears
(c) speed of gear D using tabular method
(d) direction of rotation of gear D
(14 marks)
June-July 2019

68. rA+ rB = rC+ rD
TA+ TB = TC+ TD
40+ TB = 36+ 24
TB = 20

71. Wheel A is fixed.
Arm F rotates at 300 rpm clockwise.
TA=40 TB = 20 TC=36 TD=24
Y= -300 rpm
y- 𝒙
𝑻𝑩
𝑻𝑨
=0 -300- 𝒙
𝟐𝟎
𝟒𝟎
=0
X=-600

72. Wheel A is fixed.
Arm F rotates at 300 rpm clockwise.
TA=40 TB = 20 TC=36 TD=24 X=-600 Y= -300 rpm
ND= y- 𝒙
𝑻𝑪
𝑻𝑫
= - 300 - [−𝟔𝟎𝟎 𝑿
𝟑𝟔
𝟐𝟒
]
ND= + 600 (Anti-Clockwise)

73. EXAMPLE 2

77. EXAMPLE 2

85. An epicyclic train of gears is arranged as shown
in Fig How many revolutions does the arm, to
which the gears B and C are attached, make :
1. when A makes one revolution clockwise and D
makes half a revolution anticlockwise, and
2. when A makes one revolution clockwise and D
is stationary ?
The number of teeth on the gears A and D are 40
and 90 respectively.
JUNE/JULY 2018

86. TA = 40
TD = 90
dA + dC+ dB = dD OR dA + 2dB = dD
TA + TC+ TB = TD OR TA + 2TB = TD
TB = 25 TC = 25

89. 1. Speed of arm when A makes 1 revolution clockwise and D makes
half revolution anticlockwise
- x – y = - 1 OR x + y = 1 (1)
TA = 40 TD = 90 TB = 25 TC = 25
𝐱 𝐗
𝐓𝐀
𝐓𝐃
-Y =
𝟏
𝟐
OR 𝐱 𝐗
𝟒𝟎
𝟗𝟎
-Y =
𝟏
𝟐
𝟒𝟎 𝐱 − 𝟗𝟎Y = 𝟒𝟓 OR 𝐱 − 𝟐. 𝟐𝟓Y = 𝟏. 𝟏𝟐𝟓(2)
𝐱 = 𝟏. 𝟎𝟒 Y = −𝟎. 𝟎𝟒
Speed of arm = – y = – (– 0.04) = + 0.04

90. 2. Speed of arm when A makes 1 revolution clockwise and D is
stationary
- x – y = - 1 OR x + y = 1 (1)
TA = 40 TD = 90 TB = 25 TC = 25
𝐱 𝐗
𝐓𝐀
𝐓𝐃
-Y = 𝟎 OR 𝐱 𝐗
𝟒𝟎
𝟗𝟎
-Y = 𝟎
𝟒𝟎 𝐱 − 𝟗𝟎Y = 𝟎 OR 𝐱 − 𝟐. 𝟐𝟓Y = 𝟎 (2)
𝐱 = 0. 𝟔𝟗𝟐 Y = 𝟎. 𝟑𝟎𝟖
Speed of arm = – y = – ( 0.308) = - 0.308 REV

91. EXAMPLE 3

95. In an epicyclic gear train, the internal wheels A and B and
compound wheels C and D rotate independently about
axis O. The wheels E and F rotate on pins fixed to the arm
G. E gears with A and C and F gears with B and D. All the
wheels have the same module and the number of teeth
are: TC = 28; TD = 26; TE = TF = 18.
a) Sketch the arrangement; ( 4 marks)
b) Find the number of teeth on A and B ; (2 marks)
c) If the arm G makes 100 r.p.m. clockwise and A is fixed,
find the speed of B ;
(2 marks)
d) If the arm G makes 100 r.p.m. clockwise and wheel A
makes 10 r.p.m. counter clockwise; find the speed of
wheel B. (2 marks)
December 2019/Jan 2020
December 2018

96. In an epicyclic gear train, the internal wheels A and B and compound wheels
C and D rotate independently about axis O. The wheels E and F rotate on pins
fixed to the arm G. E gears with A and C and F gears with B and D. All the
wheels have the same module and the number of teeth are: TC = 28; TD = 26;
TE = TF = 18.
a) Sketch the arrangement; ( 4 marks)
b) Find the number of teeth on A and B ; (2 marks)
c) If the arm G makes 100 r.p.m. clockwise and A is fixed, find the speed of B
;
(2 marks)
d) If the arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m.
counter clockwise; find the speed of wheel B.
(2 marks)
December 2019/Jan 2020
December 2018

98. dA = dC+ 2dE dB = dD+ 2dF
TA = TC+ 2TE TB = TD+ 2TF
TA = 64 TB = 62
TC = 28
TD = 26
TE = TF =18

102. If the arm G makes 100 r.p.m. clockwise and A is fixed, find the speed of B ;
Y= -100 rpm x+y=0 x = - y = + 100
TC = 28 TD = 26 TE = TF =18 TA = 64 TB = 62
NB = y + 𝐱 𝐗
𝐓𝐀
𝐓𝐂
X
𝐓𝐃
𝐓𝐁
NB = -100 +𝟏𝟎𝟎 𝐗
𝟔𝟒
𝟐𝟖
X
𝟐𝟔
𝟔𝟐
= -4.14 RPM
NB = -4.14 RPM (Clockwise)

103. Y= -100 rpm x+y= +10 x = 10 - y = + 110
TC = 28 TD = 26 TE = TF =18 TA = 64 TB = 62
NB = y + 𝐱 𝐗
𝐓𝐀
𝐓𝐂
X
𝐓𝐃
𝐓𝐁
NB = -100 +𝟏𝟏𝟎 𝐗
𝟔𝟒
𝟐𝟖
X
𝟐𝟔
𝟔𝟐
= + 5.43 RPM
NB = + 5.43 RPM (Counter clockwise)
If the arm G makes 100 r.p.m. clockwise and wheel A
makes 10 r.p.m. counter clockwise

104. In an epicycle gear train, the internal wheels A & B are
compound wheels C and D rotate independently about axis
“O”. The wheels E & F rotate on pins fixed to the arm G. E
gears with A and C, F gears with B and D. All the wheels
have the same module and the number of teeth are TC=28,
TD= 26, TE= TF = 20
a) Sketch the arrangement
b) Find the numbers of the teeth on A & B
c) If the arm G makes 100 rpm clockwise and A is fixed.
Find the
speed of B
d) If the arm G makes 100 rpm clockwise and wheel A
makes 10
rpm counter clockwise. Find the speed of wheel B. (14)
JUNE/JULY 2019

105. Dec 2018

106. In an epicyclic gear train, the internal wheels A and B and
compound wheels C and D rotate independently about
axis O. The wheels E and F rotate on pins fixed to the arm
G. E gears with A and C and F gears with B and D. All the
wheels have the same module and the number of teeth
are: TC = 30; TD = 28; TE = TF = 20.
a) Sketch the arrangement; ( 4 marks)
b) Find the number of teeth on A and B ; (2 marks)
c) If the arm G makes 120 r.p.m. clockwise and A is fixed,
find the speed of B ;
(2 marks)
d) If the arm G makes 120 r.p.m. clockwise and wheel A
makes 12 r.p.m. counter clockwise; find the speed of
wheel B. (2 marks)
December 2019/Jan 2020
December 2018

108. dA = dC+ 2dE dB = dD+ 2dF
TA = TC+ 2TE TB = TD+ 2TF
TA = 70 TB = 68
TC = 30
TD = 28
TE = TF =20

112. If the arm G makes 120 r.p.m. clockwise and A is fixed, find the speed of B ;
Y= -120 rpm x+y=0 X = -Y = +120
TC = 30 TD = 28 TE = TF =20 TA = 70 TB = 68
NB = y + 𝐱 𝐗
𝐓𝐀
𝐓𝐂
X
𝐓𝐃
𝐓𝐁
NB = -120 +𝟏𝟐𝟎 𝐗
𝟕𝟎
𝟑𝟎
X
𝟐𝟖
𝟔𝟖
= -4.7 RPM
NB = 4.7 RPM (Clockwise)

113. Y= -120 rpm x+y= +10 x = 10 - y = + 130
TC = 30 TD = 28 TE = TF =20 TA = 70 TB = 68
NB = y + 𝐱 𝐗
𝐓𝐀
𝐓𝐂
X
𝐓𝐃
𝐓𝐁
NB = -120 +𝟏𝟑𝟎 𝐗
𝟕𝟎
𝟑𝟎
X
𝟐𝟖
𝟔𝟖
= + 4.9 RPM
NB = + 4.9 RPM (Counter clockwise)
If the arm G makes 120 r.p.m. clockwise and wheel A
makes 10 r.p.m. counter clockwise