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1. Department of Mechanical & Manufacturing Engineering, MIT, Manipal 1 of 17
CHAPTER 5
GEAR TRAIN
KINEMATICS OF MACHINERY
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KINEMATICS OF MACHINERY
1.1 Introduction
When two or more gears are made to mesh
with each other to transmit power from one
shaft to another such a combination is called
gear train.
The nature of the train used depends upon
the velocity ratio required and the relative
position of the axes of shafts.
A gear train may consist of spur and spiral
gears.
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KINEMATICS OF MACHINERY
1.2 Types of Gear Train
Depending upon the arrangement of wheels
the different types of gear train are as follows:
1.Simple gear train
2.Compound gear train
3.Reverted gear train
4.Epicyclic gear train
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KINEMATICS OF MACHINERY
1.2 Types of Gear Train
In the first three types of gear trains, the axes of
the shafts over which the gears are mounted are
fixed relative to each other.
But in case of epicyclic gear trains, the axes of
the shafts on which the gears are mounted may
move relative to a fixed axis.
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KINEMATICS OF MACHINERY
1.2.1 Simple gear train
Figure (a).
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KINEMATICS OF MACHINERY
1.2.1 Simple gear train
Figure (b).
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KINEMATICS OF MACHINERY
1.2.1 Simple gear train
Figure (c). What is the Speed ratio ?
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KINEMATICS OF MACHINERY
1.2.2 Compound gear train
The speed ratio of
compound gear train is
given by:
Note: Since gears 2 and 3 are mounted on
one shaft B, therefore N2=N3, Similarly
gears 4 and 5 are mounted on shaft C,
therefore N4 = N5.
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KINEMATICS OF MACHINERY
1.2.3 Reverted gear train
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KINEMATICS OF MACHINERY
1.2.4 Epicyclic gear train
The epicyclic gear trains are useful for transmitting high
velocity ratios with gears of moderate size in a
comparatively lesser space.
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KINEMATICS OF MACHINERY
1.3 Automobile Differential Mechanism
Function is to,
(a) Transmit motion from the engine shaft to the rear driving
wheels, and
(b) Rotate the rear wheels at different speeds while the
automobile is taking a turn.
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KINEMATICS OF MACHINERY
1.3 Automobile Differential Mechanism
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KINEMATICS OF MACHINERY
1.3 Automobile Differential Mechanism
Table of motions
Step
No.
Condition of motion
Revolution of elements
Gear B Gear C Gear E Gear D
1
Gear B fixed-Gear C rotated
through +1 revolutions (anti
-clockwise) 0 + 1 +
𝑇𝑐
𝑇𝐸
−
𝑇𝑐
𝑇𝐸
𝑇𝐸
𝑇𝐷
= −1
(𝑇𝐶 = 𝑇𝐷)
2
Gear B fixed-Gear C rotated
through + x revolutions
0 + x +𝑥
𝑇𝑐
𝑇𝐸
- x
3
Add + y revolutions to all
elements
+ y + y + y + y
4
Total motion
+ y x + y 𝑦 + 𝑥
𝑇𝑐
𝑇𝐸
y - x
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KINEMATICS OF MACHINERY
1.4 Analysis of Epicyclic Gear Train
S
P
arm a
Carrier
S
p
a
Epicyclic trains usually have complex motions.
Therefore, comparatively simple methods are used
to analyze them which do not require accurate
visualization of the motions.
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KINEMATICS OF MACHINERY
1.4 Analysis of Epicyclic Gear Train
Step
No.
Condition of motion
Revolution of elements
Arm a Gear S Gear P
1
Fix the arm, ‘a’ and give
+1 revolutions to S 0 + 1 −
𝑇𝑆
𝑇𝑃
2
Fix the arm, ‘a’ and give
+x revolutions to S 0 + x −𝑥
𝑇𝑆
𝑇𝑃
3
Add + y revolutions to all
elements
+ y + y + y
4
Total motion
+ y x + y 𝑦 − 𝑥
𝑇𝑆
𝑇𝑃
Table of motions
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KINEMATICS OF MACHINERY
1.5 Torques in Epicyclic Gear Train
Torque is transmitted from one element to another when a
geared system transmits power.
A
S
P
arm a
Carrier
Machine
Prime
mover
System
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KINEMATICS OF MACHINERY
Numericals from
Chapter : Gear Train
End of Chapter