A gear train is used to transmit motion from one shaft to another while reducing speed. The main types are simple, compound, reverted, planetary, and differential gear trains. A simple gear train uses separate gears on fixed shafts to reduce speed through gear ratios. A compound gear train has intermediate gears sharing the same axis to reduce speed. A reverted gear train has the first and last gears sharing a common axis. A planetary gear train allows relative motion of gears around a central gear to achieve high speed reductions in a compact space. A differential gear allows the wheels of a vehicle to rotate at different speeds during turns.

1. GEAR TRAINGEAR TRAIN
A gear train is a combination of gearsA gear train is a combination of gears
used to transmit motion from one shaftused to transmit motion from one shaft
to other shaft. It becomes necessaryto other shaft. It becomes necessary
when it is required to obtain a largewhen it is required to obtain a large
reduction in speed within a smallreduction in speed within a small
space. The following are the mainspace. The following are the main
types of gear trains.types of gear trains.

2. GEAR TRAINGEAR TRAIN
 1. SIMPLE GEAR TRAIN1. SIMPLE GEAR TRAIN
 2. COMPOUND GEAR TRAIN2. COMPOUND GEAR TRAIN
 3. REVERTED GEAR TRAIN3. REVERTED GEAR TRAIN
 4. EPICYCLIC OR PLANETARY GEAR4. EPICYCLIC OR PLANETARY GEAR
TRAINTRAIN
 5. DIFFERENTIAL5. DIFFERENTIAL

3. SIMPLE GEAR TRAINSIMPLE GEAR TRAIN
A series of gears, capable of receivingA series of gears, capable of receiving
and transmitting motion from oneand transmitting motion from one
gear to another is called a Simplegear to another is called a Simple
Gear Train. In this, all the gears axesGear Train. In this, all the gears axes
remain fixed relative to the frame andremain fixed relative to the frame and
each gear is on a separate shaft. Ineach gear is on a separate shaft. In
simple gear train it is seen that thesimple gear train it is seen that the
intermediate gears have no effect onintermediate gears have no effect on
the speed ratio and therefore they arethe speed ratio and therefore they are
known as idler gears.known as idler gears.

4. SIMPLE GEAR TRAINSIMPLE GEAR TRAIN
 Consider a Simple Gear Train as shown inConsider a Simple Gear Train as shown in
the figure (1)the figure (1)
 Let N1 = Speed of driver gear in rpm.Let N1 = Speed of driver gear in rpm.
N2, N3, N4 = Speeds of the intermediateN2, N3, N4 = Speeds of the intermediate
gears in rpm.gears in rpm.
N5 = Speed of driven gear in rpm.N5 = Speed of driven gear in rpm.

5. SIMPLE GEAR TRAINSIMPLE GEAR TRAIN

6. SIMPLE GEAR TRAINSIMPLE GEAR TRAIN
T1 = Number of teeth on driver gearT1 = Number of teeth on driver gear
T2,T3, T4 = Number of teeth onT2,T3, T4 = Number of teeth on
intermediate gearsintermediate gears
T5 = Number of teeth on driven gearT5 = Number of teeth on driven gear
We have N1/ N2 = T2/T1 ; N2/ N3 = T3/ T2We have N1/ N2 = T2/T1 ; N2/ N3 = T3/ T2
And N3/ N4 = T4/ T3 ; N4/ N5 = T5/ T4And N3/ N4 = T4/ T3 ; N4/ N5 = T5/ T4
Speed Ratio of the Gear Train is obtainedSpeed Ratio of the Gear Train is obtained
by multiplyingby multiplying

7. N1 x N2 x N3 x N4 T2 x T3 x T4 x T5N1 x N2 x N3 x N4 T2 x T3 x T4 x T5
------------------------- = -------------------------------------------------- = -------------------------
N2 x N3 x N4 x N5 T1 x T2 x T3 x T4N2 x N3 x N4 x N5 T1 x T2 x T3 x T4
Or, N1/ N5 = T5 / T1Or, N1/ N5 = T5 / T1
Train Value is the inverse of Speed RatioTrain Value is the inverse of Speed Ratio
Speed of driven gear ( N5) T1Speed of driven gear ( N5) T1
Train Value = ------------------------------------- = ------Train Value = ------------------------------------- = ------
Speed of driving gear ( N1) T5Speed of driving gear ( N1) T5

8. COMPOUND GEAR TRAINCOMPOUND GEAR TRAIN
When a series of gears are arranged in suchWhen a series of gears are arranged in such
away that two or more gears rotate aboutaway that two or more gears rotate about
an axis with same angular velocity, it isan axis with same angular velocity, it is
known as compound gear train. In thisknown as compound gear train. In this
type of train, some of the intermediatetype of train, some of the intermediate
shafts i.e shafts other than input andshafts i.e shafts other than input and
output carry more than one gear.output carry more than one gear.

9. COMPOUND GEAR TRAINCOMPOUND GEAR TRAIN

10. COMPOUND GEAR TRAINCOMPOUND GEAR TRAIN
Using the same notations for speed and number of teeth for different gears,Using the same notations for speed and number of teeth for different gears,
as in case of simple gear train,as in case of simple gear train,
Here in case of compound gear train,Here in case of compound gear train,
N2 = N3 and N4 = N5N2 = N3 and N4 = N5
N1 N3 N5 N1 T2 x T4 x T6N1 N3 N5 N1 T2 x T4 x T6
Speed ratio = ---- x ----- x ----- = ----- = ------- = --------------------Speed ratio = ---- x ----- x ----- = ----- = ------- = --------------------
N2 N4 N6 N6 T1 x T3 x T5N2 N4 N6 N6 T1 x T3 x T5
Product of no.of teeth on driven gearsProduct of no.of teeth on driven gears
i.e. Speed ratio = -----------------------------------------------------i.e. Speed ratio = -----------------------------------------------------
Product of no.of teeth on driving gearsProduct of no.of teeth on driving gears

11. REVERTED GEAR TRAINREVERTED GEAR TRAIN
If the axes of first and last wheel of aIf the axes of first and last wheel of a
compound gear coincide, it is called acompound gear coincide, it is called a
reverted gear train. Such anreverted gear train. Such an
arrangement is used in automotivearrangement is used in automotive
transmissions, in clocks (where thetransmissions, in clocks (where the
minute and hour hand shafts are co-minute and hour hand shafts are co-
axial) and in simple lathe where backaxial) and in simple lathe where back
gear is used to give a slow speed togear is used to give a slow speed to
the chuck.the chuck.

12. REVERTED GEAR TRAINREVERTED GEAR TRAIN

13. PLANETARY OR EPICYCLICPLANETARY OR EPICYCLIC
GEAR TRAINGEAR TRAIN
When there exists a relative motionWhen there exists a relative motion
in a gear train, it is called ain a gear train, it is called a
planetary or an epicyclic gearplanetary or an epicyclic gear
train. Thus in an epicyclic geartrain. Thus in an epicyclic gear
train, the axis of one of the gearstrain, the axis of one of the gears
moves relative to the frame.moves relative to the frame.

14. PLANETARY OR EPICYCLICPLANETARY OR EPICYCLIC
GEAR TRAINGEAR TRAIN
Consider two gear wheels S & P, the axes ofConsider two gear wheels S & P, the axes of
which are connected by an arm ‘a’. If the arm 'a'which are connected by an arm ‘a’. If the arm 'a'
is fixed, the wheels S & P constitute a simpleis fixed, the wheels S & P constitute a simple
gear train. However, if the wheel S is fixed sogear train. However, if the wheel S is fixed so
that the arm can rotate about axis of S, thethat the arm can rotate about axis of S, the
wheel P would also move around S. Therefore, itwheel P would also move around S. Therefore, it
is epicyclic train. Usually, the wheel P is knownis epicyclic train. Usually, the wheel P is known
as epicyclic wheel. The term epicyclic emergesas epicyclic wheel. The term epicyclic emerges
from the fact that the wheel P rolls outsidefrom the fact that the wheel P rolls outside
another wheel S and traces an epicyclic path.another wheel S and traces an epicyclic path.

15. PLANETARY OR EPICYCLICPLANETARY OR EPICYCLIC
GEAR TRAINGEAR TRAIN

16. PLANETARY OR EPICYCLICPLANETARY OR EPICYCLIC
GEAR TRAINGEAR TRAIN
Epicyclic gear trains are useful forEpicyclic gear trains are useful for
transmitting high velocity ratio withtransmitting high velocity ratio with
gears of moderate size ingears of moderate size in
comparatively lesser space. Suchcomparatively lesser space. Such
gear trains are used in back gear of agear trains are used in back gear of a
lathe, differential gears of thelathe, differential gears of the
automobiles, hoists, pulley blocks,automobiles, hoists, pulley blocks,
etc.etc.

17. DIFFERENTIALDIFFERENTIAL
The fact that an epicyclic gear has twoThe fact that an epicyclic gear has two
degrees of freedom has been utilized indegrees of freedom has been utilized in
the differential gear of an automobile. Itthe differential gear of an automobile. It
permits the two wheels of the automobilepermits the two wheels of the automobile
to rotate at the same speed when drivingto rotate at the same speed when driving
straight while allowing the wheels to rotatestraight while allowing the wheels to rotate
at different speeds when taking a turn.at different speeds when taking a turn.
Thus a differential gear is a device whichThus a differential gear is a device which
adds or subtracts angular displacements.adds or subtracts angular displacements.

18. DIFFERENTIALDIFFERENTIAL
Fig. shows the arrangement of gears in aFig. shows the arrangement of gears in a
differential. The shaft S is driven by the enginedifferential. The shaft S is driven by the engine
through the gear box and has a bevel pinion Athrough the gear box and has a bevel pinion A
keyed to it. Bevel pinion A meshes with a bevelkeyed to it. Bevel pinion A meshes with a bevel
wheel B which turns loosely on the hub of gearwheel B which turns loosely on the hub of gear
C. Shafts S1 and S2 form the rear axle to whichC. Shafts S1 and S2 form the rear axle to which
are fixed rear wheels of the automobile. Gears Care fixed rear wheels of the automobile. Gears C
and D are keyed to the shafts S1 and S2­and D are keyed to the shafts S1 and S2­
respectively. C and D gear with equal bevelrespectively. C and D gear with equal bevel
pinions E and F which are free to rotate on theirpinions E and F which are free to rotate on their
respective axes. The wheel B carries tworespective axes. The wheel B carries two
brackets that supports the bearings for gears Ebrackets that supports the bearings for gears E
and F.and F.

19. DIFFERENTIALDIFFERENTIAL

20. DIFFERENTIALDIFFERENTIAL
When the automobile moves in a straight path, theWhen the automobile moves in a straight path, the
bevel pinion A drives the wheel B. The wholebevel pinion A drives the wheel B. The whole
differential acts as one unit and rotates with thedifferential acts as one unit and rotates with the
bevel wheel B so that the wheel C and D rotatebevel wheel B so that the wheel C and D rotate
with the same speed and in the same directionwith the same speed and in the same direction
as B. There is no relative motion between gearsas B. There is no relative motion between gears
C and D, E and F. Gears E and F also do notC and D, E and F. Gears E and F also do not
rotate about their own axes. When therotate about their own axes. When the
automobile takes a turn, E and F rotate aboutautomobile takes a turn, E and F rotate about
their own axes and the system works as antheir own axes and the system works as an
epicyclic gear giving two outputs at C and D withepicyclic gear giving two outputs at C and D with
one input at Bone input at B