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AUTOMATIC TRANSMISSION
Submitted to-
Bangaru Babu
Submitted by-
Sudhanshu Sekhar 153713
Contents
• Abstract
• Introduction
• Torque Converter
• Gear Box
• Epicyclic Gear Train
• Analysis & Calculation
• Result
• References
AUTOMATIC TRANSMISSION
• Automatic transmission and transaxles have similar components.
Three basic parts include:
1. Torque Converter.
2. Gear train: planetary gear sets
3. Hydraulic system
• Torque converter connects to the crankshaft and transmits engine
power to the gear train.
• Hydraulic pressure acting through the automatic-transmission fluid
(ATF) in the transmission or transaxle produces the shifts.
Fluid Coupling
• This provided a means of transferring torque from the engine
to the transmission and also allowed the vehicle to be
stopped in gear while the engine runs at idle.
• However, those early fluid couplings had one thing in
common; acceleration was poor. The engine would labour
until the vehicle picked up speed. The problem occurred
because the vanes on the impeller and turbine are curved in
the opposite direction to one another. Fluid coming off of the
turbine is thrust against the impeller in a direction opposite
to engine rotation.
Pump Impeller
• The impeller is integrated
with the torque converter
case, and many curved vanes
that are radially mounted
inside. A guide ring is
installed on the inner edges
of the vanes to provide a path
for smooth fluid flow.
• When the impeller is driven
by the engine crankshaft, the
fluid in the impeller rotates
with it. When the impeller
speed increases, centrifugal
force causes the fluid to flow
outward toward the turbine.
Turbine Runner
• The turbine is located inside the
converter case but is not
connected to it. The input shaft
of the transmission is attached by
splines to the turbine hub when
the converter is mounted to the
transmission. Many cupped
vanes are attached to the
turbine. The curvature of the
vanes is opposite from that of the
impeller vanes.
• when the fluid is thrust from the
impeller, it is caught in the
cupped vanes of the turbine and
torque is transferred to the
transmission input shaft, turning
it in the same direction as the
engine crankshaft.
Torque Converter
Role of the torque converter:
Multiplies torque generated by the engine.
Serves as an automatic clutch which transmits engine torque to the
transmission.
Absorbs torsional vibration of the engine and drivetrain.
Smooth out engine rotation.
Drives the oil pump of the hydraulic control system.
Stator
• The stator is located between
the impeller and the turbine.
• The vanes of the stator catch
the fluid as it leaves the
turbine runner and redirects
it so that it strikes the back of
the vanes of the impeller.
• giving the impeller an added
boost or torque.
• The benefit of this added
torque can be as great as 30%
to 50%.
• STATOR:
• To make the torque converter more efficient, a 3rd member or stationary reactor
called stator is placed between the impeller & turbine.
• The stator have curve vanes that change the direction of the fluid after it leaves the
turbine. This causes the fluid to pass trough the impeller & then push on the turbine
vanes again with a helping force that aid rotation. The result is torque multiplication
under certain condition.
• Torque multiplication: in many torque converter the torque is more than double.e.g,
1.35N.m of torque entering the impeller, the turbine delivers more than 2.7N.m of
torque to the transmission input shaft. Torque multiplication occurs only when the
impeller turns faster than the turbine.
Fluid flow within a torque converter. The stator redirects the fluid that is thrown out
by the turbine, thereby improving efficiency.
Fluid pumped into the turbine by the impeller not only creates rotary
fluid flow but also vortex flow that increases the efficiency of the torque
converter.
STATOR ONE- WAY CLUTCH
• As the vehicle approaches cruising speed, the turbine begins to catch
up with the impeller (coupling point).
• The fluid leaving the turbine is moving at about the same speed as
the impeller. This fluid could pass directly into the impeller without
stator action. In fact, the stator vane are now in the way. The fluid is
striking the back sides of the stator vanes.
• To allow the stator vanes to move out of the way, the stator mounts
on a one- way clutch (overrunning clutch)
One- way Clutch
• A mechanical device that tranmits torque in one direction & permits free rotation
in the opposite side.
• When the speed difference between the impeller & the turbine is large, the fluid
from the turbine tries to spin the stator backward. This causes the one- way
clutch to lock the stator to its shaft. When the speed difference is small, the
clutch unlocks & allows the stator to freewheel. 2 types of one way clutch are
roller clutch & sprag type clutch.
EPICYCLIC GEAR TRAIN
• An epicyclic gear train ,The axes of the shafts, over which the
gears are mounted, may move relative to a fixed axis.
• A simple epicyclic gear train is shown in Fig. 1
• Here a gear A and the arm C have a common axis at O1 about
which they can rotate. The gear B meshes with gear A and has
its axis on the arm at O2, about which the gear B can rotate.
• Such a motion is called epicyclic.
• The gear trains arranged in such a manner that one
or more of their members move upon and around
another member is known as epicyclic gear trains
(epi. means upon and cyclic means around).
Fig.1 (A) Epicyclic Gear Train
EPICYCLIC GEAR TRAIN
APPLICATIONS
• The epicyclic gear trains are useful for transmitting high velocity ratios
with gears of moderate size in a comparatively lesser space.
• The epicyclic gear trains are used in the back gear of lathe,
differential gears of the automobiles, hoists, pulley blocks, wrist
watches etc.
Velocity Ratios of Epicyclic Gear Train
• The following two methods may be used for finding out the velocity ratio of an epicyclic
gear train.
1. Tabular Method 2. Algebraic Method
1. Tabular Method
• Consider an epicyclic gear train as shown in Fig. 1.
• Let ,
TA = Number of teeth on gear A, and
TB = Number of teeth on gear B.
1. TABULAR METHOD
• First of all, let us suppose that the arm is fixed. Therefore the axes of both the gears are also fixed
relative to each other. When the gear A makes one revolution anticlockwise, the gear B will make TA / TB
revolutions, clockwise.
• Assuming the anticlockwise rotation as positive and clockwise as negative, we may say that when gear A
makes + 1 revolution, then the gear B will make (– TA / TB) revolutions. This statement of relative motion
is entered in the first row of the table (see Table 1).
• Secondly, if the gear A makes + x revolutions,
then the gear B will make ( – x × TA / TB)
revolutions. This statement is
entered in the second row of the table.
• In other words, multiply the each motion
(entered in the first row) by x.
1. TABULAR METHOD
• Thirdly, each element of an epicyclic train is given + y revolutions and entered in the third row.
Finally, the motion of each element of the gear train is added up and entered in the fourth row.
2. ALGEBRAIC METHOD
• In this method ,the motion of each elements of the epicyclic train relative to the arm is set down in the
form of equation.
• The number of the equations depends on the number of the elements in the gear train.
• But the two conditions are ,usually, supplied in any epicyclic train viz. (1)some elements is the fixed and
(2) the other has specified motion.
• These two conditions are sufficient to solve all
the equation; hence to determine the motion
of any element in the epicyclic gear train.
• Let the arm C fixed in an epicyclic Gear train
as shown in fig. 1
2. ALGEBRAIC METHOD
• The speed of the gear A relative to the arm C = NA- Nc .
• The speed of the gear B relative to the arm C = NB- Nc .
• Since the gears A and B are meshing directly, therefore they will revolve in opposite directions.
 NB – NC TA
NA – NC TB
• Since the arm C is fixed therefore its speed,
NC = 0 then NB TA
NA TB
• If the gear A is fixed therefore its speed,
NA = 0 then NB TA
NC TB 1 +
Compound Epicyclic Gear Train
Sun and Planet Gear:
• A compound epicyclic gear train is shown in Fig (2).
• The gear at the centre is called the Sun gear and the gears whose axes move are called Planet gears.
Compound Epicyclic Gear Train
Sun and Planet Gear:
• It consists of two co-axial shafts S1 and S2, an annulus gear A
which is fixed, the compound gear B-C, the sun gearD and the arm H.
• The annulus gear has internal teeth and the compound gear is carried by the arm and revolves freely on
a pin of the arm H. The sun gear is co-axial with the annulus gear and the arm but independent of them.
Compound Epicyclic Gear Train
Sun and Planet Gear:
• The annulus gear A meshes with the gear B and the sun gear D meshes with the gear C. It may be noted
that when the annulus gear is fixed, the sun gear provides the drive and when the sun gear is fixed, the
annulus gear provides the drive. In both cases, the arm acts as a follower.
Compound Epicyclic Gear Train
Sun and Planet Gear
• Let Ta, Tb, Tc, and Td be the teeth and Na, Nb, Nc and Nd be the speeds for the gears A, B, C and D
respectively. A little consideration will show that when the arm is fixed and the sun gear D is turned
anticlockwise, then the compound gear B-C and the annulus gear A will rotate in the clockwise
direction.
• The motions of rotations of the various elements are shown in the table below.
Epicyclic Gear Train with Bevel Gear
• The bevel gears are used to make a more compact epicyclic system and they permit a very high speed
reduction with few gears.
• The epicyclic gear train with bevel gears is used in
1. Humpage’s speed reduction gear
2. differential gear of an automobile
HUMPAGE’S SPEED REDUCTION GEAR
• The Humpage’s speed reduction gear was originally designed as a substitute for back gearing of a
lathe, but its use is now considerably extended to all kinds of workshop machines and also in
electrical machinery. In Humpage’s speed reduction gear, as shown in Fig. 3.
HUMPAGE’S SPEED REDUCTION GEAR
• The driving shaft X and the driven shaft Y are co-axial. The driving shaft carries a bevel gear A and driven
shaft carries a bevel gear E. The bevel gear B meshes with gear A (also known as pinion) and a fixed gear
C.
• The gear E meshes with gear D
which is compound with gear B.
• This compound gear B-D is
mounted on the arm or spindle F
which is rigidly connected with
a hollow sleeve G.
• The sleeve revolves freely
loose on the axes of
the driving and driven shafts.
Fig.3. Humpage’s speed reduction gear
DIFFERENTIAL GEAR OF AN AUTOMOBILE
• The differential gear used in the rear drive of an automobile is shown in Fig. (4)
• Its function is
(a) to transmit motion from the engine shaft to the rear driving wheels, and
(b) to rotate the rear wheels at different speeds while the automobile is taking a turn.
• As long as the automobile is running on a straight path, the rear wheels are driven directly by
the engine and speed of both the wheels is same. But when the automobile is taking a turn,
the outer wheel will run faster than the inner wheel because at that time the outer rear wheel
has to cover more distance than the inner rear wheel.
• The bevel gear A (known as pinion) is keyed to the propeller shaft driven from the engine shaft through
universal coupling. This gear A drives the gear B (known as crown gear) which rotates freely on the axle
P. Two equal gears C and D are mounted on two separate parts P and Q of
the rear axles respectively.
• These gears, in turn, mesh with
equal pinions E and F which can
rotate freely on the spindle provided
on the arm attached to gear B.
• When the automobile runs on a
straight path, the gears C and D must
rotate together.
• These gears are rotated through
the spindle on the gear B.
Fig.4 Differential gear of an automobile
DIFFERENTIAL GEAR OF AN AUTOMOBILE
TORQUES IN EPICYCLIC GEAR TRAINS
• When the rotating parts of an epicyclic gear train, as shown in Fig. 5, have no angular acceleration, the
gear train is kept in equilibrium by the three externally applied torques, viz.
1. Input torque on the driving
member (T1),
2. Output torque or resisting or
load torque on the driven
member (T2),
3. Holding or braking or
fixing torque on the fixed
member (T3).
• The net torque applied to the gear
train must be zero. Fig.5 Torques in epicyclic gear trains
• In other words,
T1 + T2 + T 3 = 0 ...(I)
F1.r1 + F2.r2 + F 3.r 3 = 0 ...(ii)
where F1, F2 and F3 are the corresponding externally applied forces at radius r1, r2 and r3 .
• Further, if 1, 2 and 3 are the angular speeds of the driving, driven and fixed members respectively,
and the friction be neglected, then the net kinetic energy dissipated by the gear train must be zero, i.e.
 T1. 1 + T2.2 + T3.3 = 0 ...(iii)
• But, for a fixed member, 3 = 0
 T1. 1 + T2.2 = 0 ...(iv)
TORQUES IN EPICYCLIC GEAR TRAINS
• Notes:
1. From equations (I) and (iv), the holding or braking torque T3 may be obtained as follows:
T3 = – (T1 + T 2 ) ...[From equation (I)]
...[From equation (iv)]
2. When input shaft (or driving shaft) and output shaft (or driven shaft) rotate in the same
direction, then the input and output torques will be in opposite directions. Similarly, when the
input and output shafts rotate in opposite directions, then the input and output torques will be
in the same direction.
T2 = T1 x
1
2
TORQUES IN EPICYCLIC GEAR TRAINS
Automatic transmission

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Automatic transmission

  • 1. AUTOMATIC TRANSMISSION Submitted to- Bangaru Babu Submitted by- Sudhanshu Sekhar 153713
  • 2. Contents • Abstract • Introduction • Torque Converter • Gear Box • Epicyclic Gear Train • Analysis & Calculation • Result • References
  • 3. AUTOMATIC TRANSMISSION • Automatic transmission and transaxles have similar components. Three basic parts include: 1. Torque Converter. 2. Gear train: planetary gear sets 3. Hydraulic system • Torque converter connects to the crankshaft and transmits engine power to the gear train. • Hydraulic pressure acting through the automatic-transmission fluid (ATF) in the transmission or transaxle produces the shifts.
  • 4. Fluid Coupling • This provided a means of transferring torque from the engine to the transmission and also allowed the vehicle to be stopped in gear while the engine runs at idle. • However, those early fluid couplings had one thing in common; acceleration was poor. The engine would labour until the vehicle picked up speed. The problem occurred because the vanes on the impeller and turbine are curved in the opposite direction to one another. Fluid coming off of the turbine is thrust against the impeller in a direction opposite to engine rotation.
  • 5. Pump Impeller • The impeller is integrated with the torque converter case, and many curved vanes that are radially mounted inside. A guide ring is installed on the inner edges of the vanes to provide a path for smooth fluid flow. • When the impeller is driven by the engine crankshaft, the fluid in the impeller rotates with it. When the impeller speed increases, centrifugal force causes the fluid to flow outward toward the turbine.
  • 6. Turbine Runner • The turbine is located inside the converter case but is not connected to it. The input shaft of the transmission is attached by splines to the turbine hub when the converter is mounted to the transmission. Many cupped vanes are attached to the turbine. The curvature of the vanes is opposite from that of the impeller vanes. • when the fluid is thrust from the impeller, it is caught in the cupped vanes of the turbine and torque is transferred to the transmission input shaft, turning it in the same direction as the engine crankshaft.
  • 8. Role of the torque converter: Multiplies torque generated by the engine. Serves as an automatic clutch which transmits engine torque to the transmission. Absorbs torsional vibration of the engine and drivetrain. Smooth out engine rotation. Drives the oil pump of the hydraulic control system.
  • 9. Stator • The stator is located between the impeller and the turbine. • The vanes of the stator catch the fluid as it leaves the turbine runner and redirects it so that it strikes the back of the vanes of the impeller. • giving the impeller an added boost or torque. • The benefit of this added torque can be as great as 30% to 50%.
  • 10. • STATOR: • To make the torque converter more efficient, a 3rd member or stationary reactor called stator is placed between the impeller & turbine. • The stator have curve vanes that change the direction of the fluid after it leaves the turbine. This causes the fluid to pass trough the impeller & then push on the turbine vanes again with a helping force that aid rotation. The result is torque multiplication under certain condition. • Torque multiplication: in many torque converter the torque is more than double.e.g, 1.35N.m of torque entering the impeller, the turbine delivers more than 2.7N.m of torque to the transmission input shaft. Torque multiplication occurs only when the impeller turns faster than the turbine.
  • 11. Fluid flow within a torque converter. The stator redirects the fluid that is thrown out by the turbine, thereby improving efficiency.
  • 12.
  • 13. Fluid pumped into the turbine by the impeller not only creates rotary fluid flow but also vortex flow that increases the efficiency of the torque converter.
  • 14. STATOR ONE- WAY CLUTCH • As the vehicle approaches cruising speed, the turbine begins to catch up with the impeller (coupling point). • The fluid leaving the turbine is moving at about the same speed as the impeller. This fluid could pass directly into the impeller without stator action. In fact, the stator vane are now in the way. The fluid is striking the back sides of the stator vanes. • To allow the stator vanes to move out of the way, the stator mounts on a one- way clutch (overrunning clutch)
  • 15. One- way Clutch • A mechanical device that tranmits torque in one direction & permits free rotation in the opposite side. • When the speed difference between the impeller & the turbine is large, the fluid from the turbine tries to spin the stator backward. This causes the one- way clutch to lock the stator to its shaft. When the speed difference is small, the clutch unlocks & allows the stator to freewheel. 2 types of one way clutch are roller clutch & sprag type clutch.
  • 16.
  • 17. EPICYCLIC GEAR TRAIN • An epicyclic gear train ,The axes of the shafts, over which the gears are mounted, may move relative to a fixed axis. • A simple epicyclic gear train is shown in Fig. 1 • Here a gear A and the arm C have a common axis at O1 about which they can rotate. The gear B meshes with gear A and has its axis on the arm at O2, about which the gear B can rotate.
  • 18. • Such a motion is called epicyclic. • The gear trains arranged in such a manner that one or more of their members move upon and around another member is known as epicyclic gear trains (epi. means upon and cyclic means around). Fig.1 (A) Epicyclic Gear Train EPICYCLIC GEAR TRAIN
  • 19. APPLICATIONS • The epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. • The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.
  • 20. Velocity Ratios of Epicyclic Gear Train • The following two methods may be used for finding out the velocity ratio of an epicyclic gear train. 1. Tabular Method 2. Algebraic Method 1. Tabular Method • Consider an epicyclic gear train as shown in Fig. 1. • Let , TA = Number of teeth on gear A, and TB = Number of teeth on gear B.
  • 21. 1. TABULAR METHOD • First of all, let us suppose that the arm is fixed. Therefore the axes of both the gears are also fixed relative to each other. When the gear A makes one revolution anticlockwise, the gear B will make TA / TB revolutions, clockwise. • Assuming the anticlockwise rotation as positive and clockwise as negative, we may say that when gear A makes + 1 revolution, then the gear B will make (– TA / TB) revolutions. This statement of relative motion is entered in the first row of the table (see Table 1). • Secondly, if the gear A makes + x revolutions, then the gear B will make ( – x × TA / TB) revolutions. This statement is entered in the second row of the table. • In other words, multiply the each motion (entered in the first row) by x.
  • 22. 1. TABULAR METHOD • Thirdly, each element of an epicyclic train is given + y revolutions and entered in the third row. Finally, the motion of each element of the gear train is added up and entered in the fourth row.
  • 23. 2. ALGEBRAIC METHOD • In this method ,the motion of each elements of the epicyclic train relative to the arm is set down in the form of equation. • The number of the equations depends on the number of the elements in the gear train. • But the two conditions are ,usually, supplied in any epicyclic train viz. (1)some elements is the fixed and (2) the other has specified motion. • These two conditions are sufficient to solve all the equation; hence to determine the motion of any element in the epicyclic gear train. • Let the arm C fixed in an epicyclic Gear train as shown in fig. 1
  • 24. 2. ALGEBRAIC METHOD • The speed of the gear A relative to the arm C = NA- Nc . • The speed of the gear B relative to the arm C = NB- Nc . • Since the gears A and B are meshing directly, therefore they will revolve in opposite directions.  NB – NC TA NA – NC TB • Since the arm C is fixed therefore its speed, NC = 0 then NB TA NA TB • If the gear A is fixed therefore its speed, NA = 0 then NB TA NC TB 1 +
  • 25. Compound Epicyclic Gear Train Sun and Planet Gear: • A compound epicyclic gear train is shown in Fig (2). • The gear at the centre is called the Sun gear and the gears whose axes move are called Planet gears.
  • 26. Compound Epicyclic Gear Train Sun and Planet Gear: • It consists of two co-axial shafts S1 and S2, an annulus gear A which is fixed, the compound gear B-C, the sun gearD and the arm H. • The annulus gear has internal teeth and the compound gear is carried by the arm and revolves freely on a pin of the arm H. The sun gear is co-axial with the annulus gear and the arm but independent of them.
  • 27. Compound Epicyclic Gear Train Sun and Planet Gear: • The annulus gear A meshes with the gear B and the sun gear D meshes with the gear C. It may be noted that when the annulus gear is fixed, the sun gear provides the drive and when the sun gear is fixed, the annulus gear provides the drive. In both cases, the arm acts as a follower.
  • 28. Compound Epicyclic Gear Train Sun and Planet Gear • Let Ta, Tb, Tc, and Td be the teeth and Na, Nb, Nc and Nd be the speeds for the gears A, B, C and D respectively. A little consideration will show that when the arm is fixed and the sun gear D is turned anticlockwise, then the compound gear B-C and the annulus gear A will rotate in the clockwise direction. • The motions of rotations of the various elements are shown in the table below.
  • 29. Epicyclic Gear Train with Bevel Gear • The bevel gears are used to make a more compact epicyclic system and they permit a very high speed reduction with few gears. • The epicyclic gear train with bevel gears is used in 1. Humpage’s speed reduction gear 2. differential gear of an automobile HUMPAGE’S SPEED REDUCTION GEAR • The Humpage’s speed reduction gear was originally designed as a substitute for back gearing of a lathe, but its use is now considerably extended to all kinds of workshop machines and also in electrical machinery. In Humpage’s speed reduction gear, as shown in Fig. 3.
  • 30. HUMPAGE’S SPEED REDUCTION GEAR • The driving shaft X and the driven shaft Y are co-axial. The driving shaft carries a bevel gear A and driven shaft carries a bevel gear E. The bevel gear B meshes with gear A (also known as pinion) and a fixed gear C. • The gear E meshes with gear D which is compound with gear B. • This compound gear B-D is mounted on the arm or spindle F which is rigidly connected with a hollow sleeve G. • The sleeve revolves freely loose on the axes of the driving and driven shafts. Fig.3. Humpage’s speed reduction gear
  • 31. DIFFERENTIAL GEAR OF AN AUTOMOBILE • The differential gear used in the rear drive of an automobile is shown in Fig. (4) • Its function is (a) to transmit motion from the engine shaft to the rear driving wheels, and (b) to rotate the rear wheels at different speeds while the automobile is taking a turn. • As long as the automobile is running on a straight path, the rear wheels are driven directly by the engine and speed of both the wheels is same. But when the automobile is taking a turn, the outer wheel will run faster than the inner wheel because at that time the outer rear wheel has to cover more distance than the inner rear wheel.
  • 32. • The bevel gear A (known as pinion) is keyed to the propeller shaft driven from the engine shaft through universal coupling. This gear A drives the gear B (known as crown gear) which rotates freely on the axle P. Two equal gears C and D are mounted on two separate parts P and Q of the rear axles respectively. • These gears, in turn, mesh with equal pinions E and F which can rotate freely on the spindle provided on the arm attached to gear B. • When the automobile runs on a straight path, the gears C and D must rotate together. • These gears are rotated through the spindle on the gear B. Fig.4 Differential gear of an automobile DIFFERENTIAL GEAR OF AN AUTOMOBILE
  • 33. TORQUES IN EPICYCLIC GEAR TRAINS • When the rotating parts of an epicyclic gear train, as shown in Fig. 5, have no angular acceleration, the gear train is kept in equilibrium by the three externally applied torques, viz. 1. Input torque on the driving member (T1), 2. Output torque or resisting or load torque on the driven member (T2), 3. Holding or braking or fixing torque on the fixed member (T3). • The net torque applied to the gear train must be zero. Fig.5 Torques in epicyclic gear trains
  • 34. • In other words, T1 + T2 + T 3 = 0 ...(I) F1.r1 + F2.r2 + F 3.r 3 = 0 ...(ii) where F1, F2 and F3 are the corresponding externally applied forces at radius r1, r2 and r3 . • Further, if 1, 2 and 3 are the angular speeds of the driving, driven and fixed members respectively, and the friction be neglected, then the net kinetic energy dissipated by the gear train must be zero, i.e.  T1. 1 + T2.2 + T3.3 = 0 ...(iii) • But, for a fixed member, 3 = 0  T1. 1 + T2.2 = 0 ...(iv) TORQUES IN EPICYCLIC GEAR TRAINS
  • 35. • Notes: 1. From equations (I) and (iv), the holding or braking torque T3 may be obtained as follows: T3 = – (T1 + T 2 ) ...[From equation (I)] ...[From equation (iv)] 2. When input shaft (or driving shaft) and output shaft (or driven shaft) rotate in the same direction, then the input and output torques will be in opposite directions. Similarly, when the input and output shafts rotate in opposite directions, then the input and output torques will be in the same direction. T2 = T1 x 1 2 TORQUES IN EPICYCLIC GEAR TRAINS