In the extreme positions, AP1 and AP2 the length of the belt, velocity ratio

L = Arc GJE + EF + Arc FKH + HG it is the ratio between the velocities of the
are tangential to the circle and the cutting = 2 (Arc JE + EF + Arc FK).............(i) driver and the follower or driven.
tool is at the end of the stroke. The From the geometry of the figure, we let, d1 = Diameter of the driver,
forward or cutting stroke occurs when the find that d2 = Diameter of the follower,
sin ∝=O1M /O1O2 N1 = Speed of the driver in r.p.m., and
crank rotates from the position CB1 to
=O1E – EM / O1O2 N2 = Speed of the follower in r.p.m.
CB2 (or through an angle β) in the =𝑟1−𝑟2 / 𝑥 ............(ii) Velocity ratio, N2/N1=d1/d2.
clockwise direction. The return stroke Since α is very small, there fore When the thickness of the belt (t) is
occurs when the crank rotates from the putting considered
sin ∝=∝= 𝑟1−𝑟2 / 𝑥 then the velocity ratio
position CB2 to CB1 (or through angle α)
Arc JE=r1(𝜋/2 +∝) ...................(iii) 𝑁2/𝑁1 = 𝑑1/𝑑2
in the clockwise direction. Arc FK=r2(𝜋/2 −∝)....................(iv)
and EF =MO2= √{(O1O2)2 − (O1M)2}
Since the tool travels a distance of R1 to = √{(𝑥)2 − (𝑟1 – 𝑟2)2}
R2 during cutting and return stroke, =x √{(1)2 − (𝑟1−𝑟2)2 / 𝑥2}
therefore travel of the tool or length of
Expanding this equation by binomial
stroke
theorem,
𝐸𝐹 = 𝑥 [1 – 1/2 * (𝑟1−𝑟2)2 /𝑥2 + ⋯ . ]
= (𝑥) − (𝑟1−𝑟2)2 / 2𝑥 ...................(v)
Substituting the values of arc JE from
Whitworth quick-return mechanism-
equation (iii), arc FK from equation (iv)
This mechanism is obtained by fixing the shortest and EF from equation (v) in equation (i),
link. The link CD (link 2) forming the turning pair is we get
fixed, as shown in Figure. The driving crank CA (link L=2[r1(𝜋/2 +∝)+(𝑥) − (𝑟1−𝑟2)2 /2𝑥 +
3) rotates at a uniform angular speed. r2(𝜋/2 −∝)] ratio of tight side and slack side tension
The slider (link 4) attached to the crank pin at A =𝜋(𝑟1 + 𝑟2) + 2𝛼(𝑟1 – 𝑟2) + 2𝑥 − (𝑟1−𝑟2)2 T1 = Tension in the belt on the tight side,
slides along the slotted bar PA (link 1) which /𝑥 T2 = Tension in the belt on the slack side, and
oscillates at a pivoted point D. The connecting rod Substituting the value of 𝛼 = (r1−r2) θ = Angle of contact in radians (i.e. angle
PR carries the ram at R to which a cutting tool is x from equ (ii) subtended by the arc A B, along which the belt
fixed. The motion of the tool is constrained along L=𝜋(𝑟1 + 𝑟2) + 2(𝑟1 – 𝑟2)(𝑟1 – 𝑟2)/𝑥 + 2𝑥 − touches the pulley at the centre).
the line RD produced, i.e. along a line passing (𝑟1−𝑟2)2 / 𝑥 Now consider a small portion of the belt PQ,
L=𝝅(𝒓1 + 𝒓2) + 𝟐𝒙 + (𝒓1−𝒓1)2 / 𝒙 subtending an angle δθ at the centre of the pulley
through D and perpendicular to CD. When the Time of cutting stroke / time of return Angle of lap or contact
driving crank CA moves from the position CA1 to as shown in Fig. The belt PQ is in equilibrium
stroke= β / ∝ = β/360°- β R1 = radius of larger pulley
CA2 (or the link DP from the position DP1 to DP2 ) under the following forces :
R2 = radius of smaller pulley and
through an angle α in the clockwise direction, the 1. Tension T in the belt at P,
Unit: 2 Power Transmission X = distance between centers of two pulley (i.e.
2. Tension (T + δ T) in the belt at Q,
tool moves from the left hand end of its stroke to Types of Pullyes O1O2).
the right hand end through a distance 2 PD. 3. Normal reaction RN , and
1. Fixed pulley From fig .a
Now when the driving crank moves from the 2. Moving pulley sin∝ = O1M/O1O2 =O1E – ME / O1O2 =r1 – r2 /x 4. Frictional force, F = μ × RN , where μ is the
position CA2 to CA1 (or the link DP from DP2 to DP1 3. Compound Pulley ‫ ؞‬angle of contact or lap , coefficient of friction between the belt and pullet
) through an angle β in the clockwise direction, the 4. Block and lackle pulley θ = (180° - 2∝) 𝜋/180 rad Resolving all the forces horizontally and equating
tool moves back from right hand end of its stroke to 5. Cone pulley a little consideration will show that when the two the same,
6. Swivel eye pulley pulleys ae connected by means of a crossed belt as RN=(T+𝛿𝑇) sin 𝛿𝜃/2 +Tsin 𝛿𝜃/2 ..........(i)
the left hand end.
7. Fixed eye pulley shown in fig (b) then the angle of contact or lap (θ) Since the angle δθ is very small, therefore putting
A little consideration will show that the time taken
during the left to right movement of the ram will be on both the pulley is same . From sin δ θ / 2 = δθ / 2 in equation
Belt drive fig (b). RN =T𝛿𝜃 ................(ii)
equal to the time taken by the driving crank to
i) Belt-Belt drives are called flexible machine sin∝ = O1M/O1O2 =O1E + ME / O1O2 Now resolving the forces vertically, we have
move from CA1 to CA2 . Similarly, the time taken
elements. The belts or ropes are used to transmit =r1 + r2 /x
during the right to left movement of the ram,willbe 𝜇.RN=(T+𝛿𝑇) cos 𝛿𝜃/2 − 𝑇 cos 𝛿𝜃/2
power from one shaft to another by means of pulleys ‫ ؞‬angle of contact or lap ,
equal to the time taken by the driving crank to ……………(iii)
which rotate at the same speed or at different speed. θ = (180° + 2∝) 𝜋/180 rad
move from CA2 to CA1 . Since the angle δ θ is very small, therefore putting
a little consideration will show that when the two
Since the crank link CA rotates at uniform angular • Types of belt drive- cos δ θ / 2 = 1 in equation
pulleys ae connected by means of a crossed belt as
velocity therefore time taken during the cutting • Flat Belt- The flat belt is rectangular section as shown in fig (b) then the angle of contact or lap (θ) 𝜇.RN=T+𝛿𝑇 − 𝑇 = 𝛿𝑇
stroke (or forward stroke) is more than the time shown in Fig. it is mostly used in the factories and on both the pulley is same . From or, RN =𝛿𝑇/ 𝜇 ..........(iv)
taken during the return stroke. workshops, where a moderate amount of power is to fig (b). Equating the values of RN from equations (ii) and
The ratio between the time taken during the be transmitted, from one pulley to another when the sin∝ = O1M/O1O2 =O1E + ME / O1O2 =r1 + r2 /x (iv),
cutting and return strokes is given by two pulleys are not more than 8 metres apart. in case ‫ ؞‬angle of contact or lap , T𝛿𝜃 =𝛿𝑇/𝜇
Time of cutting stroke/time of return stroke= ∝/β of a flat belt, the rim of the pulley is slightly Crowned θ = (180° + 2∝) 𝜋/180 rad 𝛿𝑇/𝑇 = 𝜇𝛿𝜃 .....(v)
=∝/360°-∝ which helps to keep the belt running centally on the Integrating both sides between the limits T2 and
This mechanism is used in shaper machine, pulley rim. T1 and from 0 to θ respectively
T1 θ
APPLICATION- They are commonly used for driving T2∫ 𝛿𝑇/T =𝜇 0 ∫ 𝛿𝜃
also in planar slotted machine.
and conveying equipment, such as spinning and log 𝑇1/𝑇2 =𝜇𝜃
weaving machines, calenders, and finishing machines. 𝑻1/𝑻2 =𝒆𝝁𝜽
• V-Belt- It is trapezoidal section, as shown in Fig. ,the
groove of the rim of the pulley of a V belt drive made
deeper to take advantage of the wedge action. It is
mostly used in the factories and workshops, where a
moderate amount of power is to be transmitted, from
a) Open belt drive
one pulley to another, when the two pulleys are very
near to each other.
APPLICATIONS- lathes, milling machines, drilling
machine etc.

centrifugal tension and initial tension

Slip and creep and its effect in power
The belt continuously runs over the pulleys,
transmission therefore, some centrifugal force is caused, whose
●Slip- effect is to increase the tension on both, tight as
1) Slip occurs because of insufficient frictional
grip between the pulley and belt. well as the slack sides. The tension caused by
Material Of the Belt centrifugal force is called centrifugal tension.
1. Leather-Oak tanned or chrome tanned. 2) The immediate effect of slip is a reduction in
the velocity ratio of the transmission system. Consider a small portion PQ of the belt
Crank and slotted lever quick 2. Rubber-Canvas or cotton duck impregnated
with rubber. For greater tensile strength, the 3 )Slip is solely a function of friction between the subtending an angle dθ the centre of the pulley
return mechanism
belt and pulley. as shown in Fig.
rubber or nylon cords.
3. Plastics -Thin plastic sheets with rubber layers 4) Theoretically, slip can be calculated as it Let, m = Mass of the belt per unit length in kg,
In this mechanism, the link AC (i.e. link 3) forming relates to the rotational speed of the pulleys and
4. Fabric -Canvas or woven cotton ducks v = Linear velocity of the belt in m/s,
the turning pair is fixed. The link 3 corresponds to
The belt thickness can be built up with a number their diameter.
r = Radius of the pulley over which the belt runs in
the connecting rod of a reciprocating steam engine. of layers. The number of layers is known as ply. ●Creep-
1) Creep is due to the elastic property of the belt metres,
The belt material is chosen
material. and
The driving crank CB revolves with uniform depending on the use and application. Leather
angular speed about the fixed centreC. oak tanned belts and rubber belts are the most 2) The immediate effect of creep is the reduction TC = Centrifugal tension acting tangentially at P
commonly used but the plastic belts have a very of the velocity of the driven pulley, then and Q in
A sliding block attached to the crank pin at B slides
good strength almost ultimately, the velocity ratio of the transmission newtons.
along the slotted bar AP and thus causes AP to system.
twice the strength of leather belt. Fabric belts are We know that length of the belt PQ
oscillate about the pivoted point A. used for temporary or short period operations. 3) Because the occurrence of creep relates to
= r. dθ
A short link PR transmits the motion from AP to Length of the belt the belt material property, it is a function of the
load, temperature, and the amount of time the and mass of the belt PQ = m. r. dθ
the ram which carries the tool and reciprocates R1 and R2 = Radii of the larger and smaller
drive operates. Centrifugal force acting on the belt PQ
along the line of stroke R1 R2 . The line of stroke of pulleys,
4) Theoretically, creep cannot be calculated, but FC=(m.r.d𝜃) 𝑣2/2 =m.d𝜃. 𝑣2
the ram (i.e. R1 R2 ) is perpendicular to AC x = Distance between the centres of two pulleys
(i.e. O1 O2), and L = Total length of the belt its impact on the speed ratio of the pulleys can The centrifugal tension TC acting tangentially at P
produced.
be calculated using the belt’s Young’s modulus, and Q keeps the belt in equilibrium.
Let the belt leaves the larger pulley at E and G
and the smaller pulley at F and H as shown in. stress in the slack and tight side, and the Now resolving the forces horizontally and
diameters of the pulley.
Through O2, draw O2 M parallel to FE. From the equating the same, we have
geometry of the figure, we
find that O2 M will be perpendicular to O1 E
Let the angle MO2 O1 = α radians We know that
TC sin 𝑑𝜃/2 +TC sin 𝑑𝜃/2 2. Engine start:- In general , N is rpm & N and ω (angular speed)
= FC =m.d𝜃. 𝑣2 The Flywheel plays another role when starting are related by ω =2πN/60
Since the angle dθ is very small, therefore, the engine. The gear teeth on the Flywheel are Basically , Nmean is the average speed that we
putting sin 𝑑𝜃/2 = 𝑑𝜃/2 in the above expression, connected to the starter motor. This starter want the engine crank shaft to maintain.
2TC(𝑑𝜃/2 )=m.d𝜃. 𝑣2 motor is controlled by the car key, so when the
TC=mv2 car starts, the starter motor spins the Flywheel.
Immediately the engine spins, the combustion
Governor
effect keeps the engine running. The Flywheel Function or purpose
condition for maximum The function of a governor is to regulate the
retracts the Bendix gear in the started motor to
power transmission mean speed of an engine, when there are
rotate freely.
We know that power transmitted by a belt variations in the load e.g. when the load on an
3.Drivetrain stress reduction:-
P = (T1 – T2) v
Another function of a flywheel is achieved by engine increases, its speed decreases, therefore
T1 = Tension in the tight side of the belt in
stabilizing engine speed. It also smooths it becomes necessary to increase the supply of
newtons,
engine speed and reduces wear and tear on working fluid. On the other hand, when the load
T2 = Tension in the slack side of the belt in
drivetrain components.The Flywheel also limits on the engine decreases, its speed increases and
newtons, and
the wear between the transmission shaft and thus less working fluid is required. The governor
v = Velocity of the belt in m/s
the driveshaft. These two are connected by a automatically controls the supply of working
we have also seen that the ratio of driving
universal joint. fluid to the engine with the varying load
tensions is,
4. Engine speed soothing:- conditions and keeps the mean speed within
𝑻1/𝑻2 = 𝒆𝝁𝜽
The crankshaft converts piston movement into
or, 𝑻1/𝒆𝝁𝜽 =T2 certain limits.
rotary motion, which is jerky when power is
Substituting the value of T2 in equation Types of governor
generated. The rotational speed of the
P=(T1- 𝑻𝟏/𝒆𝝁𝜽).v=T1(1- 𝟏/𝒆𝝁𝜽)v=T1.v.C [C=1- 1. Centrifugal governor:-
crankshaft is constants, & the engine runs
𝟏/𝒆𝝁𝜽]
smoothly. This is because the mass of the
We know that ,T1 = T – TC [where T=Maximum
Flywheels applies inertia that keeps the engine
tension to which the belt can be subjected in 2. Inertia governor:-
crankshaft rotating between each piston firing.
newtons and TC=Centrifugal
5. Weight manipulation:- • The principle of inertia governors is different
tension in newtons] 2. Intersecting- The weight of the Flywheel determines engine from that of centrifugal type.
Substituting the value of T1 in equation (iii), ■ Bevel gear- performance. The weight is designed based on • The balls of the governor are so arranged that
P = (T – TC) v.C • Used to transmit rotary motion between
the performance of the vehicles. The heavy the inertia forces caused by an angular
=(T-mv2).v.C=T.v.C--m.v3.C intersecting shafts
• Tooth-bearing faces of the gears are conically Flywheel allows the engine to operate under acceleration or retardation of the governor shaft
For maximum power, differentiate the above
shaped loads that can cause engine failure. A larger tend to alter their positions.
expression with respect to v and equate to zero
• Bevel gears are most often mounted on shafts truck or trailer does well with a heavy flywheel, • The amount of displacement of the governor
𝑑𝑃/𝑑𝑣=0 or 𝑑/𝑑𝑣(Tv-mv3)C=0
that are 90 degrees apart, but can be designed to while sports cars and some commercial cars
or, T-3mv2=0 balls caused by the inertia forces is controlled by
work at other angles as well. make good use of a lighter flywheel.
or, T-3Tc=0 suitable springs and through the governor
or, T max =3TC
• The pitch surface of bevel gears is a cone. Application mechanism, alters the amount of energy
3. Non-intersecting: • In wind turbines
or, T-3mv2=0 supplied to the engine.
or, T-3Tc=0
■ Worm and worm wheel- • With a motorized generator to store energy
• The advantage of this type lies in its more
• Used for high Gear ratios • In automobile engine
or, Tmax=3TC rapid response to the effect of a change of load,
• Direction of transmission (input shaft vs output • In electric cars, to increase speed (in the
It shows that when the power transmitted is shaft) is not reversible when using large reduction since the displacement of the balls is
experimental phase)
maximum, 1/3rd of the maximum tension is ratios determined by the rate of change of speed of
• In advanced locomotive propulsion systems
absorbed as centrifugal tension. • Used in wiper motors. rotation. But, in centrifugal type, the
• Advanced Technology in Transit Buses
Putting the Value of TC on the above equation GEAR TRAIN displacement is based on the actual change of
• To control the direction of satellites.
we can find maximum velocity, A gear train is two or more gear working together • In large power grids for protection against speed of rotation.
T=3mv2 by meshing their teeth and turning each other in a
interruptions. • The disadvantage of inertia type lies with the
Gear Drives system to transmit power from one shaft to
another. Effect of use of flywheel with the help practical difficulty of arranging for the complete
GEAR-A gear is a component within a balance of the revolving parts of the governor.
transmission device that transmits rotational Types of gear train of suitable turning moment diagram
A machine's flywheel functions as a reservoir, • So, the centrifugal type are more frequently
force to another gear or device. • Simple gear train- Simple gear train is a
storing energy when supply exceeds demand used than the inertia type.
Types of Gears type of gear train in which a single gear is
1. Parallel- mounted on each shaft. The speed ratio of a and releasing it when demand exceeds supply. Terms used in governor
a. Spur gear- simple gear train depends only on the driven and The turning moment diagram for one entire The following terms used in governors;
• Used in transmitting torque between parallel driven gear. cycle of operation can be used to determine 1. Height of a governor:- It is the vertical
shafts • Compound gear train energy fluctuation. Figure shows the turning distance from the center of the ball to a point
• Simplest type of gear Compound gear train uses compound gears to moment diagram for a single-cylinder double- where the axes of the arms (or arms produced)
• Teeth are cut parallel to shaft axis obtain a higher gear ratio. It is a kind of gear train acting steam engine.At locations B, C, D, and intersect on the spindle axis. It is usually
• Easy to manufacture in which compound gears are mounted on one or E, AF's mean resisting torque line cut the
more intermediate shafts. The compound gear denoted by h.
• If one of the gear has infinite diameter, then it turning moment. The work done by the engine
consists of two or more gears of different sizes 2. Equilibrium speed:- It is the speed at which
is called rack, ( Rack and pinion) is equal to the area aBp when the crank moves
fixed together to rotate at the same speed. from a to p, but the energy required is
the governor balls, arms etc., are in complete
• Reverted gear train represented by the area aABp. In other words, equilibrium and the sleeve does not tend to
When the axes of the first gear (i.e. first driver) the engine has completed less work (equivalent move upwards or downwards.
and the last gear (i.e. last driven or follower) are 3. Mean equilibrium speed:- It is the speed at
to the area AB) than was required. The flywheel
co-axial, then the gear train is known as reverted the mean position of the balls or the sleeve.
gear train. loses this quantity of energy and the speed of
the flywheel drops. Now that the crank has 4. Maximum and minimum equilibrium
• Planetary gear train (Epicyclic gear
moved from p to q, the engine's work is equal to speeds:- The speeds at the maximum and
train)
the area pBbCq, Whereas the energy required minimum radius of rotation of the balls, without
The gear trains arranged in such a manner that
is represented by the area pBCq. As a result, tending to move either way are known as
one or more of their members move upon and
around another member are known as epicyclic the engine has completed more work than was maximum and minimum equilibrium speeds
gear trains. required. Because this extra work (equivalent to respectively.
SPEED RATIO- the area BbC) is stored in the flywheel, the 5. Sleeve lift:- It is the vertical distance which
= Speed of the first driver/speed of large driven or flywheel's speed increases as the crank go the sleeve travels due to change in equilibrium
follower. from p to q. speed.
=product of the number of teeth on the drivens/ Characteristics of governor
Product of the number of teeth on the driver.
■Sensitiveness
TRAIN VALUE-
b. Helical gear- = speed of large driven or follower/ Speed of the • It is generally used to compare
• Used in transmitting torque between parallel first driver theperformance of two governors.Thus, a
shafts =Product of the number of teeth on the driver/ governor is said to be more sensitive if the
• Teeth are cut at an angle with the shaft axis product of the number of teeth on the drivens. change in lift of its sleeve is more for a given
• Helical gears can be meshed in parallel or LAW OF GEARING percentage change in speed compared to the
crossed orientations. The law of gearing states that the common other. It is sometimes defined as the change in
• The angled teeth engage more gradually than
normal at the point of contact between a pair of levels of the balls for one percent change in
spur gear teeth,
causing them to run more smoothly and quietly teeth must always pass through the pitch point. ... speed.
• Double Helical gear- In other words, the angular velocity of a gear in • As a governor is used to limit the change of
CO-EFFICIENT OF FLUCTUATION OF
• In helical gears, teeth are cut at an angle mesh is inversely proportional to distance
ENERGY speed of the engine between a minimum to full
(called helix angle) with the gear axis in the form between the centre of gear and the pitch point.
It is defined as the ratio of the maximum load conditions, the sensitiveness is also defined
of helix on the cylindrical gear blank.
fluctuation of energy to the work done per as the ratio of the range of speed (difference of
• It replaces sudden engagement and Unit: 3 cycle. CE = ratio of maximum fluctuation of maximum and minimum speeds) to the mean
disengagement of teeth (as in spur gear) by Flywheel energy to work done per cycle = ∆E/work done equilibrium speed.
gradual mating and thereby reduces wear,
flywheel used in machines serves as a reservoir, per cycle ■Stability: A governor is said to stable when for
vibration and noise.
which stores energy during the period when the CO-EFFICIENT OF FLUCTUATION OF each speed within the working range, there is
supply of energy is more than the requirement, SPEED only one radius of rotation of the governor balls
c. Rack and Pinion- and releases it during the period when the The difference between the maximum and
• A rack is a gear whose pitch diameter has at which governor is in equilibrium.
requirement of energy is more than the supply. minimum speeds during a cycle is called the ■Isochronism: A governor is termed isochronous
become infinite in size
Flywheel controls the speed variations caused maximum fluctuation of speed.
• a straight line for the pitch circle, which is when the equilibrium speed is constant for all
called the pitch line by the fluctuation of the engine turning moment The ratio of the maximum fluctuation of
radii of rotation of balls with in working range.
• An involute of a very large base circle during each cycle of operation. speed to the mean speed is called the
For slightest change of speed due to change in
approaches a straight line. Function / purpose coefficient of fluctuation of speed.
CO-EFFICIENT OF FLUCTUATION OF SPEED load, such a governor would jump from one
• Therefore, surfaces of the rack teeth are flat, 1.Engine balance:- Because the piston is offset
=Cs extreme position to another. Thus, an
but mesh properly with the involute surfaces of from the center of crankshaft vibration and
the mating pinion = (ωmax- ω min)/ ωmean ; isochronous governor is oversensitive.
wobble, this is also because each piston fires at a
different angle. The function of the Flywheel in ωmean ■Hunting: It is a condition in which the speed of
this situation is to suppress the side-to-side = (ωmax+ ωmin)/2 the engine controlled by the governor fluctuates
motion. This is achieved due to the heavyweight In terms of N , Cs continuously above and below the mean speed.
of the Flywheel. The Flywheel reduces vibrations = (Nmax- Nmin)/Nmean ; This is caused by too sensitive governor. Its
throughout the engine as the engine is stable the Nmean result would be to cause wide fluctuation ins in
engine is stable and balances on the mounts. = (Nmax+ Nmin)/2 speed of rotation.
Unit -1 C. Rolling Pair- This consists of two elements B. Force Closed Pair-When two elements of pair .3. Double Slider Crank Chain-
● KINEMATIC OF MACHINES connected in such a manner that one is constrained are not held together mechanically but are kept in
STATICS- to roll in another element which is fixed. contact by the action of external forces the pair is A kinematic chain which consists of two turning pairs and
It is the branch of engineering which Example: said to be Force closed pair. Example: Cam and two sliding pairs is known as double slider crank chain.
deals with study of forces and its effect • Ball and roller bearings. Spring loaded follower pair. • The link 2 and link 1 form one turning pair
on bodies at rest. • Wheel rolling on a flat surface. CONSTRAINED MOTION- • The link 2 and link 3 form the second turning pair.
DYNAMICS- When an object is forced to move in a restricted • The link 3 and link 4 form one sliding pair and
way, it results in constrained motion. • link 1 and link 4 form the second sliding pair.
It is the branch of engineering which
Types of Constrained Motion-
deals with the study of forces and its
effect on bodies in motion. 1. Completely Constrained Motion- When
the motion between a pair is limited to a definite
KINEMATICS direction irrespective of the direction of force
It is the branch of dynamics which deals
applied, then the motion is said to be a Completely
with the study of forces and their effect
on bodies in motion without considering Constrained Motion.
mass.
KINETICS
It is the branch of dynamics which deals D. Screw Pair-
with study of forces and their effect on This consists of two elements connected in such a
bodies in motion considering mass of manner that one element turns about the other
the body. element by means of threads. The motion, in this
KINEMATICS LINK- case, is a combination of sliding and turning.
A Kinematic Link or Element or Link is a Example:
resistant body that constitutes part of • The lead screw of a lathe and nut. MECHANISM
the machine and connecting other parts • Screw with nut of screw jack. A combination of number of bodies (usually rigid
which have motion relative to it. assembled) in such a way that the motion of one causes
2. Incompletely Constrained Motion- When constrained and predictable motion to the other.
the motion between a pair can take place in more MACHINE-
than one direction, then the motion is called an A machine is a mechanism on a combination of
mechanism which apart from imparting definite motion
incompletely constrained motion. The change in
to the parts also transmits and modifies the available
the direction of the impressed force may alter the
mechanical energy into some kind of desire work.
direction of relative motion between the pair.
STRUCTURE
Structure is an assemblage of a number of resistant
bodies (known as members) having no relative motion
between them and meant for carrying loads having
straining action. A railway bridge, a roof truss, machine
Types of kinematics link :- E. Spherical Pair-
frames etc., are the examples of a structure.
1. Rigid link: A rigid link is one that This consists of two elements connected in such a
manner that one element in the form of a sphere
INVERSION OF MECHANISM
does not undergo any deformation 1. The method of obtaining different mechanisms by
turns about the other fixed element.
while transmitting motion, and it is fixing different links in a kinematic chain, is known as
Example:
elastic in nature. Example: crank and inversion of the mechanism.
• Pen stand
connecting rod 2. The relative motions between the various links is not
2. Flexible link: A flexible link is one changed in any manner through the process of inversion,
which while transmitting motion is 3. Successfully Constrained Motion- Partially but their absolute motions (those measured with respect
partly deformed in a manner not to or successfully constrained motion can have motion to the fixed link) may be changed drastically.
affect the transmission of motion. in more than one direction without any external 3. Example: Beam Engine, Pendulum pump, Oscillating
Example: forces. But when external forces are applied, it can Cylinder Engine etc.
Spring, Chain, Rope, Belt, etc. have motion only in one direction.
KINEMATIC CHAIN Working principle of Mechanisms:
3. Fluid link: A fluid link is one that is When the kinematic pairs are coupled in such a way
deformed by having fluid in a closed that the last link is joined to the first link to transmit
vessel and the motion is transmitted
definite motion (i.e. completely or successfully
●four bar chain mechanism- The simplest and the basic
through the fluid by pressure. Example, kinematic chain is a four bar chain or quadric cycle chain.
2. Contact motion- constrained motion), it is called a kinematic chain.
hydraulic press and hydraulic jack. • It consists of four links, each of them forms a turning
● According to Type of Contact- pair.
KINEMATICS PAIR Types of Kinematic Chain-
A. Lower Pair- When the two elements of a pair • The four links may be of different lengths.
When the two links or elements of a 1. Four bar chain or quadric cyclic chain-
have surface contact when relative motion takes • According to Grashof’s law for a four bar mechanism,
machine contact with each other, they The simplest and the basic kinematic chain is a four
place and the surface of one element slides over the the sum of the shortest and longest link lengths should
are then said to form a pair. If the relative bar chain or quadric cycle chain.
motion between them is completely or surface of another element, the pair formed as not be greater than the sum of the remaining two link
• It consists of four links, each of them forms a lengths if there is to be continuous relative motion
successfully constrained in a definite lower pair. Example: All sliding, Turning and Screw
turning pair.
direction, the pair is known as the pairs are lower pair. between the two links.
• The four links may be of different lengths.
Kinematic pair. • According to Grashof’s law for a four bar
A kinematic pair is a connection
between two physical objects that mechanism, the sum of the shortest and longest
imposes constraints on their relative link lengths should not be greater than the sum of
movement. the remaining two link lengths if there is to be
Types of kinematics pair- continuous relative motion between the two links.
1.Relative motion
●According to Types of Relative
Motion:-
A. Sliding Pair- This consists of two
elements connected in such a manner B. Higher Pair- When the two elements of a pair
that one is constrained to have a sliding have line or point contact when relative motion ●Pantograph- A pantograph is a system of mechanical
motion relative to another. takes place and the motion between the two linkages which reproduces the motion of one point of
Example : elements is partly turning and sliding then the pair is the linkage at a second point, usually at an increased or
•Piston and cylinder of an IC engine. decreased size
known as higher pair. Example: Toothed gearing.
•Tail-stock and lathe bed, etc. The pantograph is a four bar mechanism which has four
Belt and rope drives.
2. Single slider crank chain- links
A single slider crank chain is a modification of the It is an instrument for duplicating a motion or copying a
basic four bar chain. geometric shape to a reduced or enlarged scale
• It consist of one sliding pair and three turning Its basis is a parallelogram of four links with joints
pairs.
• It is, usually, found in reciprocating steam engine
mechanism.
B. Turning Pair- This consists of two •This type of mechanism converts rotary motion
elements connected in such a manner into reciprocating motion and vice versa.
that one is constrained to turn or
revolve about a fixed axis of another
element. 3. Closure motion-
Example:
●The crankshaft of an IC engine turning ●According to Type of Closure-
in a bearing. A. Self Closed Pair-When two elements of pair ●Slider Crank mechanism-
●Cycle wheel revolving about there axles. are held together mechanically in such a way that A single simple crank chain is a modification of the basic
only required type of relative motion occurs called four bar chain. It consist of one sliding pair and three
Self closed pair or closed pair. Example: All lower turning pairs. This type of mechanism converts rotary
pairs. motion into reciprocating motion and vice versa.
The link 1 corresponds to the frame of the engine, which
is fixed. The link 2 corresponds to the crank ; link 3
corresponds to the connecting rod and link 4 corresponds
to cross-head. As the crank rotates, the cross-head
reciprocates in the guides and thus the piston
reciprocates in the cylinder.
Comparison between Flywheel and • There is a rolling motion when it gets contact with Construction and working Disc Brake:-
the cam. ●Shoe brake:- Construction:
Governor.
• This is used in heavy engines like aircrafts engines, Construction: ➔A disc brake consists a rotating disc, two
Flywheel
gas engines. due to less wear and tear and side thrust ➔It consists of a block or shoe which is pressed friction pads, and calipers.
●The function of flywheel is to control the
between guide and follower. against the rim of a revolving brake wheel drum. ➔Disc brakes use a cast iron rotor, inboard
speed of the vehicle wheel.
Variations caused by the fluctuations of
• It is not recommended at step rise due to it gets ➔ The block is made of a softer material than the
jams the cam. rim of the wheel. ➔The brake pads rub on both sides of the
turning moment during a cycle.
• In this rolling motion is occurring. ➔ The block is pressed against the wheel by a rotor, which are machined smooth.
●Mathematically, a flywheel controls ΔN/Δt
■ According to the motion of the follower- force applied to one end of a lever to which the ➔For optimum cooling, the two surfaces are
●It regulates the speed during one cycle only.
1. Oscillating or rotating follower- block is rigidly fixed. usually separated by a finned center piece.
●A flywheel stores the energy and gives up the
In this case the follower oscillates when the cam Working: ➔The pads are connected to metal shoes,
energy whenever required during a cycle.
rotates. The follower is pivoted at a fix position where When break pedal is applied, the friction between which are controlled by pistons housed in
●A flywheel has no control over the quantity of the block and the wheel causes a tangential
oscillating or rotating motion in the follower takes the brake caliper.
charge. braking force to act on the wheel, which retard the
place. ➔When the brakes are not engaged, the
Governor rotation of the wheel. friction pads on each side of the disc remain
2. Reciprocating or translating followers:
●The function of a governor is to keep the free. When the brakes are engaged, they rub
In this type the motion of the follower is
variation in mean speed of the engine, within on the disc to bring the car to a stop.
reciprocating or translating in the guides where as
prescribed limit due to the fluctuations in load Working:-
cam rotates uniformly.
over a period of time. ➔When the brake pedal is pressed, the
●Mathematically, a governor controls ΔN ■ According to the path of motion of the
piston inside the caliper pushes the brake
●It regulates the speed over a period of time. follower. pads toward each other.
●A governor regulates the speed 1. Radial follower: When the line of action of the ➔The rotor (disc) is located between the
by regulating the quantity of charge of the motion of the follower is passes through the center of pads.
prime mover. rotation of the cam then it is known as the radial ➔Caliper compress pads to apply force on
●A governor takes care of quantity of working follower. the surfaces of the rotor (disc).
fluid. 2. Off-set followers: When the line of action of ➔Friction is created as a result of this
motion of the follower is offset/ away from the ●Band brake squeezing action, which causes the car to
center of rotation of the cam then it is known as off- Construction: slow or stop.
Unit: 4 Cams and Followers
set followers. ➔The band brake is made of rope or belt band
●CAM AND FOLLOWER which is lined with a friction material.
The cam and follower is a mechanical DIFFERENT FOLLOWER MOTION
• Uniform velocity ➔The band is partly wrapped around a drum and
device used to achieve the desired
its free ends are attached to a lever.
reciprocating motion. The cam is the
rotating member, and the follower is the ➔For breaking, an external force can be applied
reciprocating member. The cam is a to the free ends of this lever.
profiled disc, cylinder or sphere that ➔There is friction between the bands due to the
rotates. The shape or profile of the cam presence of an external force.
influences the motion of the follower. ➔The Band tightens as a result of the friction
APPLICATION OF CAM AND force, and a tangential force applies on the drum.
FOLLOWER ➔The tension in the band is created by tightening
• In IC Engines: The reciprocating motion the bands.
of an IC engine's inlet and exhaust valves ➔It slow or stop the wheel connected.
is achieved by the cam and follower Working:
mechanism. ➔When the brake band is applied, hydraulic
• In Children Toys: This cam and follower pressure is provided to the servo, tightening
mechanism is used in many toys where • Uniform acceleration and retardation the band around the drum. Concept of Self Locking & Self energizing
simple periodic motion is required. ➔As a result, the drum is fixed in a stationary brakes
• In Automatic Lathe Machines: The position, causing an output change from the ➔When the frictional force helps to
motion of tools in an automatic lathe planetary gearset. apply the brake, then such type of
machine is controlled by this mechanism. ➔When the brake band is released, no hydraulic brakes are said to be self energizing
Also, the feed mechanism in lathe pressure applied to the servo, allowing the drum brakes.
machines is done by the cam and follower to revolve freely within the band. ➔When the frictional force is great
mechanism. enough to apply the brake with no
CLASSIFICATION OF CAM external force, then the brake is said to
1. Wedge Cam: be self-locking brake.
• It has a wedge of specified contour and Concept of braking force and
has translational motion. braking torque for shoe brake
• The follower can either translate or oscillate. Let,
• It may be in contact with a roller follower or • 𝑃 = Force applied at the end of the
knife-edge follower. lever
2. Plate cam: • 𝑅𝑁 = Normal force pressing the brake
• The disk (or plate) cam has an irregular block on the wheel
contour to impart a specific motion to the • Simple harmonic motion • 𝑟 = Radius of the wheel
follower. • 2𝜃 =Angle of contact surface of the
• Here, the follower moves in a radial direction block
• 𝜇 = Coefficient of friction
from the centre of rotation of the cam
• 𝐹𝑡 = Tangential braking force or the
• Also known as radial or disc cam. ●Internal expanding shoe brake frictional force acting at the contact
3. Cylindrical cam: Construction: surface of the block and the wheel
• A cylinder has a circumferential contour cut ➔It is made of two semi-circular brake shoes • 𝑂 = Fixed fulcrum
in the surface and the cam rotates about its having friction lining on their outer surface. ➔If the angle of contact is less than
axis. ➔An anchor pin connects the bottom end of the 60°, then it may be assumed that the
• The follower motion is either oscillating or brake shoes to the backplate, while the other end normal pressure between the block and
reciprocating type. rests on the cam. the wheel is uniform In such cases,
• These cams are also called drum or barrel ➔The cams are turned or actuated by the tangential braking force on the wheel,
cams. Unit: 5 Brakes & Clutches crankshaft passing through the backplate hole. 𝑭𝒕 = 𝝁𝑹𝑵
4. Face cam- Brakes ➔The camshaft can be operated by a brake pedal and the braking torque,
• This rotary cam has a groove cut in its flat A brake is a device by means of which through linkage. 𝑻𝑩 = 𝝁𝑹𝑵𝒓
surface, within which a constrained follower artificial frictional ➔The brake drum is the outside section of the
moves. The groove ensures no need for a resistance is applied to a moving brake, and it encloses and protects the whole
return spring. machine member, in order braking system from dust and moisture.
5. End cam: to retard or stop the motion of a Working:
In this case, the end of a cylindrical cam has machine. It absorbs energy from the ➔When break pedal is applied, the cam turn to
the profile machined on the end moving part and slows down the
outwear by expanding the brake shoe against the
vehicle with the help of friction. The
CLASSIFICATION OF FOLLOWER retractor spring force.
energy absorbed by brake is released
■ According to the surface in contact- ➔When the friction lining comes into contact with
to surrounding in form of heat.
1. Knife edge follower- the drum, friction is created.
Functions of Brake System
• In this type of follower, the contact end of ➔This frictional force opposes the direction of
The function of the brake system is to
the follower is Knife edge which is used to i) retard the motion of a vehicle, motion, slowing or stopping the vehicle.
contact with the surface of the cam. ii) stop the vehicle within the smallest ➔When brake pedal is released, the retracting
• Due to the high wear rate, the use of Knife possible distance, spring pull the brake shoe inward which turn the Case 1:-
edge follower is used less. iii) hold the vehicle at rest on an cam and brakes are released. When the line of action of tangential braking
• In this sliding motion is occurring. inclined road against the pull of gravity. force passes through the fulcrum of the
2. Roller follower- Types of Brake lever.
(a) Brake wheel rotates clockwise
• In this type of follower, The contact end of The brakes, according to the means
the follower is Roller at contacting surface. used for transforming the energy by When the line of action of tangential
• There is a rolling motion when it gets contact the braking elements, are classified as: braking force (𝐹𝑡) passes through the
with the cam. fulcrum 𝑂 of the lever, and the brake wheel
• This is used in heavy engines like aircrafts rotates clockwise. then for equilibrium, taking
moments about the fulcrum 𝑂, we have
engines, gas engines. due to less wear and tear
𝑅𝑁 × 𝑥 = 𝑃 × 𝑙
and side thrust between guide and follower.
𝑹𝑵 = 𝑷 × 𝒍 /𝒙.
• It is not recommended at step rise due to it
∴ Braking torque,
gets jams the cam. 𝑇𝐵 = 𝜇 × 𝑅𝑁 × 𝑟
• In this rolling motion is occurring. 𝑇𝐵 = 𝜇 × 𝑃 × 𝑙/ 𝑥 × 𝑟
3. Plate type follower- ∴ 𝑻𝑩 = 𝝁𝑷𝒍𝒓/𝒙
• In this follower, the contact end of the
follower is the flat face at contacting surface.
• This is used mainly in steep rise case.
• Due to more contact surface, it produces a
high wear rate.
4. Spherical follower-
• In this type of follower, The contact end of
the follower is Roller at contacting surface.
balancing of a single rotating mass. Concept vibration in machines Comparison of Belt ,Rope ,Chain and
Balancing a single rotating mass refers to the Vibration in machines refers to the oscillatory Gear.
process of minimizing the vibration caused by an motion or movement of a machine or its
imbalance in a rotating system. When a rotating components. It is an inherent characteristic of
mass is not evenly distributed around its axis of Belt and Rope Drive
most mechanical systems and can be caused by
rotation, it can create vibrations, which can lead to ➔Belt drive is one type of friction drive . These
various factors, including unbalanced forces,
reduced performance, increased wear and tear, and are flexible type of connectors bent easily.
misalignment, structural resonance, mechanical
even failure of the machinery. ➔It is non positive drive as slip and creep occur
defects, or external disturbances.
Here are the general steps involved in balancing a frequently
single rotating mass: Types of Vibration:
➔Here area contact occurs between belt and
➔Identify the imbalance: Determine the location ➔Free Vibration: Occurs when a machine or
pulley. So power loss is more due to high friction,
and magnitude of the imbalance in the rotating component vibrates after being set into motion
which also results in lower efficiency.
system. This can be done using various methods, and is free to move without any external forces
➔Belt drive is not preferred for large torque and
such as vibration analysis, visual inspection, or acting on it.
power transmission
specialized balancing equipment. ➔Forced Vibration: Results from external forces
➔They are used in longer centre distance
Mark the reference point: Choose a reference point or excitation applied to a machine or component,
on the rotating mass or the rotating shaft to ➔belt ,ropes are strained during motion as
such as an unbalanced rotating part or an
measure the amount and direction of imbalance. tension devlope in them.
external disturbance.
This reference point will serve as a baseline for Vibration Measurement: Chain drive
making adjustments.
Displacement: The distance a vibrating ➔Chain drive is one type of engagement drive. it
➔Determine the correction plane: Based on the is flexible type of connectors bent easily
component moves from its equilibrium position.
analysis of the imbalance, determine the plane ➔It is a positive drive; so velocity ratio remains
where the correction needs to be made. This is Velocity: The rate at which the displacement
changes with time. constant.
usually perpendicular to the axis of rotation and ➔High transmission efficiency due to no slip’
represents the plane where the mass needs to be Acceleration: The rate at which the velocity
changes with time. ➔Its transmit modarate power.
added or removed to achieve balance.
➔They are used in longer centre distance
➔Add or remove mass: To balance the rotating Frequency: The number of oscillations per unit of
mass, you can either add mass to the lighter side or time, measured in Hertz (Hz). ➔There is gradual streching and increase in
remove mass from the heavier side. The amount of length.
Causes of Vibration:
mass to be added or removed can be calculated ➔Unbalance: Occurs when the mass distribution Gear drive
using balancing equations, taking into account the of a rotating component is not uniform, leading ➔Gear drive is one type of engagement drive.It
mass distribution and the desired balance criteria. does not reuare any connector.
to centrifugal forces and resulting in vibration.
➔Adding mass: This can be done by attaching ➔It is a positive drive; so velocity ratio remains
➔Misalignment: When machine parts are not
weights, such as balance weights or counterweights, constant.
to the lighter side of the rotating mass. The weights properly aligned, it can lead to uneven forces,
increased wear, and vibration. ➔Here line contact occurs between two mating
can be adjusted incrementally until the balance is
➔Resonance: When the natural frequency of a gears, which results low friction and low power
achieved.
➔Removing mass: In some cases, if the rotating machine or component matches the frequency of loss. So it provides high efficiency.
mass has excess material, it may be possible to external forces, resonance can occur, resulting in ➔It can transmit large torque and power.
remove material from the heavier side to achieve amplified vibration. ➔They are used in Smaller centre Distance.
balance. This process requires precision machining ➔Mechanical Defects: Faulty bearings, worn-out ➔this is a rigid body.
and should be done carefully to avoid compromising gears, or damaged components can generate
the structural integrity of the rotating mass. vibration in a machine.
➔Test and verify balance: After making ➔External Disturbances: Environmental factors
adjustments, retest the system to check if the
like wind, earthquakes, or nearby machinery can
balance has been improved. This can be done using
introduce vibrations into a system.
vibration analysis equipment or other balancing
tools. Repeat the process if necessary until the Effects of Vibration:
Types of governor
desired level of balance is achieved. Increased Stress: Excessive vibration can subject
1. Centrifugal governor:-
machine components to higher stress levels,
leading to premature wear, fatigue, and potential A centrifugal governor is a device used to
● Balancing of Several Masses Rotating in
failure. regulate the speed of machinery, such as
the Same Plane
Consider any number of masses (say four) of Reduced Efficiency: Vibrations can cause energy engines or turbines. It operates on the
magnitude m1, m2, m3 and m4 at distances of r1, r2, r3 losses, increased friction, and reduced overall principle of centrifugal force and is
and r4 from the axis ofthe rotating shaft. Let θ1, θ2, machine efficiency. commonly used in steam engines, internal
θ3 and θ4 be the angles of these masses with the Degraded Performance: Vibrations can negatively
combustion engines, and other rotating
horizontal line OX, as shown in Fig. Let these masses impact the accuracy, precision, and stability of
rotate about an axis through O and perpendicular to machines, affecting their performance and output systems.
the plane of paper, with a constant angular velocity quality. The governor consists of a set of rotating
of ω rad/s. Health and Safety Concerns: High levels of weights or balls attached to a spindle. As
vibration can create discomfort for operators, the speed of the machine increases, the
cause fatigue, and even lead to long-term health centrifugal force acting on the weights
issues like hand-arm vibration syndrome (HAVS)
also increases. This force causes the
or whole-body vibration (WBV).
weights to move outward, away from the
axis of rotation.
Remedies of vibration on machine The movement of the weights is
Check for Proper Installation: Ensure that the connected to a control mechanism, which
machine is properly installed and aligned adjusts the fuel or steam supply to the
according to the manufacturer's guidelines. engine. If the speed of the machine
Improper alignment or mounting can cause exceeds a certain set point, the weights
excessive vibration.
Graphical method move outward, and the control
Balance Rotating Parts: Rotating components
− First of all, draw the space diagram with the such as shafts, pulleys, and fans should be mechanism reduces the fuel or steam
positions of the several masses, as shown in supply. This action slows down the
balanced to minimize vibration. Unbalanced parts
Fig.
− Find out the centrifugal force (or product of can create significant vibration, leading to machine, bringing it back to the desired
the mass and radius of rotation) exerted by premature failure. Balancing can be done through speed.
each mass on the rotating shaft. dynamic balancing techniques. Conversely, if the speed of the machine
−Now draw the vector diagram with the Lubrication: Insufficient or improper lubrication
drops below the set point, the weights
obtained centrifugal forces (or the product of the can increase friction and vibration in moving
masses and their radii of rotation), such that ab parts. Make sure to use the recommended move inward, and the control mechanism
represents the centrifugal force exerted by the lubricants and follow the manufacturer's increases the fuel or steam supply,
mass m 1 (or m1.r1) in magnitude and direction
guidelines for lubrication intervals. accelerating the machine to
to some suitable scale. Similarly, draw bc, cd
and de to represent centrifugal forces of other Check for Loose Connections: Examine the the desired speed.
masses m2, m3 and m4 (or m2.r2,m3.r3 and m4.r4). machine for loose bolts, fasteners, or other
− Now, as per polygon law of forces, the closing connections. Vibrations can cause these
side ae represents the resultant force in connections to loosen over time, leading to
magnitude and direction, as shown in Fig increased vibration. Tighten any loose
− The balancing force is, then, equal to resultant connections appropriately.
force, but in opposite direction
Dampening Systems: Install vibration dampening
− Now find out the magnitude of the balancing
mass (m) at a given radius of rotation (r), such systems such as rubber mounts, shock absorbers,
that m.r.𝜔 = Resultant centrifugal force or m.r = or anti-vibration pads. These devices can absorb
Resultant of m 1.r1, m2.r2, m3.r3 and m4.r4 or reduce the transmission of vibration from the
− (In general for graphical solution, vectors m machine to its surroundings.
1.r1, m2.r2, m3.r3, m4.r4, etc., are added. If they Structural Reinforcement: In some cases,
close in a loop, the system is balanced. reinforcing the structure or foundation of the
Otherwise, the closing vector will be giving
machine can help reduce vibration. This may
mc.rc. Its direction identifies the angular position
of the counter-mass relative to the other mass.) involve adding additional supports or stiffening
the existing structure to minimize excessive
movement.
Regular Maintenance: Implement a routine
maintenance schedule to inspect and address any
potential vibration issues. This includes checking
for wear and tear, replacing worn-out parts, and
performing necessary repairs or adjustments.
Concept of braking force and is same. Working
braking torque band brake P = W/A =Constant; where, W= load, A= area When clutch is in engage position, clutch
Let, (ii) Uniform wear: plates are gripped between friction plates
• 𝑃 = Force applied to the lever at C When clutch, bearing become old after being with the help of thrust spring also known as
• 𝑇1 = Tension in the tight side of the band used for a given period, then all parts of the pressure spring.
• 𝑇2 = Tension in the slack side of the band rubbing surfaces will not move with the same All the plates pressed together causing to
• 𝜃 = Angle of lap (or embrace) of the band velocity. The velocity of rubbing surface
on the drum rotate at same speed
increases with the distance from the axis of the
• 𝜇 = Coefficient of friction between the band The drive is transmitted from flywheel to
rotating element. It means that wear may be
and the drum different at different radii and rate of wear outer plates then outer plates or friction
• 𝑟 = Radius of the drum depends upon the intensity of pressure (P) and plates to clutch plates and finally it
• 𝑡 = Thickness of the band the velocity of rubbing surfaces (V).It is assumed transmitted to clutch shaft.
• 𝑟𝑒= Effective radius of the drum = 𝑟 + 𝑡/2 that the rate of wear is proportional to the As shown in fig. clutch is in disengage
➔We know that limiting ratio of the tensions product of intensity of pressure and velocity of position, When pressure is applied on the
is given by the relation 𝑇1 /𝑇2= 𝑒𝜇𝜃 and rubbing surfaces. friction plates with help of push pedal.
braking force on the drum = 𝑇1-𝑇2 This condition assumes that rate of wear is Clutch plates and friction plates gets
∴Braking torque on the drum, uniform; separate from each other so that clutch
𝑇𝐵 = (𝑇1-𝑇2)𝑟 (Neglecting thickness of band) P*r = Constant; where, P = intensity of pressure, plates rotate separately due to inertia and
= (𝑇1 − 𝑇2)𝑟𝑒 (Considering thickness of band) r = radius of rotation. then stops.
Function of clutch thus clutch gets disengage so drive is not
•In an Automobile, Clutch is used to engage transmitted from friction plates to clutch shaft 5) Diaphragm clutch.
and disengage the engine to the Construction
transmission ●It consist of pressure plate , diaphragm spring ,fulcrum
•The clutch is disengaged when starting the ring, cover bolted to flywheel ,release bearing and fork.
engine, shifting gears, when stopping the ●The diaphragm is conical steel disk, with its outer
vehicle and when idling the engine periphery located in pressure plate but pivoted to cover
•The clutch is engaged only when the vehicle
by fulcrum rings and locating studs.
is to move and is kept engaged when the
●There are slots starting from center of diaphragm to
vehicle is moving
form a number of release fingers . This release bearing
•When properly operated, it prevents jerky
motion of the vehicle and avoids undue applies pressure at the center of diaphragm.
strain on the remaining part of the power Working principle
transmission system ●When clutch is in engaged position. The conical
•Provides a link between the prime mover and diaphragm has been flattened in order to exert thrust
(a) Drum rotates clockwise the transmission on the pressure plate and friction facings.
•Allow for a smooth take up of the drive when the
When the drum rotates in the clockwise ●When the clutch pedal is pressed, the release bearing
vehicle is moved from rest 3) centrifugal clutch
direction, as , the end of the band attached exerts pressure at center of the diaphragm spring.
•Allow for a brief disengagement between
to the fulcrum 𝑂 will be slack with tension 𝑇2 Construction ●The outer edge of diaphragm moves away from the
engine and gearbox when gear change is done.
and end of the band attached to B will be A centrifugal clutch has a spring, spider or flywheel, disengaging the pressure plate from the
tight with tension 𝑇1. Now taking moments Construction and working of
guides, sliding shoes, friction lining and clutch plate.
about the fulcrum O, we have 1.) single plate clutch driving and driven member. The driving
𝑃 × 𝑙 = 𝑇1 × 𝑏 ●construction ●The pedal efforts required to disengage the clutch is
member is the input shaft from the engine, little compared to conventional (coil spring type) clutch.
∴ 𝑷 = 𝑻𝟏 × 𝒃/𝒍 1)Single plate clutch Is consists of main three and the driven member is the output shaft
parts are friction plate, pressure plate, flywheel. ●This is because of fact that little force required to
connected to the transmission system. The
And other parts are clutch pedal, clutch spring, press the diaphragm spring when it gets curved.
driven member looks like a drum and has a
and bearings. friction lining on its inner surface. The driving
2) The flywheel is a connected engine shaft & member encloses the driven member and is
the pressure plate is mounted on the clutch shaft attached to the spiders. The spiders have
which is connected to the flywheel with the help sliding shoes with friction lining on their outer
of a bolt & spring. end. The shoes are connected to the driving
3) Clutch shaft has a splines hence friction plate shaft by springs on their inner surface.
freely moves on the clutch shaft. Working principle
4) Spring is used to press the pressure plate The centrifugal clutch mechanism is very
against friction plate to keep the clutch in an simple to understand. When the engine
engaged position. starts, the driving shaft along with the spider
5] The clutch pedal is connected to the pressure rotates. The sliding shoes tend to move
plate with the help of linkages. away due to the centrifugal force, but the
(b) Drum rotates anticlockwise Working principle spring holds it in its position. When the
When the drum rotates in the anticlockwise A Single Plate Clutch Works By Using The engine speed increases, the centrifugal
direction, the end of the band attached to the Pressure Plate To Apply Pressure To The Clutch force overcomes the spring force. Hence the
fulcrum 𝑂 will be tight with tension 𝑇1 and Plate, Which In Turn Transmits Torque From The shoes move away from the centre and press
end of the band attached to B will be slack Engine To The Transmission. When The Clutch
with tension 𝑇2. against the drum. This makes the driven
Pedal Is Depressed, The Release Bearing member rotate at the speed of the driving Unit: 6 Balancing Of Rotating Masses &
Now taking moments about the fulcrum O, Separates The Pressure Plate From The Clutch
we have member. Thus the clutch automatically Vibrations
Plate, Causing The Clutch To Disengage. This engages at a predetermined speed. When
𝑃 × 𝑙 = 𝑇2 × 𝑏
Allows The Engine To Run Independently Of The the engine's speed is decreased, the
∴ 𝑷 = 𝑻𝟐 × 𝒃/𝒍 Concept of balancing of high speed rotating
Transmission, Allowing The Driver To Shift Gears centrifugal force also decreases. Therefore
Without Interrupting Power Transfer. When The the shoes disengage the driven shaft and masses
Clutch Pedal Is Released, The Pressure Plate come back to their original position. This is Balancing high-speed rotating masses is an important
Returns To Its Normal Position, Re-Engaging how a centrifugal clutch works. concept in engineering and machinery design. When a
The Clutch And Transmitting Torque From The rotating mass, such as a rotor or a wheel, is not
Engine To The Transmission. balanced, it can lead to various issues such as
vibrations, reduced performance, increased wear and
tear, and even structural damage.
The concept of balancing involves redistributing the
mass of a rotating system in such a way that the center
of mass coincides with the axis of rotation. This ensures
that the system operates smoothly without excessive
vibrations.
There are two types of balancing: static
Clutches balancing and dynamic balancing.
Clutch is a device used to transmit the rotary
●Static Balancing: Static balancing involves
motion of one shaft (Driving shaft) to another
balancing the mass distribution of a rotating system in a
shaft (Driven shaft) when desired
single plane. In static balancing, the center of mass is
• Driven shaft start or stop at operator’s will
without stopping the driving shaft aligned with the axis of rotation, which means that the
4) cone clutch
• Two inertias, I 1 and I 2 ,(one is driving and system will not experience unbalanced forces in that
2) multi-plate clutch Construction
another is driven) rotating at the respective plane. This can be achieved by adding or removing
Construction ●It is consists of inner cone, Outer Cone,
angular velocities ω 1 and ω 2 one of which weight at specific locations until the system is balanced.
Multi plate clutch has more than one clutch plate Spring.
may be zero, are to be brought to the same ●The outer cone has friction lining on its For example, in the case of a car tire, small weights can
known as metal plates and also it consist of
speed by engaging the clutch Slippage inner conical surface & inner cone has be attached to the rim to balance it.
number of outer plates known as friction plates.
occurs because the friction lining on its outer conical surface. ●Dynamic Balancing: Dynamic balancing is more
Friction plates are slides and engages by means
two elements are running at different speeds ●The Outer cone is connected to the input complex and involves balancing the rotating system in
of slots on the cover which is bolted to the
and energy is dissipated during actuation, shaft & inner cone is connected to clutch multiple planes. It takes into account the effects of
flywheel.
resulting in a temperature rise shaft.
A pair of lining made of an asbestos based centrifugal forces and unbalanced moments caused by
Uniform pressure material is riveted to the both the side of clutch ●The Inner cone is connected to clutch the rotational motion. Dynamic balancing is necessary
When the mating component in clutch, plate and clutch plate is sandwiched between pedal through a linkage. when the rotating system operates at high speeds or
bearing are new, then the contact between two friction plates in multi plate clutch. Working principle when precision is crucial. Dynamic balancing typically
surfaces may be good over the whole The inner splines of clutch plates are fitted on the ●Cone clutch works on principle of Friction. involves measuring the unbalance using specialized
surface. It means that the pressure over the splined hub.they also slides on the splined ●The outer cone has friction lining on its
equipment, such as vibration analyzers or balancing
rubbing surfaces is uniform distributed. This hub. Trust spring push the plates together to inner conical surface & Inner cone has
machines. Based on the measurement results, weights
condition is not valid for old clutches, form a drive.the size of clutch plates is small as friction lining on its outer conical surface.
bearings because mating surfaces may can be added or removed at specific locations to
compared to single plate clutch which makes ●Friction between this two cones is cause
have uneven friction. The condition assumes for the power transmission from the flywheel minimize the unbalance and achieve smooth operation.
clutch plates compact.
that intensity of pressure to the gearbox.