Mechanisms of Textile Machine

MECHANISMS OF TEXTILE
MACHINE
BY
MUKTAR SEID HUSSEN

BASIC DEFINITION
 Mechanisms is a division of machine design,
 which concerned with the kinematics design of links,
cams, gears, gear trains etc.
Kinematics design is the design on the basis of
motion requirement.
 Mechanism is a system of rigid elements,
 which arranged and connected to transmit motion in a
predetermined fashion.
 Mechanism is a heart of a machine,
 Machine is mechanical device used to accomplish work.
 Machine is a mechanism or a collection of mechanisms
which transmits force from the source of power to the
output.

 Mechanisms is formed by a combination of rigid bodies,
 which connected to move upon each other with a defined
relative motion.
Relative - a position, velocity, etc. is measured based
on a moving point.
Absolute - a position, velocity, etc. is measured based
on a fixed point.
 Link - rigid body between joints,
Pair or Joint - a connection between two links
 Binary Link - has two joints only
 Ternary Link - has three joints
 Quaternary Link - has four joints
 Frame - a grounded or fixed link in a mechanism
 Driver / Follower - the driver link will be driving the
follower.

CLASSIFICATION OF CONSTANT SPEED MECHANICAL
POWER TRANSMISSION ELEMENTS
DEPENDS ON RELATIVE SHAFT POSITION
Coupling
Clutch
Belt
Chain
Rope
Spur gear
Helical gear
Friction drive
Bevel gear
Friction drive Worm gear
Friction drive

APPLICATION PERCENTAGE OF POWER
TRANSMISSION ELEMENT IN TEXTILE MACHINE

BELT DRIVE
 The belt drives primarily operate on the friction principle,
 the friction between the belt and the pulley is responsible for
transmitting power from one pulley to the other.
 In other words the driving pulley will give a motion to
the belt and the motion of the belt will be transmitted to the
driven pulley.
 Belts, ropes, chains, and other similar elastic or flexible machine
elements are used,
 in conveying systems,
 Transportation of coal, mineral ores etc. over a long distance
 in the transmission of power,
 Mainly used for running of various industrial appliances
using prime movers like electric motors, I.C. Engine etc.
 as a replacement for gears, shafts, bearings, and other
relatively rigid power-transmission devices.

 The amount of power transmitted depends upon the following
factors:
 The velocity of the belt.
 The tension under which the belt is placed on the pulleys.
 The arc of contact between the belt and the smaller pulley.
 The conditions under which the belt is used.

 The shafts should be
properly in line,
 to insure uniform tension
across the belt section.
 The pulleys should not be
too close together,
 to make the arc contact
on the smaller pulley
large as possible.
 The pulleys should not be so
far apart as,
 it cause the belt to weight
heavily on the shafts,
 thus increasing the
friction load on the
bearings.
 it tends to swing a long belt from
side to side,
 causes the belt to run out of the
pulleys which develops crooked
spots in the belt.
 The tight side of the belt should be at the
bottom,
 so that sag is present on the loose
side,
 by increasing the arc contact at
the pulleys.
 In order to obtain good results with flat
belts,
 maximum distance between the
shafts should not exceed 10 metre.
 minimum should not be less than
3.5 times the diameter of the larger
pulley.
It may be noted that:

ADVANTAGES OF BELT DRIVE
 Simplifies the design of a machine and substantially reduces the
cost.
 economical because the shafts are separated by large distances.
 Plays an important role in absorbing shock loads and in damping
out and isolating the effects of vibration. (shock-absorbed)
 because the elements are elastic and usually quite long,
 machinery life is prolonged because load fluctuations are
cushioned.
 Noise and vibration are damped out.
 No lubrication is required. (oil must be kept off the belt)
 Relatively cheap to install and to maintain.
 Medium to long distance power transmission is possible as
compared to other transmission systems.
 They are highly efficient. (90 – 98% usually 95%)

DISADVANTAGES OF BELT DRIVE
 Speed is limited, usually 7000 feet per minute (35 meters per
second).
 Operating temperatures are usually restricted to –35 to 85°C.
 Belt drives have some slip and creep.
 Due to the belt extending slightly under load and therefore do
not have an exact drive ratio.
 Some adjustment of centre distance or use of an idler pulley is
necessary,
 For wear and stretch compensation.
 It is important to establish an inspection schedule to protect against
wear, aging and loss of elasticity.
 The elements should be replaced at the first sign of
deterioration.
 Belts can wear rapidly in abrasive (dusty) conditions.
 Most flexible elements do not have an infinite life.

TYPES OF BELT DRIVES
 The belt drives are usually classified into three groups based on
peripheral speed:
1) Light drives
 Used to transmit small powers at belt speeds up to 10 m/s,
 in agricultural machines and small machine tools.
2) Medium drives
 Used to transmit medium powers in belt speeds of 10 up to
22 m/s,
 in machine tools.
3) Heavy drives
 Used to transmit large powers at belt speeds above 22 m/s,
 in compressors and generators.

TYPES OF BELTS
The four principal types of belts are:
1) Flat belt
 Moderate amount of power is transmitted and the two
pulleys are not more than 8 metres apart.
2) V-belt
 Great amount of power is transmitted and the two pulleys
are very near to each other.
3) Circular belt
 Great amount of power is transmitted and the two pulleys
are more than 8 metres apart.
4) Timing belts
 Teeth formed on the belt match the grooves on the
pulleys and acting almost like a chain running on
sprockets.

TYPES OF FLAT BELT DRIVES
Open belt drive
 Shafts arranged parallel and rotating in the same direction.
 The driver pulls the belt from one side (lower side) and delivers
it to the other side (upper side).
 The tension in the lower side belt will be more than in the upper
side belt.
 The lower side belt (because of more tension) is tight side
whereas the upper side belt (because of less tension) is slack side

Crossed or twist belt drive
 Shafts arranged parallel and rotating in the opposite directions
and also angle of contact of belt on both the pulleys is equal.
 The tension in the belt RQ will be more than in the belt LM.
 The belt RQ (because of more tension) is tight side whereas the
belt LM (because of less tension) is slack side.
A little consideration at a point where the belt crosses, it rubs against
each other and there will be excessive wear and tear.
In order to avoid this, the shafts should be placed at a
maximum distance of 20 times belt width and the belt speed
should be less than 15 m/s.

Quarter turn or right angle belt drive
 Shafts arranged at right angles and rotating in one definite direction.
 In order to prevent belt leaving from the pulley, the width of the face
of the pulley should be greater or equal to 1.4 times belt width.
Compound belt drive
Power is transmitted from one shaft to another through a number of
pulleys.

Belt drive with idler or jockey pulley drive
 Shafts arranged parallel with many idler pulleys,
 It is desirable to transmit motion from one shaft to several
shafts.
 This type of drive is provided to obtain high velocity ratio.

Stepped or cone pulley drive
 Used for changing the speed of the driven shaft while the main or
driving shaft runs at constant speed.
 This is accomplished by shifting the belt from one part of
the steps to the other.

Fast and loose pulley drive
 Used when the driven shaft is to
be started or stopped without
interfering with the driving shaft.
 A fast pulley is keyed to the
driven shaft and runs at the
same speed as driven shaft.
 A loose pulley runs freely over
the driven shaft and incapable
of transmitting any power.
 When the driven shaft is required
to be stopped,
 The belt is pushed on to the
loose pulley by means of
sliding bar having belt forks.

VELOCITY RATIO OF A BELT DRIVE
 It is the ratio between the velocities of the driver and driven.
 Let
 Length of the belt that passes over the driver in one minute,
 Length of the belt that passes over the driven in one minute,
 Length of belt that passes over the driver in one minute is equal to
the length of belt that passes over the driven in one minute,
 So that the velocity ratio can be,

 When thickness of the belt (t) is considered, then velocity ratio
OR
 Peripheral velocity of the belt on the driving pulley,
 Peripheral velocity of the belt on the driven pulley,
 When there is no slip,
 For a compound belt drive,

SLIP OF THE BELT
 The motion of belts and pulleys assuming a firm frictional grip
between the belts and the pulleys.
 But sometimes, the frictional grip becomes insufficient.
This may cause some forward motion of the driver
without carrying the belt.
This is called slip of the belt and is generally
expressed as a percentage.
 The result of the belt slipping is to reduce the velocity ratio of the
system.
 Velocity of the belt passing over the driver per second,

 Velocity of the belt passing over the follower per second,
 So that the velocity ratio will be,
 If thickness of the belt (t) is considered,

RATIO OF DRIVING TENSIONS FOR FLAT BELT DRIVE
 Resolving all the forces horizontally,
 Since the angle δθ is very small, therefore putting sin δθ/2 = δθ/2

 Now resolving the forces vertically,
 Since the angle δθ is very small, therefore putting cos δθ/2 = 1
 Equating the values of RN,
 Integrating the above equation between the limits T2 and T1 and
from 0 to θ,
 The equation can be expressed in terms of corresponding
logarithm to the base 10,

CENTRIFUGAL TENSION
 Since the belt continuously runs over the pulleys, therefore, some
centrifugal force is caused,
 Whose effect is to increase the tension on both the tight as
well as the slack sides.
The tension caused by centrifugal force is called
centrifugal tension.
 At lower belt speeds (less than 10 m/s), the centrifugal tension is
very small,
 But at higher belt speeds (more than 10 m/s), its effect is
considerable and thus should be taken into account.

 Length of the belt PQ,
 Mass of the belt PQ,
 Centrifugal force acting on the belt PQ,
 Now resolving the forces horizontally, (centrifugal force and
centrifugal tension)
 When centrifugal tension is taken in to account, total tension in the
tight side and total tension in the slack side will be,

POWER TRANSMITTED BY A BELT
 The driving pulley pulls the belt from one side and delivers it to the
other side.
 The tension on the tight side will be greater than the slack side.
 The effective turning (driving) force at the circumference of the
driven pulley or follower is the difference between the two tensions,
 Transmitted power will be,

Maximum power transmission by belt
and
 By substituting the value of T2 and
 By substituting the value of T1 and
 For maximum power, differentiate the above expression with
respect to v and equate to zero,
 And,

GEAR DRIVE
 We have discussed earlier that the slipping of a belt or rope is a
common phenomenon in the transmission of motion or power
between two shafts.
The effect of slipping is to reduce the velocity ratio of
the system.
 In precision machines,
Definite velocity ratio is importance,
The positive drive is by gears or toothed wheels.
E.g. watch mechanism
 A gear drive is also provided,
When the distance between the driver and the follower
is very small.
When the driver and follower have direct contact.

 In order to understand motion transmitted by two toothed wheels,
 Consider two plain circular wheels A and B mounted on
shafts.
 The wheels have sufficient rough surfaces and press
against each other
 The wheel A is keyed to the rotating shaft and the wheel B
to the shaft to be rotated.
 The wheel A is rotated by a rotating shaft and it
will rotate the wheel B in the opposite direction
 The wheel B will be rotated by the wheel A.
 The tangential force exerted by the wheel A does not exceed
the maximum frictional resistance between the two wheels.
 When the tangential force (P) exceeds the frictional
resistance (F), slipping will take place between the two
wheels.

 In order to avoid the slipping,
 a number of projections called teeth are provided on the
periphery of the wheel A,
which will fit into the corresponding recesses on the
periphery of the wheel B.
 A friction wheel with the teeth cut on it is known as gear or
toothed wheel.

ADVANTAGES OF GEAR DRIVE
 The following are some of the advantages of gear drive as
compared to the other drives; such as belt, rope and chain drives.
 It transmits exact velocity ratio,
Constancy of speed ratio with out any slippage.
 It may be used to transmit large power,
Can drive much heavier loads
Can be used for a wide range of transmitted power.
 If properly lubricated and operated,
gear drives have the longest service life as compare to
other mechanical drives.
 It has compact layout,
It may be used for small centre distances of shafts.
 It has high efficiency.
 It has reliable service.

 The following are some of the disadvantages of the gear drive as
compared to the other drives. (belt, rope and chain drives)
 Complex to manufacture,
Since the manufacture of gears require special tools and
equipment,
 Therefore it is costlier than other drives.
(expensive)
 The error in cutting teeth,
May cause vibrations and noise during operation.
 It requires suitable lubricant and reliable method of applying
it,
For the proper operation of gear drives.
 They are not suitable for large centre to centre distance,
Because the drive will become bulky.
DISADVANTAGES OF GEAR DRIVE

CLASSIFICATION OF GEARS
According to the position of axis of the shafts:
Parallel
 The two parallel shafts connected by the gears.
 These gears are called spur gears and the arrangement is
known as spur gearing.
These gears have teeth parallel to the axis of the wheel.
 Another gear is helical gear, in which the teeth are inclined
to the axis.
 Single and double helical gears connecting parallel shafts,
The double helical gear is used to balance out the end
thrusts that are induced in single helical gears when
transmitting load.
 The double helical gears are known as herringbone
gears.

Intersecting
 The two non-parallel and intersecting shafts connected by gears,
 These gears are called bevel gears and the arrangement is
known as bevel gearing.
 The bevel gears may have their teeth inclined to the face
of the bevel are known as helical bevel gears.
Non-intersecting
 The two non-intersecting and non-parallel shafts connected by
gears,
 These gears are called skew bevel gears or spiral gears and
the arrangement is known as skew bevel gearing or spiral
gearing.
Having a line contact and the rotation about the axes
generates the two pitch surfaces known as
hyperboloids

According to the peripheral velocity of the gears:
 Low velocity
 The gears having velocity less than 3 m/s
 Medium velocity
 The gears having velocity between 3 and 15 m/s
 High velocity
 The gears having more than 15 m/s
According to the type of gearing:
 External gearing
 The gears of the two shafts mesh externally with each
other.
 The larger of these two wheels is called spur gear and the
smaller wheel is called pinion.
 The motion of the two wheels is always unlike.

 Internal gearing
 The gears of the two shafts mesh internally with each
other.
 The larger of these two wheels is called annular wheel
and the smaller wheel is called pinion.
 The motion of the wheels is always like.

 Rack and pinion
 The gear of a shaft meshes
externally or internally with the
gears in a straight line.
 The straight line gear is called
rack and the circular wheel is
called pinion.
 The rack and pinion can convert
linear motion into rotary motion
and vice-versa.
According to the position of teeth on the gear surface.
 Straight
 The spur gears have straight teeth to the wheel rim.
 Inclined
 The helical gears have inclined teeth to the wheel rim.
 Curved
 The teeth are curved over the rim surface.

TERMS USED IN GEARS
 Pitch circle
 It is an imaginary circle which by pure rolling action, would give the
same motion as the actual gear
 Pitch circle diameter
 It is the diameter of the pitch circle. The size of the gear is usually
specified by the pitch circle diameter. It is also called as pitch
diameter.
 Pitch point
 It is a common point of contact between two pitch circles.
 Pitch surface
 It is the surface of the rolling discs which the meshing gears have
replaced at the pitch circle.
 Pressure angle or angle of obliquity
 It is the angle between the common normal to two gear teeth at the
point of contact and the common tangent at the pitch point. It is
usually denoted by φ. The standard is14 1/2°and 20°.

 Addendum
 It is the radial distance of a tooth from the pitch circle to the top of the
tooth.
 Dedendum
 It is the radial distance of a tooth from the pitch circle to the bottom of
the tooth.
 Addendum circle
 It is the circle drawn through the top of the teeth and is concentric with
the pitch circle.
 Dedendum circle
 It is the circle drawn through the bottom of the teeth. It is also called
root circle.
 Root circle diameter = Pitch circle diameter × cos φ
 Circular pitch
 It is the distance measured on the circumference of the pitch circle from
a point of one tooth to the corresponding point on the next tooth. It is
usually denoted by pc

 Diametral pitch
 It is the ratio of number of teeth to the pitch circle diameter in millimetres.
It denoted by pd.
 Module
 It is the ratio of the pitch circle diameter in millimetres to the number of
teeth. It is usually denoted by m.
 Clearance
 It is the radial distance from the top of the tooth to the bottom of the tooth,
in a meshing gear. A circle passing through the top of the meshing gear is
known as clearance circle.
 Total depth
 It is the radial distance between the addendum and the dedendum circle of
a gear. It is equal to the sum of the addendum and dedendum.
 Working depth
 It is radial distance from the addendum circle to the clearance circle. It is
equal to the sum of the addendum of the two meshing gears.

 Tooth thickness
 It is the width of the tooth measured along the pitch circle.
 Tooth space
 It is the width of space between the two adjacent teeth measured along the
pitch circle.
 Backlash
 It is the difference between the tooth space and the tooth thickness, as
measured on the pitch circle.
 Face of the tooth
 It is surface of the tooth above the pitch surface.
 Top land
 It is the surface of the top of the tooth.
 Flank of the tooth
 It is the surface of the tooth below the pitch surface.
 Face width
 It is the width of the gear tooth measured parallel to its axis.
 Profile
 It is the curve formed by the face and flank of the tooth.
 Fillet radius
 It is the radius that connects the root circle to the profile of the tooth.

 Path of contact
 It is the path traced by the point of contact of two teeth from the beginning
to the end of engagement.
 Length of the path of contact
 It is the length of the common normal cut-off by the addendum circles of
the wheel and pinion.
 Arc of contact
 It is the path traced by a point on the pitch circle from the beginning to the
end of engagement of a given pair of teeth.
 The arc of contact consists of two parts
 Arc of approach
 It is the portion of the path of contact from the beginning of the
engagement to the pitch point.
 Arc of recess
 It is the portion of the path of contact from the pitch point to the
end of the engagement of a pair of teeth.
 The ratio of the length of arc of contact to the circular pitch is
known as contact ratio i.e. number of pairs of teeth in contact.

DESIGN CONSIDERATIONS FOR A GEAR DRIVE
 The following requirements must be meet in the design of a gear
drive:
 The gear teeth should have sufficient strength
So that they will not fail under static loading or
dynamic loading during normal running conditions.
 The gear teeth should have wear characteristics
So that their life is satisfactory.
 The use of space and material should be economical.
 The alignment of the gears and deflections of the shafts
must be considered
Because they effect on the performance of the gears.
 The lubrication of the gears must be satisfactory.

 In the design of a gear drive, the following data is usually given
 The power to be transmitted
 The speed of the driving gear
 The speed of the driven gear or the velocity ratio
 The centre distance
 The phenomenon when the tip of a tooth undercuts the root on its
mating gear is known as interference.
 For example,
 In a pinion gearing with a wheel,
 MN is the common tangent to the base circles.
 KL is the path of contact between the two mating teeth.
INTERFERENCE

 If the radius of the addendum circle of pinion is increased to
O1N,
 The point of contact L will move from L to N.
 When this radius is further increased,
 The point of contact L will be on the inside of base circle of
wheel and not on the profile of tooth on wheel.

 The tip of tooth on the pinion will then undercut the tooth
on the wheel at the root and remove part of the profile of
tooth on the wheel.
 This effect is known as interference and occurs when
the teeth are being cut.
 Similarly, if the radius of the addendum circle of the wheel
increases beyond O2M,
 Then the tip of tooth on wheel will cause interference with
the tooth on pinion.
 The points M and N are called interference points.
 Obviously interference may be avoided if the path of
contact does not extend beyond interference points.
 The limiting value of the radius of the addendum circle
of the pinion is O1N and of the wheel is O2M.

FORMS OF TEETH
In actual practice two types of teeth commonly used:
 Cycloidal teeth
 Have different surface for face (Convex) and for flank
(concave)
When it mesh, the convex of one gear mesh with
concave of other
This gives little wear on the surface
Cycloidal gears are stronger than the involute gears for
the same pitch.
Because cycloidal teeth have wider flanks
Interference does not occur at all.
 But it is difficult to produce the exact profile so that it is
obsolescence.

 Involute teeth
 Involute is a curve traced by a point on a line as the line
rolls on another curve (base circle)
 The surface is ether straight or curved (mostly convex) for
both face and flank
 It is universally acceptable because of,
Simplicity to manufacture
Interchange ability of gear in case of changes the
speed ratio
Possibility of a certain increase in the centre
distance without affecting the velocity ratio
 But it will occurs interference,
avoided by altering the heights of addendum and
dedendum of the mating teeth.

 Let A be the starting point of the
involute.
 The base circle is divided into equal
number of parts AP1, P1P2, P2P3 etc.
 Tangents at P1, P2, P3 etc., are drawn
 The length P1A1, P2A2, P3A3 is
equal to the arcs AP1, AP2 and AP3
 By joining the points A, A1, A2, A3
etc., we obtain the involute curve AR.
 The radii of the base circles is
 By equating
 The centre distance between
the base circles

SYSTEMS OF GEAR TEETH
Four systems of gear teeth are commonly used in practice:
 Composite system,
 The tooth profile is cycloidal at the top and bottom and
involute curve at the middle portion.
 Full depth involute system,
 The full height of the tooth is full addendum plus full
dedendum.
 When the pressure angle is increased, the number of teeth
will be decreased but the capacity of teeth increased.
 Stub involute system,
 The tooth has less working depth, usually 20% less than the
full depth system.

VELOCITY RATIO IN GEAR DRIVE
 The speed ratio is defined as the ratio of the number of revolutions
of the driver to the number of revolution of the driven gear.
 When there is no slippage,
 Velocity ratio (VR) = driver number of revolution (N1)
driven number of revolution (N2)
 VR =
 If the centre distance between the driving and driven shaft is quite
large,
 Connecting by a single mesh gear is not recommended but by
using large number of gears mounted on parallel shafts which
transmit same velocity ratio.

FORCE ANALYSIS OF SPUR GEARING
 let us agree on the notation to be used.
 1 for the frame of the machine,
 designate the input gear as gear 2,
 and then number the gears successively 3, 4, etc., until the last gear,
 F23 is force exerted by gear 2 against gear 3
 Next, there may be several shafts involved and usually one or two gears
are mounted on each shaft as well as other elements.
 Designate shafts using lowercase letters of the alphabet, a, b, c, etc.
 F2a is force of gear 2 against a shaft a
 Fa2 is force of a shaft a against gear 2
 It is also necessary to use superscripts to indicate directions.
 The directions usually indicated by the x, y, and z coordinates,
 Radial and tangential directions by superscripts r and t.
 Ft43 is the tangential component of the force of gear 4 acting
against gear 3.

 Fig. shows a pinion mounted on
shaft a rotating clockwise at n2
rev/min and driving a gear on
shaft b at n3 rev/min.
 The reactions between the
mating teeth occur along the
pressure line.
 Fig. shows pinion and gear has
been separated from each other
and shaft, and their effects have
been replaced by forces.

 Fa2 and Ta2 are the force and torque, respectively, exerted
by shaft a against pinion 2.
 F32 is the force exerted by gear 3 against the pinion.
 The free-body diagram of the pinion has been redrawn and the
forces have been resolved into tangential and radial components.

 The tangential load is really the useful component and it define
as the transmitted load,
 because the radial component serves no useful purpose and it
does not transmit power.
 The applied torque and the transmitted load are seen to be related
by the equation
 Where T = Ta2 and d = d2 to obtain a general relation.
 The power H transmitted through a rotating gear can be obtained
from the standard relationship of the product of torque T and
angular velocity ω.

FORCE ANALYSIS OF BEVEL GEARING
 The usual practice is to use the tangential or transmitted load that
would occur,
 If all the forces were concentrated at the midpoint of the tooth.
While the actual resultant occurs somewhere between the
midpoint and the large end of the tooth.
 For the transmitted load,
 Where T is the torque and rav is the pitch radius at the midpoint
of the tooth for the gear under consideration.
 The resultant force W has three components:
 Tangential force (Wt)
 Radial force (Wr)
 Axial force (Wa)

CAM DRIVE
 Cam is a mechanical element used to drive another element,
called the follower,
 Through a specified motion by direct contact.
So that cam system consists of the cam itself and the
follower.
 Cam may translate or rotate while the follower may translate or
oscillate which provides the output motion.
 A cam converts an input motion (usually rotary motion) into
either reciprocating or oscillatory output action.
Usually cams rotate at a constant angular speed.

 Cam and follower mechanisms are used extensively in modern
machinery because of,
 Simple and inexpensive ,
Cam is versatility and flexibility in the design.
Follower motions having almost any desired
characteristics are not difficult to design.
 Having few moving parts.
 Occupy a very small space.

CLASSIFICATION OF FOLLOWER
Follower may be classified based on the following:
By follower surface contact
 Knife edge follower,
 A sharp knife edge is in contact with the cam.
 It produces excessive wear of the cam.
So that have no practical application.
 Roller follower,
 A cylindrical roller held by a pin to the follower
assembly with a contact to cam.
 These type of follower reduce wear on cam surface at
high speed.

 Flat face follower,
The flat face is in contact with the cam.
This type of follower cause high frictional force.
 Spherical face follower,
To reduce frictional force, the flat surface is modified
to a spherical surface with a large radius.
 The spherical face is in contact with the cam.

By type of follower motion
 Oscillatory follower,
For a uniform rotary motion of the cam, the follower
oscillates through a certain angle.
 Translatory follower,
As the cam rotates, the follower reciprocates in the
guides.

By follower line of motion
 Radial follower,
The follower translate along an axis passing through the
cam centre of rotation
 Off set follower,
The axis of follower movement is displaced from the
cam centre of rotation
 Oscillating follower,
The follower oscillate about the axis of the follower
through a certain angle.

CLASSIFICATION OF CAM
Cam may be classified based on the following:
By cam shape
 Plate, disk or radial cam,
 This cam has an irregular contour to impart a specific
motion to the follower.
 The follower moves in a plane perpendicular to the axis
of rotation of the cam shaft.

 Wedge or translating cam,
 This cam is a contoured plate sliding
on a guiding surface(s).
 The contour shape is determined by
the specified motion of the follower.
 The follower may oscillate or
reciprocate.
 Cylindrical or barrel cam,
 This cam has a groove cut along its
cylindrical surface.
 The roller follows the groove, and the
follower moves in a plane parallel to
the axis of rotation of the cylinder.
 End or face cam,
 This cam has a groove cut on its face.

 The least common in practical application is the wedge cam,
 Because of its need for a reciprocating rather than continues
input motion.
 So that the most common is plate cam.
By follower motion
 Translatory,
 Oscillatory,
By cam constraint
 Spring or pre-load cam,
 Cam and follower is in contact by external force provided
by springs.
 Gravity,
 It is a positive return cam because it does not required
external force to keep the contact between cam and
follower.

CAM NOMENCLATURE
Trace point:
A theoretical point on the follower, corresponding to the point of a
fictitious knife-edge follower. In the case of a roller follower, the trace
point is at the center of the roller or on the surface in flat face follower.
Pitch curve:
The path generated by the trace point as the follower moves relative to
the cam. For knife edge follower the pitch curve is identical to cam
profile.
Prime circle (reference circle):
The smallest circle from the cam center through the pitch curve.
Base circle:
The smallest circle from the cam center through the cam profile curve.
For flat face follower the prime and base circle is identical.
 Follower displacement:
 The position of the follower from a specific zero or rest position
(usually its the position when the follower contacts with the base
circle of the cam) in relation to time or the rotary angle of the cam.

DISPLACEMENT DIAGRAMS
 During the rotation of the cam through one cycle of input
motion,
 The follower executes a series of events which is shown by
a graphical form known as a displacement diagram.
 The known input denoted by ‘θ’ and the output denoted
by ‘Y’
‘Y’ is a translational distance for a reciprocating
follower and is an angle for oscillatory follower.
 The x-axis represents one cycle of the input motion ‘θ’
Which is one revolution of the cam and drawn to any
convenient scale.
 The y-axis represents the follower travel ‘Y’
Usually reciprocating follower, drawn at full scale.

Rise:
It is a portion on graph when the follower is moving away
from the cam centre.
The maximum rise is called lift.
Dwell:
It is a portion on graph when the period of follower is at rest
or stationary.
Return:
It is a portion on graph when the follower moves back
towards the cam centre.

Key steps in cam design,
1. Choosing the suitable forms of motion,
2. Set the exact relationship between the input ‘θ’
and the out put (Y) motion,
 By representing the displacement
diagram with the functional relationship,
 Y = Y(θ),
(this equation is developed with the
exact shape of final cam)
3. Construct the displacement diagram precisely.
4. Finally, construct the cam profile.

Displacement diagram for uniform motion,
Is straight line with the constant slope.
For constant input, the velocity of the follower also
constant.
Is not useful because the corner produced at the boundaries
with the other section of the displacement diagram.
So that used between other curve by eliminating the
corners.

 Displacement diagram for modified uniform motion,
 The central portion of the diagram is uniform motion
For a cam angle of B2 and lift L2.
 The end portion of the diagram is parabolic motion
For a cam angle of B1 and B3 and also the lift L1 and
L3.

To match the parabolic motion with the
uniform motion,
First take one end either L1 for B1 or L3 for
B3 which can form a rectangular boundary.
And divided in to a convenient and equal
number of divisions for both x and y-axis.
Then construct a line which is started from the
origin in to every division of y-axis and also
construct a line which start from every
division of x-axis.
Finally, mark at the point of intersection for
those line and joined every points.

 Displacement diagram for parabolic motion,
 The first portion of the diagram is upward parabolic motion
For a cam angle of B/2 and lift L/2.
 The second portion of the diagram is downward parabolic
motion
For a cam angle of B and lift L.

 Displacement diagram for simple harmonic motion,
 Use the a semi-circle having a diameter equal to the
rise (L) to construct the graph.
 The semi-circle and the x- axis are divided in to an
equal parts.
 And construction of graph is by joining the mark
which is formed by the intersection of the line from
the x-axis and semi-circle division.

GRAPHICAL LAYOUT OF CAM PROFILE
 To determine the exact shape of a cam surface required
to deliver a specified follower motion.
By determining the required motion graphically,
analytically or numerically completely.
The complete displacement diagram can be drawn
to a scale for the entire cam rotation.
 In constructing the cam profile,
Employ the principle of kinematics inversion.
Imagining the cam to be stationary.
Allowing the follower to rotate opposite to
the direction of cam rotation.

Cam profile construction for radial follower,
 First draw a base circle and prime circle with the given data from
the same centre of point (point of rotation for cam)
 Second divided both circle in to a number of segments and assign
station number to the boundaries of these segments.
 Then transfer distance, by means of divider, from the
displacement diagram directly on to the cam layout to locate the
corresponding positions of the trace point and other.
 Finally, a smooth curve through these point is the pitch curve and
cam profile.

Cam profile construction for offset follower,
 First draw an offset circle by using a radius which is equal to
the amount of offset distance from the same centre of point
(point of rotation for cam).
 Second draw a base circle and prime circle with the given
data from the same centre of point (point of rotation for cam)
 Third divided offset circle in to a number of segments and
assign station number to the boundaries of these segments.
 And construct a tangent line for every station from offset
circle and intersect both base and prime circle.
 Then transfer distance, by means of divider, from the
displacement diagram directly on to the cam layout to locate
the corresponding positions of the trace point and other.
 Finally, a smooth curve through these point is the pitch curve
and cam profile.

SHAFT
 A shaft is a rotating machine element,
 Which is used to transmit power from one place to another.
 In order to transfer the power from one shaft to another,
 The revolving parts of a machine or various members such
as pulleys, gears, flywheels ..., are mounted on it.
The various members are mounted on the shaft by
means of keys or spline.
 An axles only support the revolving part,
 An axle is a non-rotating member that carries no torque
Can readily be designed and analyzed as a static
beam
 Hence the load carried by the revolving parts is taken by the
axle as a bending load.
The load exerted upon causes the shaft to bending.

 The power is delivered to the shaft set up within the shaft,
 Permits the power to be transferred to various machines
linked up to the shaft.
By some tangential force and the resultant torque
(twisting moment)
 In other words,
We may say that a shaft is used for the transmission of
torque and bending moment.
 The shafts,
Are usually cylindrical but may be square in cross-
sectional shape.
Are also solid in cross-section but sometimes hollow
shafts are used.

 An axle,
Similar in shape to the shaft,
It simply acts as a support for some rotating body,
Such as a car wheel, hoisting drum.
It is a stationary machine element,
Used for the transmission of bending moment
only.
 A spindle,
It is a short shaft that imparts motion,
Either to a cutting tool (e.g. drill press spindles) or
to a work piece (e.g. lathe spindles).

CLASSIFICATION OF SHAFT
 Depends upon the form of geometrical axis of the shaft,
 Straight shaft,
It may be either solid or hollow shaft.
It may be also flexible with changing form of the
geometrical axis.
 Crank shaft,
 Depends upon their use,
 Prime mover shaft,
Motor shaft, turbine shaft, engine shaft
 Machine shaft,
These shafts form an integral part of the machine itself.
Such as crank shaft
 Power transmittion shaft,

 These shafts transmit power between the source and the
machines absorbing power.
 Since these shafts carry machine parts such as pulleys, gears
etc., therefore they are subjected to bending in addition to
twisting.
 Such as counter shafts, jack shafts, line shafts.
 Line shaft,
 It is a long and continues shaft which used for the
distribution of power.
 Used in workshops and factories.
 Counter shaft,
 Employed in between a line shaft and a machine shaft.
 Jack shaft,
 This shaft directly connected to the power source.
 From this shaft drive is given to the other shafts.

STRESSES IN SHAFTS
The following stresses are induced in the shafts:
Shear stresses,
Due to the transmission of torque (torsional
load).
Bending stresses,
Due to the forces acting upon machine elements
Like gears, pulleys etc. as well as due to the
weight of the shaft itself.
It may be tensile or compressive stresses.
Combined stresses,
Due to combined torsional and bending loads.

CAUSES OF FAILURE IN SHAFT
 Failure is not meant actual breaking of the material.
 Some machine parts are said to fail when they have plastic
deformation set in them,
 And they no more perform their function satisfactory.
 Shafts usually fail due to fatigue,
 Which arises due to the following reason,
The presence of cyclic over loads
Maximum stress concentration in a point
 Due to production or operation cause (under cut,
machining traces, knotches)
 Due to the presence of fillets, keyways, drilled
holes
Wrong adjustment of bearings, insufficient clearance
 Shafts may also fail due to traverse or tortional vibrations,

DESIGN OF SHAFTS
 The shafts may be designed on the basis of,
Strength
Rigidity or stiffness
 In designing shafts on the basis of strength,
The following cases may be considered:
Shafts subjected to twisting moment or torque
only,
Shafts subjected to bending moment only,
Shafts subjected to combined twisting and
bending moments, and
Shafts subjected to axial loads in addition to
combined torsional and bending loads.

SHAFTS SUBJECTED TO TWISTING MOMENT ONLY
 When the shaft is subjected to a twisting moment (or torque)
only, then the diameter of the shaft may be obtained by using the
torsion equation.
 We know that,
 We know that for round solid shaft, polar moment of inertia,
 The equation may now be written as,

 We also know that for hollow shaft, polar moment of inertia,
 Substituting these values in equation, we have
 Let k = Ratio of inside diameter and outside diameter of the shaft
 Now the equation may be written as,

 The hollow shafts are usually used in marine work.
 These shafts are stronger per kg of material
 They may be forged on a mandrel,
 Thus making the material more homogeneous than would be
possible for a solid shaft.
 When a hollow shaft is to be made equal in strength to a solid
shaft,
 The twisting moment of both the shafts must be same.(the
same material of both the shafts)
 Therefore,

 We know that the power transmitted (in watts) by the shaft
 Where ,
 In case of belt drives,
 The twisting moment (T) is given by,
 Where ,

SHAFTS SUBJECTED TO BENDING MOMENT ONLY
 When the shaft is subjected to a bending moment only, then the
maximum stress (tensile or compressive) is given by the bending
equation.
 We know that,
 Where ,
 We know that for a round solid shaft, moment of inertia,
 Substituting these values,

 We also know that for a hollow shaft, moment of inertia
 Again substituting these values in equation, we have
 From this equation, the outside diameter of the shaft (do) may be
obtained.
 The axles are used to transmit bending moment only.
 Axles are designed on the basis of bending moment only,

SHAFTS SUBJECTED TO COMBINED TWISTING MOMENT
AND BENDING MOMENT
 When the shaft is subjected to combined twisting moment and
bending moment,
 The shaft must be designed on the basis of the two moments
simultaneously.
 Various theories have been suggested to account for the elastic
failure of the materials when they are subjected to various types
of combined stresses.
 The following two theories are important from the subject
point of view:
 Maximum shear stress theory or Guest's theory.
It is used for ductile materials such as mild steel.
 Maximum normal stress theory or Rankine’s theory.
It is used for brittle materials such as cast iron

 Let,
According to maximum shear stress theory,
 The maximum shear stress in the shaft,
 Substituting the values of τ and σb
 Or

 The expression is known as equivalent twisting moment,
 It is denoted by Te.
 It may be defined as twisting moment which when acting
alone,
Produces the same shear stress (τ) as the actual twisting
moment.
By limiting the maximum shear stress (τ max) equal to
the allowable shear stress (τ) for the material,
 According to maximum normal stress theory,
 The maximum normal stress in the shaft,

 Or,
 The expression is known as equivalent bending moment,
 It is denoted by Me.
 The equivalent bending moment may be defined as that
moment which when acting alone,
 Produces the same tensile or compressive stress (σb) as the
actual bending moment.
 By limiting the maximum normal stress [σb(max)] equal to
the allowable bending stress (σb),

 In case of a hollow shaft,
 Both equations may be written a,
 And,
 It is suggested that diameter of the shaft may be obtained by
using both the theories and the larger of the two values is
adopted.

CLUTCHES AND BRAKES
 Both clutch and brake are a motion controlling elements,
 Which permits the machine systems to achieve intermittent
motion.
So that start and stop operations can cycle frequently.
 Clutch is a devices which used to transmit power on an
intermittent basis,
By connecting and/or disconnecting a driven
component to and/or from the prime mover.
 Motor operates efficiently at continuous speeds.
Avoids accelerating and/or de-accelerating the
rotor of the motor each time.
 Brake is a device that absorbs the kinetic energy of a system
and thus controls the motion of the system by slowing down
the system and/or bringing the system to rest.

Functions of a clutch,
Connect a rapidly turning shaft to one that is initially
stationary.
Cause two shafts to turn at the same speed
Limit torque that is transmitted or to prevent torque
from being transmitted in a reverse direction.
 Note:
One very important requirement to be satisfied by the
shaft and other parts connected by clutches is that,
They should be strictly collinear.
Misalignment,
Greatly deteriorates the performance of a clutch
and results in rapid failure.

TYPES OF CLUTCHES
Clutch can be classified as,
 Mechanical clutch
 Electro-magnetic clutch
 Fluid clutch
Mechanical clutch can be classified as,
Positive contact
Square Jaw
Spiral Jaw
Friction clutches
Plate
Cone

Square Jaw Plate
Spiral Jaw Cone

Positive Contact Clutches,
It is operate by meshing jaws or teeth of the
driving member with corresponding elements of
the driven member.
The fixed half of the clutch is mounted
tightly on its shaft with the help of a key,
where as the other half which is the movable
is free to slide axially on its shaft.
The engaging surfaces are usually of jaw or
teeth type.
The jaws may be,
Square jaw type or,
Spiral jaw type.

Advantages of positive clutch,
No slip operation.
Develop very little heat,
Since they do not depend on friction.
Generally lighter and less costly than a friction
clutch of similar torque capacity.
Disadvantages of positive clutch,
Cannot be engaged at high speeds.
Shock accompanies engagement at any speed.
When both driven and drive shafts are at rest,
Some relative motion may be required to
engage.

 Friction Clutches,
Friction clutches work on the basis of the frictional
forces developed between the two or more surfaces in
contact.
Input disc is free to move axially along the shaft
but is splined, or keyed to shaft so disc will rotate
with shaft.
The friction force that can be transmitted depends on
axial force developed between disc.
Axial force can be applied in several ways.
Levers
Springs
Linkages
The engaging surfaces are usually cone or plate type.

Advantages of friction clutch,
The friction surfaces can slip during engagement
which enables the driver to pickup and accelerate
the load with minimum shock.
It can be used at high engagement speeds since
they do not have jaw or teeth.
Smooth engagement due to the gradual increase
in normal force.
Disadvantages of friction clutch,
Slippages not suitable for applications that require
positive transmission.
Wear.

Single plate clutch,
A single plate friction clutch consisting of two flanges,
One flange is rigidly keyed in to the driving shaft, while
the other is free to move along the driven shaft due to
spliced connection.
The actuating force is provided by a spring force, which
forces the driven flange to move towards the driving flange.
The face of the drive flange is linked with friction material
such as cork or leather.

If the discs or plates used in the clutch are relatively flexible,
It is possible to obtain relatively uniform pressure on the
friction surfaces when the actuating forces presses the
disc together.
If the plates are relatively rigid,
The wearing of the friction surface is approximately
uniform after an initial wearing-in has taken place.
When analyzing the clutch,
Either the assumption of uniform wear or uniform
pressure must be made.
A conservative approach is to design with the
assumption of uniform wear.

Wear may be assumed to be directly proportional to pressure and velocity at
a particular point on the plate of the clutch.
Recall velocity is proportional to the radius.
 Accordingly,
 Uniform wear implies local pressure P times r is constant.
 Where,
W = Wear
K = Proportionality Constant
P = Local Pressure
R = radius to arbitrary point on disc
 Under the assumption of uniform wear, the product of pressure and radius
is a constant
 Where,
K= proportionality constant
 Accordingly the maximum pressure must occur at the minimum radius.
K= pr = p max r i
*W kP r
*
W
P r k
k
 

 Solving for P from the above equation,
 Pressure varies from a max at r i to a minimum at r o
 Where ,
 Outer Radius = r o
 Actuating force = F
 Actuating force is normal to the friction surface
which is a force pressing the two discs together.
 It can be obtained by multiplying the pressure
between the friction surfaces by the area of the
surfaces
 Since pressure varies with ‘ri‘ we must integrate to
obtain ‘F’.
r
r
PP i
max

 For the case of uniform wear,
 The following relationship exists between the activation force
and the pressure ‘P’ existing at ‘r’
2
o
a
i
r
F p rdr
r
  max 2
o
o
i
r
rp rdrr
r
  max2
o
i
r
rp dr
r
  max2 [ ]
o
i
i
r
rp r
r
 
max2 [ ]i o irp r r 

 The torque that can be transmitted by a disc type of clutch can
also be related to the activating force.
 For the case of uniform wear, The frictional torque for the
elemental annular area must be integrated over the area of the
discs.
2 2
max 0[ ] 2 [ ]
o o
f i i
i i
r r
T rFdr r f p rdr fr p r r
r r
     
max 0 0[ ][ ]i i iT fr p r r r r  
0[ ]
2
a iF f r r
T


f = Coefficient of friction

Wear rating,
 Where,
WR = Wear rating
A = Area of friction surface
Pf = Power transmitted by frictional surfaces of discs
 Note:
WR = 0.04 hp/in2 for frequent applications,
= 0.10 hp/in2 for average service,
= 0.40 hp/in2 for infrequently used
Transferred power by friction,
A
P
WR
f

ff TP 

Energy Absorption/ Heat Dissipation
When using a clutch to accelerate an object or a brake
to stop a rotating object, heat is generated due to
friction.
Heat is transferred from the clutch and/or brake to the
surroundings and equilibrium temperature is
established.
Temperature of components can effect life time.
The energy to be absorbed or dissipated by the unit on
operational cycle is equal to the change in kinetic
energy of the components being accelerated or stopped.
 22
2
1
fimJKEE  

 Where,
Energy absorbed or dissipated
Mass moment of inertia
Initial Angular velocity
Final Angular velocity
Change in Kinetic energy
 The temperature rise of the clutch assembly can be approximately
determined by the equation:
T = E / Cm, in degree centigrade
 Where,
C = specific heat, J/kg degree cent
m = mass of clutch assembly, kg
E = internal energy, J
E
mJ
i
f
KE

BALANCING AND VIBRATION
 Balancing is,
The process of aligning a principal inertia axis with
the geometric axis of rotation through the addition
or removal of material.
By doing so, the centrifugal forces are reduced,
minimizing vibration, noise and associated
wear.
 The process of designing or modifying machinery,
In order to reduce unbalance to an acceptable level
is called balancing.

 Mass center:
 The center of mass is the point about which the total mass
of a rigid body is equally distributed.
 It is useful to assume that all the mass is concentrated at
this one point for simple dynamic analyses.
 Axis of rotation:
 The axis of rotation is the true centerline of rotation.
 The instantaneous line about which a part rotates.
 It is also referred to as the shaft axis or the geometric
axis.
 Centrifugal force:
 A particle made to travel along a circular path generates a
centrifugal force directed outward along the radial line
form the center of rotation to the particle.

 A rotor consisting of a disk of mass ‘m’ attached to a rigid shaft
with an assumed negligible mass. Constant angular velocity of w,
The center of mass ‘G’, of the disk does not coincide with the
bearing centerline ‘AB’, with the amount of this eccentricity
represented by ‘e’. The rotor is acted upon by the centrifugal
force

Similarly, a rotor with mass center slightly displaced from the axis
of rotation will generate centrifugal force. This is the force
associated with static unbalance. The shaft supports counteract the
forces of unbalance.
It should be noted here that the quantity m·r is known as
unbalance and that centrifugal force is the product of unbalance and
angular velocity squared. While unbalance force (Fcentrifugal)
increases rapidly with speed, the unbalance quantity itself (m·r)
does not change at all.

For a body to be completely balanced, it must have two things.
Static balance
This occurs when there is no resultant centrifugal force
and,
The Centre of gravity is on the axis of rotation.
Also called one plane balance.
Dynamic balance
This occurs when there is no resulting turning moment
along the axis,
Also referred to as two plane unbalance,
Indicating that correction is required in two planes to
fully eliminate dynamic unbalance.
A two plane balance specification is normally expressed in
terms of w·r per plane and,
Must include the axial location of the correction
planes to be complete.
Dynamic unbalance captures all the unbalance exists in a rotor.

Mechanisms of Textile Machine

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