Kom unit 1 - jntuh syllabus- R16 regulation

August 4, 2017 1Kinematics of Machinery - Unit - I
KINEMATICS OFKINEMATICS OF
MACHINERYMACHINERY

COURSE INFORMATIONCOURSE INFORMATION
Course code:Course code: ME302ESME302ES
Course Title:Course Title: Kinematics of MachineryKinematics of Machinery
Course structure:Course structure: Lecture – 4 hrs/weekLecture – 4 hrs/week
Tutorials – 1hr/week Practical’s - Credits 4Tutorials – 1hr/week Practical’s - Credits 4
Lab Course name:Lab Course name: Kinematics andKinematics and
Dynamics LabDynamics Lab
Lab Course code:Lab Course code: ME406ESME406ES

COURSE INFORMATIONCOURSE INFORMATION
TEXT BOOKS
T1. Theory of Machines and
Mechanisms/JOSEPH E. SHIGLEY/ Oxford
T2. Theory of Machines / S.S.Rattan / Mc Graw
Hill Publishers.
REFERENCE BOOKS
R1. Theory of Machines / Sadhu Singh / Pearson.
R2. Theory of Machines / Thomas Bevan/CBS.
R3. Theory of Machines / R.S. Khurmi and J.K.
Gupta/ S.Chand
R4. Theory of Machines / R.S. Bansal and J.S.
Brar / LP

SYLLABUSSYLLABUS
UNIT DETAILS HOURS
I Mechanisms, Mechanism and Machines 10
II
Kinematics, Plane motion of body and Analysis of
Mechanisms 13
III
Straight-line motion mechanisms, Steering gears
and Hooke’s Joint 10
IV Cams and Analysis of motion of followers 12
V Higher pair and Gear Trains 12
TOTAL HOURS 57

KOMKOM
Course Objectives: The objective is to study
1. The working of various Inversions of mechanisms,
2. The relative motion, velocity, and accelerations of the
various elements in a mechanism,
3. Displacement, Velocity and Acceleration diagrams for
followers with various types of motions,
4. Conditions for correct steering gears,
5. Cam and followers – their uses.

KOMKOM
Course Outcome: Student will demonstrate knowledge in
1. Designing a suitable mechanism depending on
application,
2. Drawing velocity and acceleration diagrams for different
mechanisms,
3. Selecting gear and gear train depending on application,
4. Drawing displacement diagrams for followers executing
different types of motions and various, configurations of
followers.

COURSE PREREQUISITESCOURSE PREREQUISITES
Course name : Engineering mechanics
List of topics:
1)Force and Force systems
2)Friction and its applications
3)Centre of gravity and Moment of inertia
4)Mass moment of inertia and Virtual work
5)Vibrations and Kinetics

UNIT- 1UNIT- 1
Mechanisms, Mechanism andMechanisms, Mechanism and
MachinesMachines
Mechanisms : Elements or Links
Classification – Rigid Link, flexible and
fluid link
Types of kinematics pairs – sliding, turning, rolling,
screw and spherical pairs – lower and higher pairs
– closed and open pairs constrained motion –
completely, partially or successfully and
incompletely constrained

UNIT- 1UNIT- 1
MachinesMachines
Mechanism and Machines –
Mobility of Mechanisms : Grubler’s criterion
classification of machines – kinematics chain
Inversions of mechanism – inversions of quadric
cycle chain,
inversions of single slider crank chain and
inversions of double slider crank chains,
Mechanical Advantage.

UNIT- 1UNIT- 1
MachinesMachines
L.No Name of the Topic
Reference Book/
Text book
(pgno )
Delivery
method
1
Introduction to theory of machines, mechanism
and machine
T-2
PPT
Differences between mechanism and machine T-2
Rigid and Resistant bodies, Elements (or Links
or Members)
R-4

INTRODUCTIONINTRODUCTION
THEORY OF MACHINE: It is the branch of science
which deals with the study of relative motion between the
various parts of a machine, and forces which act on
them.
Theory of machine
Kinematics of machines Dynamics of machine

KINEMATICS OF MACHINE: It is the branch of
theory of machine which deals with the study of
relative motion between the various parts of a
machine.
Here the various forces involved in the motion,
are not considered.
Thus kinematics is the study to know the
displacement, velocity and acceleration of a part
of the machine.

DYNAMICS OF MACHINE: It is the branch
of theory of machine which deals with the
study of various forces involved in the
various parts of a machine.
Here the various forces involved in the
motion, are considered.
The forces may be either static or
dynamic. Discuss examples

EXAMPLE FOR STATIC & DYNAMIC LOADEXAMPLE FOR STATIC & DYNAMIC LOAD

MECHANISMMECHANISM
A mechanism is a combination of rigid bodiesA mechanism is a combination of rigid bodies
which are so shaped and connected that theywhich are so shaped and connected that they
move upon each other with definite relativemove upon each other with definite relative
motion.motion.
Examples: discuss , go to next slideExamples: discuss , go to next slide

Slider Crank MechanismSlider Crank Mechanism

Bore Water Pump MechanismBore Water Pump Mechanism

Cam and Follower MechanismCam and Follower Mechanism

Some other example for MechanismSome other example for Mechanism
1) Watches, stop watches, all types of wall clocks
2) Spring Toys(all types), simple balance
3) Typewriters etc….
In each of these , the force provided is not more
than what is required to overcome the friction
of the parts and which is utilized just to get the
desired motion of the mechanism

Example for MechanismExample for Mechanism

MACHINEMACHINE
A machine is a mechanism or collection ofA machine is a mechanism or collection of
mechanisms, which apart from impartingmechanisms, which apart from imparting
definite motions to the parts, also transmitsdefinite motions to the parts, also transmits
and modifies the available mechanical energyand modifies the available mechanical energy
into some kind of desired work.into some kind of desired work.
Examples : discuss, go to the next slideExamples : discuss, go to the next slide

MACHINEMACHINE

Some other example for MachineSome other example for Machine
1) Reciprocating pumps, reciprocating
compressors
2) Steam engine
3) Lathe, Shaper, Planer….etc

DIFFERENCESDIFFERENCES
S.NO MECHANISM MACHINE
I
It transmits and modifies
motion
It uses the available energy to
perform some useful work
II
It is the skeleton outline of the
machine to produce definite
motion
It may have many mechanisms
for transmitting power
III
It is the working model of any
machine
It is a practical development of
any mechanism
IV
When kinematic chain is
analyzed as mechanism no
special considerations need to
be given to the forms and the
cross-sectional proportions of
the links
Cross-sectional proportions are
required to provide strength,
stiffness, clearance etc…
V
Ex: Watch, typewriter, spring
toys etc….
Ex: Lathe, shaper, planer,
steam engine.

Though all machines are mechanisms, allThough all machines are mechanisms, all
mechanisms are not machinesmechanisms are not machines

RIGID BODYRIGID BODY
Rigid Body: A body is said to be rigid if under the action
of forces, it does not suffer any distortion or the distance
between any two points on it remain constant.
But, in real life, there would be some force under which
the body starts to deform. For example, a bridge does
not deform under the weight of a single man but it may
deform under the load of a truck or ten trucks. However,
the deformation is small. Since, no object is rigid body in
real life; we have to introduce another concept that is
concept of resistant body so that we would be able to
use it in engineering problems.

RESISTANT BODIESRESISTANT BODIES
Resistant body: A body which is rigid for the purpose
it has to serve. (OR) A body is said to be a resistant body,
if it does not deform for the purpose for which it is made.
Apart from rigid bodies, there are semi-rigid bodies which
are normally flexible, but under certain loading conditions
act as rigid bodies for limited purpose and thus are
resistant bodies.
Ex: A chair does not deform if a person sits on it.
Ex: A belt is rigid when subjected to tensile forces.
Therefore the belt-drives acts as resistant bodies.
Ex: A fluid is rigid when subjected to compressive forces
as in case of hydraulic press.

Some examples of resistantSome examples of resistant
bodiesbodies
Belt- resistant body

KINEMATIC LINK (OR) LINK (OR) ELEMENTKINEMATIC LINK (OR) LINK (OR) ELEMENT
LINK: A link is defined as a member orLINK: A link is defined as a member or
combination of members, connecting othercombination of members, connecting other
members and having motion relative tomembers and having motion relative to
them. ( OR )them. ( OR )
A kinematic link is a resistant body or anA kinematic link is a resistant body or an
assembly of resistant bodies which go toassembly of resistant bodies which go to
make a part or parts of a machinemake a part or parts of a machine
connecting other parts which have motion.connecting other parts which have motion.
Ex: next slide….Ex: next slide….

CLASSIFICATION OF LINK-DEPENDINGCLASSIFICATION OF LINK-DEPENDING
ON TRANSMISSION OF POWERON TRANSMISSION OF POWER
Following are the links generally used in transmission ofFollowing are the links generally used in transmission of
motion of power.motion of power.
1)1) Rigid linkRigid link :: it is the link which does not undergo any
deformation while transmitting motion. Ex: connecting
rod, crank pin etc..
2)2) Flexible linkFlexible link : it is the link which is deformed appreciably
( without affecting its functions ) while transmitting
motion. Ex: ropes, chain, belts, spring
3)3) Fluid linkFluid link : fluid in a tube or container capable of
transmitting motion by pressure or by compression is
called fluid link. Ex: fluid in hydraulic lift, hydraulic press.

ON TRANSMISSION OF POWERON TRANSMISSION OF POWER
 Rigid link (fig –a)Rigid link (fig –a)
 Flexible link (fig-b)Flexible link (fig-b)
 Fluid link (fig-c)Fluid link (fig-c) A- connecting rod
B- betls / chains/ ropes

ON THEIR ENDSON THEIR ENDS
Following are the linksFollowing are the links
1)1) Binary link :Binary link : A link to which two other links are
connected is known as binary link.
2)2) Ternary linkTernary link : A link to which three other links are
connected is known as ternary link.
3)3) Quaternary linkQuaternary link : A link to which four other links
are connected is known as quaternary link.

 Binary link (fig –a)Binary link (fig –a)
 Ternary link (fig-b)Ternary link (fig-b)
 Quaternary link (fig-c)Quaternary link (fig-c)
Fig-a Binary link
Fig-b Ternary link Fig-c Quaternary link

KINEMATIC PAIRSKINEMATIC PAIRS
A kinematic pair is a joint of two links having relativeA kinematic pair is a joint of two links having relative
motion between themmotion between them
in the fig shown below link 2 rotates relative to link 1in the fig shown below link 2 rotates relative to link 1
hence link 1 and 2 is a set of kinematic pair.hence link 1 and 2 is a set of kinematic pair.
Similarly link 2 is having relative motion to link 3 andSimilarly link 2 is having relative motion to link 3 and
hence links 2 and 3 is also a kinematic pair.hence links 2 and 3 is also a kinematic pair.
Link 3 is having relative motion to link 4. also link4Link 3 is having relative motion to link 4. also link4
having motion relative to link 1. Hence links 4, 3 andhaving motion relative to link 1. Hence links 4, 3 and
4,1 forms kinematic pairs.4,1 forms kinematic pairs.

CLASSIFICATION OF KINEMATIC PAIRSCLASSIFICATION OF KINEMATIC PAIRS
1) Nature of contact between the links
Ex: i) Lower pair ii) Higher pair
2) Nature of relative motion between the
links
Ex: i) sliding pair ii) turning pair iii) rolling
pair iv) screw pair v) spherical pair
3) Nature of mechanical constraint between
the links
Ex: i) closed pair ii) open pair

(i) Lower pair:(i) Lower pair: A pair of links having surface orA pair of links having surface or
area contact between them is known as lowerarea contact between them is known as lower
pair. ORpair. OR
If a pair has surface contact between the twoIf a pair has surface contact between the two
elements while in motion, it is called a lowerelements while in motion, it is called a lower
pair.pair.
The relative motion is purely turning or sliding.The relative motion is purely turning or sliding.
Ex: a) Nut turning on a screw, b) shaft rotating inEx: a) Nut turning on a screw, b) shaft rotating in
a bearing c) universal joint etc….a bearing c) universal joint etc….
1) Nature of contact between the links

Ex: a) Nut turning on a screw,Ex: a) Nut turning on a screw,

Ex: b) shaft rotating in a bearing,Ex: b) shaft rotating in a bearing,

Ex: c) universal jointEx: c) universal joint

(ii) Higher pair:(ii) Higher pair: A pair of links having point orA pair of links having point or
line contact between them is known as lowerline contact between them is known as lower
pair. ORpair. OR
If a pair has point or line contact between theIf a pair has point or line contact between the
two elements while in motion, it is called atwo elements while in motion, it is called a
lower pair.lower pair.
The relative motion is purely turning.The relative motion is purely turning.
Ex: a) Wheel rolling on a surface, b) toothedEx: a) Wheel rolling on a surface, b) toothed
gears c) cam and follower etc….gears c) cam and follower etc….

Ex: b) Toothed gears,Ex: b) Toothed gears,

Ex: c) Cam and Follower,Ex: c) Cam and Follower,

(i) Sliding pair:(i) Sliding pair: A pair of links having slidingA pair of links having sliding
motion between them is known as lower pair.motion between them is known as lower pair.
Ex: a) A regular shaped rod in a correspondingEx: a) A regular shaped rod in a corresponding
shaped hole b) links 4, and 1 in slider crankshaped hole b) links 4, and 1 in slider crank
mechanismmechanism
2) Nature of relative motion between the links

(ii) Turning pair:(ii) Turning pair: when one link has a turning orwhen one link has a turning or
revolving motion relative to the other is knownrevolving motion relative to the other is known
as turning pair.as turning pair.
Ex: a) in a slider crank mechanism , all the pairsEx: a) in a slider crank mechanism , all the pairs
except slider and guide are turning pairs b) aexcept slider and guide are turning pairs b) a
circular shaft revolving inside a bearingcircular shaft revolving inside a bearing

(iii) Rolling pair:(iii) Rolling pair: A pair of links having rollingA pair of links having rolling
motion relative to each other is known asmotion relative to each other is known as
rolling pairrolling pair
Ex: a) rolling wheel on flat surface.Ex: a) rolling wheel on flat surface.

(iv) Screw pair:(iv) Screw pair: If the two pair of links haveIf the two pair of links have
turning as well as sliding motion betweenturning as well as sliding motion between
them is known as screw pairthem is known as screw pair
Ex: a) the lead screw and nut of lathe machine,Ex: a) the lead screw and nut of lathe machine,
b) Bolt with a nutb) Bolt with a nut

(v) Spherical pair:(v) Spherical pair: When one link is in theWhen one link is in the
form of a sphere turns inside a fixed link isform of a sphere turns inside a fixed link is
known as spherical pairknown as spherical pair
Ex: a) the ball and socket joint,Ex: a) the ball and socket joint,
b) Pen standb) Pen stand

(i) Closed pair:(i) Closed pair: When the elements of a pair areWhen the elements of a pair are
held together mechanically is known as closedheld together mechanically is known as closed
pairpair
Ex: a) cam and follower pair (higher pair),Ex: a) cam and follower pair (higher pair),
b) Screw pair (lower pair)b) Screw pair (lower pair)
3) Nature of mechanical constraint

(ii) Open pair:(ii) Open pair: When the elements of a pair areWhen the elements of a pair are
in contact either due to force of gravity or somein contact either due to force of gravity or some
spring action is known as open pairspring action is known as open pair
Ex: a) cam and follower pairEx: a) cam and follower pair
3) Nature of mechanical constraint

STRUCTURESTRUCTURE
A structure is an assembly of resistant bodiesA structure is an assembly of resistant bodies
which are not kinematic links because there iswhich are not kinematic links because there is
no relative motion between the links.no relative motion between the links.
Examples : roof truss, bridges, buildings etc..Examples : roof truss, bridges, buildings etc..

DIFFERENCESDIFFERENCES
S.NO MACHINE STRUCTURE
I
The parts of a machine move
relative to one another.
The members of a structure
don’t move.
II
A machine transforms the
available energy into some
useful work.
A structure doesn't transform
any energy into useful work.
III
The links of a machine may
transmit both power and
motion.
The members of a structure
transmit forces only.
IV
Ex: Lathe, shaper, planer,
steam engine.
Ex: Roof truss, buildings.

CONSTRAINED MOTIONCONSTRAINED MOTION
In a kinematic pair if anIn a kinematic pair if an
element has got only oneelement has got only one
definite motion relative to thedefinite motion relative to the
other.other.

TYPES OF CONSTRAINED MOTIONTYPES OF CONSTRAINED MOTION
There are three types ofThere are three types of
constrained motionconstrained motion
1.1. Completely constrained motionCompletely constrained motion
2.2. Incompletely constrained motionIncompletely constrained motion
3.3. Successfully constrained motionSuccessfully constrained motion

(i) Completely constrained motion(i) Completely constrained motion
When the motion between two elements of a pairWhen the motion between two elements of a pair
is in a definite direction irrespective of theis in a definite direction irrespective of the
direction of force applied is known asdirection of force applied is known as
completely constrained motion.completely constrained motion.
Generally constrained motion may beGenerally constrained motion may be linear orlinear or
rotary.rotary.

(ii) Incompletely constrained motion(ii) Incompletely constrained motion
When the motion between two elements of a pair isWhen the motion between two elements of a pair is
possible in more than one direction and depends onpossible in more than one direction and depends on
the direction of force applied is known asthe direction of force applied is known as
incompletely constrained motionincompletely constrained motion..
Ex: if the turning pair doesn't have collars, the innerEx: if the turning pair doesn't have collars, the inner
shaft may have sliding or rotary motion dependingshaft may have sliding or rotary motion depending
upon the direction of force applied. And each motionupon the direction of force applied. And each motion
is independent of other.is independent of other.

(iii) Successfully constrained motion(iii) Successfully constrained motion
When the motion between two elements of a pair isWhen the motion between two elements of a pair is
possible in more than one direction but is made topossible in more than one direction but is made to
have motion only in one direction by using externalhave motion only in one direction by using external
force is known asforce is known as successfully constrained motionsuccessfully constrained motion..
Ex: A shaft in a footstep bearing may have verticalEx: A shaft in a footstep bearing may have vertical
motion apart from rotary motion, but due to loadmotion apart from rotary motion, but due to load
applied on the shaft it is constrained to move in thatapplied on the shaft it is constrained to move in that
direction.direction.

TYPES OF JOINTS IN A CHAINTYPES OF JOINTS IN A CHAIN
The following are the types of jointsThe following are the types of joints
usually found in chain:usually found in chain:
i)i)Binary jointBinary joint
ii)ii)Ternary jointTernary joint
iii)iii)Quaternary jointQuaternary joint

i) Binary joint:i) Binary joint: If two links are joined at the sameIf two links are joined at the same
connection , the joint is called a binary joint.connection , the joint is called a binary joint.
Ex: A kinematic chain shown in fig has four linksEx: A kinematic chain shown in fig has four links
and four binary joints at A, B, C and D.and four binary joints at A, B, C and D.

ii) Ternary joint:ii) Ternary joint: If three links are joined at theIf three links are joined at the
same connection , the joint is called a ternary joint.same connection , the joint is called a ternary joint.
Ex: A kinematic chain shown in fig has six linksEx: A kinematic chain shown in fig has six links
and three binary joints at A, B and D and twoand three binary joints at A, B and D and two
ternary joints at C and E .ternary joints at C and E .
Note:Note: one ternary joint isone ternary joint is
Equal to two binary jointsEqual to two binary joints..
Total no of binary jointsTotal no of binary joints
= 7.= 7.

iii) Quaternary joint:iii) Quaternary joint: If four links are joined atIf four links are joined at
the same connection , the joint is called athe same connection , the joint is called a
quaternary joint.quaternary joint.
-It is equivalent to three binary joints or inIt is equivalent to three binary joints or in
general when j no of links are joined at the samegeneral when j no of links are joined at the same
connection, the joint is equivalent to (j-1) binaryconnection, the joint is equivalent to (j-1) binary
jointsjoints
Note:Note: one quaternary joint is Equal to threeone quaternary joint is Equal to three
binary jointsbinary joints..

iii) Quaternary joint:iii) Quaternary joint:
Ex: A kinematic chain shown in fig has 11 linksEx: A kinematic chain shown in fig has 11 links
and one binary joints at D, four ternary joints atand one binary joints at D, four ternary joints at
A, B E and F, andA, B E and F, and
two quaternary jointstwo quaternary joints
at C and G.at C and G.
-Total no of-Total no of
binary joints =15binary joints =15..

KINEMATIC CHAINKINEMATIC CHAIN
When the kinematic pairs are coupledWhen the kinematic pairs are coupled
in such a way that the last link is joinedin such a way that the last link is joined
to the first link to transmit definiteto the first link to transmit definite
motion (i.e. completely or successfullymotion (i.e. completely or successfully
constrained motion ) is called aconstrained motion ) is called a
kinematic chain.kinematic chain.

NON-KINEMATIC CHAINNON-KINEMATIC CHAIN
In case the motion of a link results inIn case the motion of a link results in
indefinite motion of other links ,it is aindefinite motion of other links ,it is a
non-kinematic chainnon-kinematic chain..
In case if there is no relative motionIn case if there is no relative motion
exists between the links, it is calledexists between the links, it is called
redundant chain.redundant chain.
REDUNDANT CHAINREDUNDANT CHAIN

Kinematic ChainKinematic Chain
Relation between Links, Pairs and JointsRelation between Links, Pairs and Joints
 L = 2P-4L = 2P-4 ( relation b/w no of pairs P and no of( relation b/w no of pairs P and no of
links L )links L )
 J = (3/2) L – 2J = (3/2) L – 2 ( relation b/w no of links L and no( relation b/w no of links L and no
of joints J )of joints J )
L = No of Links, P = No of Pairs, J = No of JointsL = No of Links, P = No of Pairs, J = No of Joints
L.H.S > R.H.S => Locked chainL.H.S > R.H.S => Locked chain
L.H.S = R.H.S => Constrained Kinematic ChainL.H.S = R.H.S => Constrained Kinematic Chain
L.H.S < R.H.S => Unconstrained Kinematic ChainL.H.S < R.H.S => Unconstrained Kinematic Chain

LOCKED CHAIN (Or) STRUCTURELOCKED CHAIN (Or) STRUCTURE
Links connected in such a way that noLinks connected in such a way that no
relative motion is possible.relative motion is possible.
L=4, J=4, P=4L=4, J=4, P=4
L = 2P-4 ,L = 2P-4 , 4 = 2*4-4, 4=4 ( L.H.S=R.H.S )4 = 2*4-4, 4=4 ( L.H.S=R.H.S )
J = (3/2) L – 2,J = (3/2) L – 2, 4 = 3/2 * 4 – 2, 4=44 = 3/2 * 4 – 2, 4=4
( L.H.S=R.H.S )( L.H.S=R.H.S )

CONSTRAINED KINEMATIC CHAINCONSTRAINED KINEMATIC CHAIN
Links connected in such a way that relativeLinks connected in such a way that relative
motion is possible.motion is possible.
L=3, J=3, P=3L=3, J=3, P=3
L = 2P-4 ,L = 2P-4 , 3 = 2*3-4, 3>2 ( L.H.S>R.H.S )3 = 2*3-4, 3>2 ( L.H.S>R.H.S )
J = (3/2) L – 2,J = (3/2) L – 2, 3 = 3/2 * 3 – 2, 3> 2.53 = 3/2 * 3 – 2, 3> 2.5
( L.H.S > R.H.S )( L.H.S > R.H.S )

UNCONSTRAINED KINEMATIC CHAINUNCONSTRAINED KINEMATIC CHAIN

DEGREES OF FREEDOM (DOF):DEGREES OF FREEDOM (DOF):
It is the number of independentIt is the number of independent
coordinates required to describe thecoordinates required to describe the
position of a body.position of a body.

DEGREES OF FREEDOM (DOF):DEGREES OF FREEDOM (DOF):
An unconstrained rigid body in space can describeAn unconstrained rigid body in space can describe
the following independent motionsthe following independent motions
1 Translation motion along X, Y and Z axes. (1 Translation motion along X, Y and Z axes. ( ))
2 Rotational motion about these axes2 Rotational motion about these axes

Degrees of freedom/mobility of aDegrees of freedom/mobility of a
mechanismmechanism
It is the number of inputs (number ofIt is the number of inputs (number of
independent coordinates) required toindependent coordinates) required to
describe the configuration or position ofdescribe the configuration or position of
all the links of the mechanism, withall the links of the mechanism, with
respect to the fixed linkrespect to the fixed link at any givenat any given
instant.instant.

GRUBLER’S CRITERIONGRUBLER’S CRITERION
Number of degrees of freedom of aNumber of degrees of freedom of a
mechanism is given bymechanism is given by
F = 3(n-1)-2j-h. Where,F = 3(n-1)-2j-h. Where,
 F = Degrees of freedomF = Degrees of freedom
 n = Number of links in the mechanism.n = Number of links in the mechanism.
 j = Number of jointsj = Number of joints
 h = Number of higher pairsh = Number of higher pairs

Examples - DOFExamples - DOF
 F = 3(n-1)-2j-hF = 3(n-1)-2j-h
 Here, n = 4, j = 4 & h = 0.Here, n = 4, j = 4 & h = 0.
 F = 3(4-1)-2(4) = 1F = 3(4-1)-2(4) = 1
 I.e., one input to any oneI.e., one input to any one
link will result in definitelink will result in definite
motion of all the links.motion of all the links.

 F = 3(n-1)-2j-hF = 3(n-1)-2j-h
 Here, n = 5, j = 5 and h = 0.Here, n = 5, j = 5 and h = 0.
 F = 3(5-1)-2(5) = 2F = 3(5-1)-2(5) = 2
 I.e., two inputs to any twoI.e., two inputs to any two
links are required to yieldlinks are required to yield
definite motions indefinite motions in
all the links.all the links.

 F = 3(n-1)-2j-hF = 3(n-1)-2j-h
 Here, n = 6, j = 7 and h = 0.Here, n = 6, j = 7 and h = 0.
 F = 3(6-1)-2(7) = 1F = 3(6-1)-2(7) = 1

 F = 3(n-1)-2j-hF = 3(n-1)-2j-h
 Here, n = 6, j = 7 (at theHere, n = 6, j = 7 (at the
intersection of 2, 3 and 4,intersection of 2, 3 and 4,
two lower pairs are to betwo lower pairs are to be
considered) and h = 0.considered) and h = 0.
 F = 3(6-1)-2(7) = 1F = 3(6-1)-2(7) = 1

 F = 3(n-1)-2j-hF = 3(n-1)-2j-h
 Here, n = 11, j = 15 (two lower pairs at theHere, n = 11, j = 15 (two lower pairs at the
intersection ofintersection of 3, 4, 63, 4, 6;; 2, 4, 52, 4, 5;; 5, 7, 85, 7, 8;; 8, 10,8, 10,
1111) and h = 0.) and h = 0.
 F = 3(11-1)-2(15) = 0F = 3(11-1)-2(15) = 0
 there is no relativethere is no relative
motion between the links.motion between the links.

INVERSIONS OF MECHANISMINVERSIONS OF MECHANISM
A mechanism is one in which one of the linksA mechanism is one in which one of the links
of a kinematic chain is fixed. Differentof a kinematic chain is fixed. Different
mechanisms can be obtained by fixingmechanisms can be obtained by fixing
different links of the same kinematic chain.different links of the same kinematic chain.
These are called as inversions of theThese are called as inversions of the
mechanism.mechanism.
In the process of inversion the relativeIn the process of inversion the relative
motions of the links of the mechanismmotions of the links of the mechanism
produced remain unchanged.produced remain unchanged.

DIFFERENT TYPES OF KINEMATICDIFFERENT TYPES OF KINEMATIC
CHAINSCHAINS
 1.Four Bar Chain or Quadric cyclic1.Four Bar Chain or Quadric cyclic
chainchain
 2.Single Slider Crank chain2.Single Slider Crank chain
 3.Double Slider Crank chain3.Double Slider Crank chain

Four bar chain or Quadric cycleFour bar chain or Quadric cycle
chainchain
It is the simplest kinematic chain,
consists of four rigid links which are
connected in the form of a
quadrilateral by four pin joints.
It consists of four turning pairs
(1 &2, 2&3, 3&4, 4&1)

1. FOUR BAR CHAIN1. FOUR BAR CHAIN
 (link 1) frame(link 1) frame (link 2) crank(link 2) crank (link 3) coupler(link 3) coupler (link 4) rocker(link 4) rocker

INVERSIONS OF FOUR BAR CHAININVERSIONS OF FOUR BAR CHAIN
 1 Beam engine (Crank and lever mechanism)1 Beam engine (Crank and lever mechanism)
 2 Coupling rod of locomotive (Double crank2 Coupling rod of locomotive (Double crank
mechanism)mechanism)
 3 Watt’s indicator mechanism (Double lever3 Watt’s indicator mechanism (Double lever
mechanism)mechanism)

Beam Engine (crank &Lever)Beam Engine (crank &Lever)

CouplingCoupling rod ofrod of locomotivelocomotive (Double Crank)(Double Crank)

Watt’s indicator mechanism (Double lever)Watt’s indicator mechanism (Double lever)

Single slider crank chainSingle slider crank chain
It is a modification of the basic four bar chain.It is a modification of the basic four bar chain.
It consists of 1 sliding pair (link 4, 1)and 3It consists of 1 sliding pair (link 4, 1)and 3
turning pairs (link 1,2 link 2,3 link 3,4 )turning pairs (link 1,2 link 2,3 link 3,4 )
This type of mechanism converts rotary motionThis type of mechanism converts rotary motion
into reciprocating motion and vice versa.into reciprocating motion and vice versa.
Link1 – Frame link 2 – CrankLink1 – Frame link 2 – Crank
Link 3 – Connecting rod link 4 – Crosshead,Link 3 – Connecting rod link 4 – Crosshead,
pistonpiston

2. SINGLE SLIDER CRANK CHAIN2. SINGLE SLIDER CRANK CHAIN

INVERSIONS OF SINGLE SLIDER CHAININVERSIONS OF SINGLE SLIDER CHAIN
 1 Piston and cylinder mechanism1 Piston and cylinder mechanism
 2 Whitworth quick return mechanism2 Whitworth quick return mechanism
 3 Crank and slotted lever mechanism3 Crank and slotted lever mechanism
 4 Hand pump mechanism4 Hand pump mechanism

 3 Crank and slotted lever mechanism3 Crank and slotted lever mechanism

Quick-Return IN SHAPER M/CQuick-Return IN SHAPER M/C

 4 Hand pump mechanism4 Hand pump mechanism

Double slider crank chainDouble slider crank chain
A kinematic chain which consists of 2 slidingA kinematic chain which consists of 2 sliding
pair (link 4, 1 link 3,4) and 2 turning pairs (linkpair (link 4, 1 link 3,4) and 2 turning pairs (link
1,2 link 2,3)1,2 link 2,3)
Link 1 Frame Link 2 Slider -ILink 1 Frame Link 2 Slider -I
Link 3 Coupler Link 4 Slider - IILink 3 Coupler Link 4 Slider - II

INVERSIONS OF DOUBLE SLIDER CHAININVERSIONS OF DOUBLE SLIDER CHAIN
 1 Elliptical trammel1 Elliptical trammel
 2 Scotch yoke mechanism2 Scotch yoke mechanism
 3 Oldham’s coupling3 Oldham’s coupling

 1 Elliptical trammel1 Elliptical trammel

ELLIPTICAL TRAMMELELLIPTICAL TRAMMEL

1sincos 22
22
=+=





+





θθ
p
y
q
x
1sincos 22
22
=+=





+





θθ
p
y
q
x
Elliptical trammel
AC = p and BC = q,
then,
x = q.cosθ and
y = p.sinθ.
Rearranging,

MechanicalMechanical
AdvantageAdvantage
 Mechanical AdvantageMechanical Advantage
of the Mechanism atof the Mechanism at
angle a2 = 0angle a2 = 000
or 180or 18000
 Extreme position of theExtreme position of the
linkage is known aslinkage is known as
toggle positions.toggle positions.

TransmissionTransmission
AngleAngle
θθ = a1=Crank Angle= a1=Crank Angle
γγ = a2 =Angle between= a2 =Angle between
crank and Couplercrank and Coupler
μμ = a3 =Transmission angle= a3 =Transmission angle
Cosine LawCosine Law
aa22
+ d+ d22
-2ad cos-2ad cos θθ ==
bb22
+ c+ c22
-2 bc cos-2 bc cos μμ
Where a=AD, b=CD,Where a=AD, b=CD,
c=BC, d=ABc=BC, d=AB
DetermineDetermine μμ..

Design ofDesign of
MechanismMechanism
 1.Slider – Crank Mechanism1.Slider – Crank Mechanism
Link Lengths, Stroke Length,Link Lengths, Stroke Length,
Crank Angle specified.Crank Angle specified.
 2.Offset Quick Return2.Offset Quick Return
MechanismMechanism
Link Lengths, Stroke Length,Link Lengths, Stroke Length,
Crank Angle, Time RatioCrank Angle, Time Ratio
specified.specified.
 3.Four Bar Mechanism –3.Four Bar Mechanism –
Crank Rocker MechanismCrank Rocker Mechanism
Link Lengths and RockerLink Lengths and Rocker
angle Specified.angle Specified.

ALL THE BESTALL THE BEST

Kom unit 1 - jntuh syllabus- R16 regulation

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