118554630 Theory of Machine Module 1 Modified 1

7/30/2019 118554630 Theory of Machine Module 1 Modified 1

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DIPLOMA IN Mechnical Engineering

2011-

2012

Mr.Vaibhav V Naik

Mechanical

Engineering

2011-2012

FUNDAMENTALS AND TYPEOF MECHANISM


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MECHANICALENGINEERING MATERIALS

Fundamental and types of mechanism

FUNDAMENTALS AND TYPES OF MECHANIISM Vaibhav Vithoba Naik


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THEORY OF MACHINE

Theory of machine is Branch of engineering science which deals with thestudy of relative motion and forces between the various machine elements

:

Figure: Diagram of Theory of Machine

1. Statics

It is the branch of theory of machine, which deals with the forces and itseffect on the machine part while the latter is at rest.

2. Dynamics of machine

It is the branch of theory of machine, which deals with the forces and

effect of forces on the machine component when they act on them.

3. Kinetics

It is the branch of theory of machine, which deals with the inertia forces,

which are formed due to combined action of mass and motion of

machine elements.

4. Kinematics of machine


THEORY OF MACHINE

KINEMATICSDYNAMICS KINETICSSTATICS


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It is the branch of theory of machine, which deals with the relative motion

between the various parts of the machine, without considering the forces

1. Kinematic Link

a. Links are individual parts of a mechanism.b. Each parts of a machine which has a relative motion to some other parts isknown as Kinematic link.

Characteristics of the Kinematic link

1. It should have relative motion and

2. It should be a resistant body

Classification of the LINK

A. Depending upon the nature of the resistant bodies

1. Rigid link.

2. Flexible link.

3. Fluid link.

B. Depending upon the points at which the link is attached to mechanism

1. Binary link

2. Ternary link

3. Quaternary link



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A. Depending upon the nature of the resistant bodies

1. Rigid link

The links which do not undergo appreciable transformation while transmitting

the required motion and forces is known as rigid link.

Example:

a. Piston,

b. Connecting Rod of Steam engine.

2. Flexible Link

The links which are partly deformed transformation while transmitting the

required motion and forces in such a way that they don effect the required

transmission of motion is known as Flexible link.

Example:

a. Chain,

b. Belt and Spring

3. Fluid Link

The link which transmit the motion by fluid pressure as compression are

called fluid link.

Example:

a. Liquid used in Hydraulic presses



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B. Depending upon the points at which the link is attached to mechanism

1. Binary linkThe link which is attached to two points in the mechanism is called Binary

link.

2. Ternary linkThe link which is attached to three points in the mechanism is called Ternary

link.

3. Quaternary linkThe link which is attached to four points in the mechanism is called

Quaternary link.



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2. Kinematic Pair

The two links of the machine when in contact with each other are said to

form a pair if the relative motion between them is successfully constrained.

CLASSIFICATION OF KINEMATIC PAIR

A. According to the relative motion between them

1. Sliding pair. S

2. Turning pair.

3. Rolling pair.

4. Screw pair.

5. Spherical pair.

B. According to Nature of the contact

1. Lower pair.

2. Higher pair.

C. According to type of closure

1. Self closed pair.

2. Force closed pair.



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A. According to the relative motion between them

1. Sliding pair.

A sliding pair is said to be formed by two links such a manner that one link is

constrained to have a sliding motion relative to other link.

Example:

1. Piston and Cylinder,

2. Cross head and guides of Steam engine.


Figure: Sliding Pair


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2. Turning pair

A turning pair is said to be formed by two links such a manner that one link is

constrained to turn or revolve relative to other link.

Example:

Shaft with collar in circular hole.


Figure: Turning Pair


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3. Rolling pair.

A Rolling pair is said to be formed by two links such a manner that one link isconstrained to have a rolling motion over the other link.

Example:

Ball bearing forms Rolling pair.


Figure: Rolling Pair


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4. Screw pair.

When the two elements of pairs are connected in such a way that one

element can turn about the other by means of screw threads is known as

Screw Pair.

Example:

Bolt and nut is example of Screw Pair.


Figure: Screw Pair


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5. Spherical pair.

When the two elements of pairs are connected in such a way that one

element turn or swivels about the other fixed element, the pair formed is

known as Screw Pair.

Example:

Ball and socket is example of Spherical Pair.


Figure:Spherical Pair


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B. According to Nature of the contact

1. Lower pair.

When the two element of a pair have a surface contact when the relative

motion takes place and the surface of one element slides over the other, the

pair forced is known as lower pair.

Example:

a. The motion of piston and cylinder in the engine.

b. Shaft rotating in a bearing and

c. Nut turning on a screw.


Figure: Lower Pair


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2. Higher pair.

When the two element of a pair have a line or point contact when therelative motion takes place and the motion between the two element is

partially turning and partly sliding then the pair formed is know as Higher

pair.

Example:

The motion of cam and follower


Figure: Higher Pair


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C. Kinematic pairs according to nature of mechanical constraint

1. Self Closed pair

When the elements of a pair are held together mechanically in such a way

that only the required kind of relative motion occurs , all the lower pairs and

some of the higher pairs are closed pairs.

Example:

The lower pair is known as closed pair.

2. Force Closed pair or Unclosed pair

When two links of a pair are not connected mechanically but kept in contact

either due to force of gravity or some spring action, they constitute an

unclosed pairs.

Example:

The motion of cam and follower



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TYPE OF CONSTARINED MOTIONS.

1. Completely constrained motion.

2. Incompletely constrained motion.

3. Successfully constrained motion.

1. Completely constrained motion.

When the motion between a pair is limited to definite direction irrespective of

the direction of force applied, then the motion is said to be a completely

constrained motion.

Example:

1. The motion of the square bar in square hole.

2. The motion of shaft with collars at each end in a circular hole.


Figure: Complete Constrained Motion


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2. Incompletely constrained motion.

When the motion between a pair can take place in more than one direction,

then the motion is said to be a completely constrained motion.

Example:

1. The motion of the circular bar in circular hole.


Figure: Incomplete Constrained Motion


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3. Successfully constrained motion

When the relative motion between the link is not completely constrained by

itself but it is made by some other means is called successfully constrained

motion.

Example:

1. Shaft in Footstep Bearing

2. The motion IC engine valve and piston in reciprocating inside an engine

cylinder.


Figure: Successfully Constrained Motion


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3. Kinematic Chain

When the kinematic pairs are coupled in such a way that the last linked is

joined the first link to transmit the definite motion it is called a kinematic chain.

To determine the given assemblage of links forms the kinematic chain

or not:

The two equations are:

1. l = 2p - 4

2. J = 3/2 * l - 2

l = number of links

p = number of pairs

j = number of joints

Three possible cases are

1. If L.H.S=R.H.S then it is Constrained kinematic chain

2. If L.H.S>R.H.S then it is Locked Chain

3. If L.H.S


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1. Arrangement of three links

2. Arrangement of four links


Figure :Three Links

Figure :Four Links


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3. Arrangement of five links

4. Arrangement of six links


Figure :Five Links

Figure :Sic Links


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Types of Joints in the Chain

1. Binary joints

When the two links are joined at the same connections, the joint is known

as binary joint

W.Kliens criterion of constraint

l = number of links

h = number of higher pairs

j = number of binary joints

j=4; l=4; h=0

j+h/2 = 3/2*l - 2

4+0 = 3/2*4 - 2

4 = 4


Figure: Binary Joints


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L.H.S=R.H.S

2. Ternary Joints

When the three links are joined at the same connections, the joint is

known as ternary joints.

A.W.Kliens criterion of constraint

l = number of links



j=7; l=6; h=0

j+h/2 =3/2*l 2

7+0 =3/2*6 2

7 =7


Figure: Ternary Joints


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L.H.S=R.H.S

3. Quaternary Joints

When the four links are joined at the same connections, the joint is knownas Quaternary joints.

W.Kliens criterion of constraint

l = number of links



j=12; l=9; h=0

j+h/2 = 3/2*l 2

12+0 = 3/2*9 2

12 = 11.5


Figure: Quaternary Joints


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L.H.S>R.H.S



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Types of Kinematic chain

1. Four bar chain

2. Single slider crank chain.

3. Double slider crank chain

Inversion of the following types

1. Four bar chain

a) Beam engine.

b) Coupling rod of Locomotives.

c) Watts indicator mechanism.

d) Pantograph.

2. Single slider crank chain .

a) Pendulum pump or Bull engine.

b) Oscillating cylinder engine.

c) Rotary IC engine.

d) Crank and slotted lever quick return mechanism.

e) With worth quick return mechanism.

3. Double slider crank chain.

a) Elliptical trammel

b) Scotch yoke mechanism.

c) Oldhams coupling.



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3. MECHANISM

a. When one of the links of a kinematic chain is fixed, the chain is known as

mechanism.

b. It may be used for transmitting or transforming motion.

Example:

1. Engine indicator,

2. Typewriter.

Types of Mechanism

a. Simple mechanism (a mechanism with four links)

b. Compound mechanism (a mechanism with more than four link)

Differentiate between Machine and Mechanism

NO MACHINE MECHANISM

1. It is like the human body, ittransforms energy into usefulwork.

It is like a frame work and has adefinite motion between variouslinks.

2 It relates to energy only. It relates to motion.

3 It has many link. It also has many links.

4 Ex: lathe, shaper. Ex. watt indicator,typwriter

5



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4. Structure

It is the assemblage of a number of resistant bodies having no relative motion

between then and meant for carrying loads having a straining action.

Example:

1. A Railway bridge.

2. Roof Trusses

3. bridges,

4. buildings

5. machine frames


Figure: Structure


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Differentiate between Machine and Structure.

NO MACHINE STRUCTURE

1 Has relative motion between themembers

Has no relative motion

2 Transforms available energy intopossible work.

Does not transform.

3 Members are meant to transmitmotion and forces.

Members are meant to acceptload

4 Example Shaper, lathe Example :Bridge.

5. Inversion

The method of obtaining the different mechanism by fixing the different links in

a kinematic chain is known as inversion of the mechanism.



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Important Terminologies and Definition

1. Machine

It is device which takes in the available energy and converts it into usefulwork.

When the mechanism is required to transmit the power or to do someparticular type of work, it then becomes a Machine.

Example: Shaper, Lathe machine

2. Mechanics( Theory of Machine)

Branch of engineering which deals with the relative motion and forces

between the various machine elements.

Kinematics of machine

Deals with the relative motion without considering the forces

Dynamics of machine

Deals with the forces and effect of forces on the machine component

when they act on them.

3. Kinetics of machine

Deals with the forces, which are formed due to combined action ofmass and motion of machine elements.

4. Statics

Deals with the forces and its effect on the machine part while the latteris at rest.

5. Resistant body Abody is said to be resistant body if it is able to transmit the forces with the

least possible deformation.

Example: spring, belt oils in hydraulic presses

6. Kinematic Link



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Links are individual parts of a mechanism.

Each parts of a machine which has a relative motion to some otherparts is known as Kinematic link.

7. Kinematic Chain

When the kinematic pairs are coupled in such a way that the last linked isjoined the first link to transmit the definite motion it is called a kinematic chain.

8. Kinematic Pair

The two links of the machine when in contact with each other are said to forma pair if the relative motion between them is successfully constrained.

9. Inversion

The method of obtaining the different mechanism by fixing the different links ina kinematic chain is known as inversion of the mechanism.

10.Structure

It is the assemblage of a number of resistant bodies having no relative motionbetween then and meant for carrying loads having a straining action.

Example: a railway bridge.

11.Mechanism

When one of the links of a kinematic chain is fixed, the chain is known as

mechanism.

It may be used for transmitting or transforming motion.

Example: Engine indicator, Typewriter.



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Grashof's Law

The sum of the length of shortest and longest link must be equal or less

than the sum of the length of the other two link length, if there is to be a

continuous relative motion between the two links.

According to Grashofs law

s + l < p + q

l = length of the longest link.

s = length of the shortest link.

p & q = length of the other two

links

In a four-bar linkage, we refer to the line segment between hinges on a given link

as a bar where:

s = length of shortest bar

l = length of longest bar

p, q = lengths of intermediate bar

Grashof's theorem states that a four-bar mechanism has at least one revolving

link if

s + l p + q (2)

The inequality (1) is Grashof's criteria



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The Link opposite to the frame is called Coupler Link and the link which are

hinged to the frame are called side link.

The link which is free to rotate through 3600 with respect to second link will be

said to revolve relative to the second link (not necessarily a frame).

If it is possible for all four bar to become simultaneously aligned, such a state

is called change point.

From the table we can see that for a mechanism to have a crank, the sum of the

length of shortest and longest link must be equal or less than the sum of the

length of the other two link.

However this condition is necessary but not sufficient. Mechanism satisfying this

condition falls into following three categories.

1) When the shortest link is the side link, the mechanism is crank rocker

mechanism. The shortest link is the CRANK in the mechanism.


Case Criterion Shortest link Category

1 s+l < p+q frame double crank

2 s+l < p+q slide crank rocker

3 s+l < p+q coupler double rocker

4 s+l = p+q any change point

5 s+l < p+q any triple rocker


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2) When the shortest link is the Frame, the mechanism is double crank

mechanism.

3) When the shortest link is the coupler link, the mechanism is Double rocker

mechanism

Inversion of the following types

1. Four bar chain

a. Beam engine.

b. Coupling rod of Locomotives.c. Watts indicator mechanism.

d. Pantograph.

2. Single slider crank chain .

a. Pendulum pump or Bull engine.

b. Oscillating cylinder engine.

c. Rotary IC engine.

d. Crank and slotted lever quick return mechanism.

e. Whit worth quick return mechanism.

3. Double slider crank chain.

a. Elliptical trammel

b. Scotch yoke mechanism.

c. Oldhams coupling.



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INVERSION OF FOUR BAR CHAIN MECHANISM



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a. BEAM ENGINE

1. Beam engine is also called as Crank and lever mechanism.

2. It consist of four link

a. Link A Frame

b. Link AB Crank

c. Link BC Coupler

d. Link CELever

3. In this mechanism, when the crank rotated about the fixed centre A,

the lever oscillates about the fixed center D.

4. The end E of the lever CDE is connected to piston rod which

reciprocates due to the rotation of the crank.


Figure: Beam Engine


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5. Purpose: Convert rotary motion into reciprocating motion.

b. Coupling rod of locomotive

1. The coupling rod of the locomotive consists of four links as shown in figure.


a. Link AD frame

b. Link AB crank

c. Link BC connecting rod

d. Link CDcrank3. In this mechanism, the link AB and BC act as crank and are connected to

the respective wheel.


Figure: Coupling Rod of locomotive


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4. The link CD act as a coupling rod and the link AB is fixed in order to

maintain a constrain motion between them.

5. Purpose: meant for transmitting rotary motion from one wheel to another

wheel.

c. Watts indicator mechanism

A watt indicator mechanism has a four link as shown in figure.

1. The four links are fixed link at A, link AC, link CE, and link BFD.

2. It may be noted that BF and FD forms one link because two parts have no

relative motion between them.

3. The link CE and BFD act as lever.

4. The displacement of link BFD is directly proportional to the pressure of gas

or steam which acts on the indicator plunger.

5. On any small displacement of the mechanism, the tracing point E at the end

of the link CE traces out approximately straight line.


Figure: Watts Indicator Mechanism


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6. The initial position of the mechanism is shown in full line whereas the dotted

lines shows the position of mechanism when the gas or steam pressure acts

on the indicator plunger.

d. Pantograph

A pantograph is an instrument used to reproduce an enlarged or reduce scale

and as exactly as possible the path described by a given point.

1. It is a based on four based kinematic chain.

2. It consists of jointed parallelogram ABCD.

3. It is made up of bar connected by turning pair. It has a four turning pair.

4. Link BA and BC are extended to O and E respectively such that

OA/OE = AD/BE.


Figure: Pantograph


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5. For all relative position of bars the triangle OAD and OBE are similar and

the point O,D,E are in straight line.

6. The point E describes the same path as described by point D.

INVERSION OF SINGLE SLIDER CRANK CHAIN

MECHANISM



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a. Pendulum pump or Bull engine.

1. In this mechanism, the inversion is obtained by fixing the link 4 or cylinder

(sliding pair).


a. Link 1 Piston rod

b. Link 2 AB-Crank

c. Link 3 -BC -connecting rod

d. Link 4 Cylinder.

3. In this case, the crank rotates the connecting rod oscillates about the pin

pivoted to the fixed link.

4. The piston attached to the piston rod reciprocates inside the cylinder.


Figure: Pendulum pump or Bull engine


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b. Oscillating cylinder engine.

1. In this mechanism, the inversion is obtained by fixing the link 3 or

connecting rod (turning pair).


e. Link 1 -AB- Piston rod

f. Link 2 -BD-Crank

g. Link 3 -AD -Connecting rod

h. Link 4 Cylinder.

3. The link 3 (AD-connecting rod) is corresponds to the connecting rod of the

reciprocating steam engine mechanism.


Figure: Oscillating Cylinder Engine


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4. When the link 2 rotates (BD-Crank) rotates, the piston attached to the

piston rod reciprocates and the cylinder oscillates about the pin pivoted to

the fixed link at A.

d. Rotary IC engine.

1. In this mechanism, the inversion is obtained by fixing the link 2 or crank.


a. Link 1 - Cylinder.

b. Link 2 -Fixed Crank

c. Link 3 -Piston

d. Link 4 Connecting rod

3. The link 4 (AD-connecting rod) rotates, the piston reciprocates inside the

cylinder forming link1.


Figure: Rotary IC Engine


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a. Crank and slotted lever quick return mechanism

1. In this mechanism, the inversion is obtained by fixing the link 3 or turning

pair.


a. Link 1 -Slider

b. Link 2 Driving Crank

c. Link 3 -Fixed link

d. Link 4 Slotted lever or Slotted bar


Figure: Crank and slotted lever quick return mechanism


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3. The driving crank BC revolves with uniform angular speed about fixed

centre.

4. The sliding bock is attached to crank pin at B slides in the slotted bar AP

and thus causes AP to oscillate about the point A.

5. A short link PQ transmits the motion from AP to the Ram to which the

cutting tool is fixed

6. The motion of the tool is constrained along the line produced

b. Whitworth quick return mechanism.

1. In this mechanism, the inversion is obtained by fixing the link 3 or

turning pair.


a. Link 1 -Slider

b. Link 2 - Crank

c. Link 3 -Fixed link

d. Link 4 Slotted lever


Figure: Withworth Quick Return mechanism


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3. The driving crank BC revolves with uniform angular speed about fixed

centre.

4. The sliding bock is attached to crank pin at B slides in the slotted bar AP

and thus causes AP to oscillated about the point A.

5. A short link PQ transmits the motion from AP to the Ram to which the

cutting tool is fixed

6. The motion of the tool is constrained along the line produced.

INVERSION OF DOUBLE SLIDER CRANK CHAIN

MECHANISM



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a. Elliptical trammel

1. In this mechanism, the inversion is obtained by fixing the link 4 or slotted

plate.


a. Link 1 Sliders

b. Link 2 Bar

c. Link 3 Sliders

d. Link 4 Slotted Plate

3. The looted plate has two grooves cut in it at right angles to each other.

4. The link 1 and known as a sliders and form sliding pair with the link 4.

5. The link AB is a bar which forms the turning pair with the links 1 and link 3.


Figure: Elliptical trammel


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6. When the link 1 and link 3 slides along the respected grooves ,any point of

the link 2 such as point P traces out the ellipse on the surface.

b. Scotch yoke mechanism.

1. In this mechanism, the inversion is obtained by fixing link 1 or link3.


e. Link 1 Fixed Link

f. Link 2 Crank

g. Link 3 Slider

h. Link 4 Frame (Piston and Cylinder arrangement )

3. When the link 2 rotates about the about B as a centre the link 4

reciprocates.(Piston reciprocates inside the cylinder)

4. The fixed links guides the frame

.


Figure: Scotch Yoke Mechanism


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c. Oldhams coupling.

1. In this mechanism, the inversion is obtained by fixing link 2.


a. Link 1 Flanges

b. Link 2 Supporting Frame

c. Link 3 Flanges

d. Link 4 Intermediate Piece.

3. The flanges (link 1 and link 3) forms turning pair with the link 2.



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4. When the driving shaft is rotated, the flange (link 1) causes the

intermediated piece (link 4) to rotate at the same angle through which

the flange (link 1) is rotated.

5. It further rotates the flange (link 3) at the same angle through which the

flange (link 1) is rotated. Hence link 1,3,4, have same angular velocity.

6. A little consideration there is a sliding motion between link 4 and link 1

and 3.

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118554630 Theory of Machine Module 1 Modified 1