th1 theory of machines ch1

7/29/2019 Th1 theory of machines CH1

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Theory of Machines

042341

Day and Time:Mon ~ Wed.

12:30-2:00Instructor: Dr. Mohammad Tarawneh

Office: E3104 (Engineering Building) Tel.: 5106


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Course Description

and, the static and dynamic forces required for

the proper design of

A study of

linear and angular

Displacements Velocities Accelerations

of points and bodies

Mechanical linkages,

Cams,andGearedsystems.


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Chapter OneMechanisms and Machine

Basic Concepts


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Mechanics

Statics Dynamics

Kinematics Kinetics

Mechanics

of materials


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KinematicsIs the study of bodies (mechanisms) on the basis of

the motion requirements without referenced to theforce that act on the mechanism

Kinematics DiagramIs the diagram that used to express the complex parts

of machines for easy design process.


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KineticsIs the study of the motion in bodies (mechanisms)

under the force and torques that act on the body(mechanism)


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Mechanism

It is a combination of rigid bodies or

elements ( Linkages)Formed and connected to transmit motion

The Linkages moved upon each other with definiterelative motion

Mechanism consists of linkages and joints


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Planer and Spatial Mechanisms

In a planar mechanisms, all of the relative

motions of the rigid bodies are in one plane or inparallel planes

Motion of such mechanism is called Coplanar

If there is any relative motion that is not in the same

plane or in parallel planes, the mechanism is called the

spatial mechanism.Motion of such mechanism is called spatial motion


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Example of Mechanisms

Can crusherSimplepress

Rear-windowwiper

Moves packages from an

assembly bench to a conveyor


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Lift platform

Front loader

Device to close the

top flap of boxes


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Four-Bar Linkage

1: Frame (fixed)

2: Crank (input Link)

3: Connecting rod (coupler Link)

4: Output link ( Rocker) or (Follower)


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The Slider-Crank Mechanism

1: Frame (fixed)

2: Crank (input Link)

3: Connecting rod (coupler Link)

4: Output link (Slider)


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Machinesare mechanical devices used to accomplish work.

A mechanism is a heart of a machine.

It is the mechanical portion of the machine that has the function oftransferring motion and forces from a power source to an output.

Machine is mechanism or a collection of mechanisms


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Example of Machines

Internal Combustion Engine


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Types of Motion

(1) Plane Motion ( Planar Motion)

(1-1) Translation:The motion of a rigid body that the position of each straightline of the body is parallel to all of its other positions.

(1-1-1) Rectilinear Translation

All points of the body moves in parallel straight line paths

In this Mechanism the piston moves between 2-positions


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(1-1-2) Curvilinear Motion (Translation)

The paths of the points are identical curves parallel to a fixed frame

(1-2) RotationEach point of a rigid body having plane of motion remains ata constant distance from a fixed axis perpendicular to the planeof motion

(1-3) Rotation and Translation

(2) Spatial MotionWhen a body moves with rotation

about 3- non-parallel axes and translatein 3 - independent directions.


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Translation to Translation


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Rotational to Rotational


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Rotation to Translation

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1 4 i fi i i
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1.4 Terminology and Definitions

Linkit is a rigid body (member) with provision at each end forconnection to two (more) other links

When several links are moveable connected to each other byjoints, it is calledkinematics chain.

OR

The combination of links and pairs without a fixed link is not a

mechanism buta kinematic chain

IfNOT, thechain is said to beopen kinematics chain If these links are connected in such a way thatno motion

is possiblethen we havea locked chain ( structure)

If every link in the chain is connected to two or more linksthen

the chain form one or more closed loops

If the link form a closed loops, it is calledclosed kinematic chain


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Frameis the fixed or stationary link in the mechanism

1 11 1

1

The engine block is considered as frameeven if the automobile is moving


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Joint Is the connection between links that permitconstrained relative motion


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Pairing ElementsIt occurs when two elements are joined together so that relative motion

between these 2-elements is consistent

Higher pair (H)When the joint by which

the links are connectedhas point or line contact

Lower pair (L)When the joint by which

the links are connectedhas surface contact

I i


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InversionIn a mechanism, if the link which was originally fixed

(frame)allowed to move and another link becomes fixed,

the mechanism is said to be inverted

Cycle and Period

Cycleis the complete sequence of position of links in a mechanism( from some initial position back to the same initial position)

Periodis the time required to complete one cycle of motion

1 5 D f f d (M bilit )


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1.5 Degrees of freedom (Mobility)

The definition of the degrees of freedom(DOF) of amechanism is the number of independent relative

motions among the rigid bodies.

A body that is restricted to move in a plane (Planar) has 3-DOFTranslation in 2-directions

&

Rotation within the same plane

In generalUnconstrained (Spatial) rigid body has 6-DOF

Translation in 3-directions&

Rotation about 3-coordinate axes

C t i t d t JOINTS


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Constraint due to JOINTS

Each joint has a number

Of degrees of freedom(connectivity)

The presence of joints in a system reducesthe MOBILITY of Spatial Mechanism by

jointtheofity)(Connectivfreedomofdegreesofnumbertheis:

jointby theproducedsconstraintofnumbertheis:

;

i

c

f

n

Where

ic fn 6

E l


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Examples

sconstraint

areJointRevolutebyproducedsconstraintofnumberthe

ity)(connectivDOF-1hasJointRevoluteThe

5166

ic fn

Revolute Joint

Example

S h i l J i t


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Example Spherical Joint

sconstraint

areJointSphericalbyproducedsconstraintofnumberthe

ity)(connectivDOF-3hasJointSphericalThe

3366

ic fn

D f F d (M bilit ) f S ti l M ti


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Degrees of Freedom (Mobility) for Spatial Motion

(1.1)(DFspatial cL nn 16Where;

nL: number of links ( including the frame)nc: the total number of constraints

If nj: is the number of jointsfi: is the number of DOF for joints

Then (1.2)

jn

iijc fnn

1

6

S b E (1 2) i t E (1 1)


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Sub. Eq. (1.2) into Eq.(1.1)

(1.3))(DF

)(DF

spatial

spatial

j

j

n

iijL

n

iijL

fnn

fnn

1

1

16

616

DF 1: the mechanism has mobilityDF = 0: the mechanism is statically determinant

structure

DF -1: the mechanism statically indeterminantstructure

Example gives RSSR Mechanism


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Example gives RSSR Mechanism

1

1

3

2

4

33-6

-6joint-Sforsconstraintof

51-6

-6joint-Rforsconstraintof

)(DFspatial

i

i

L

n

i

ijL

f.No

f.No

n

fnnj

4

16

1

Example Continued


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Example Continued

DO F26)(DF

sconstrain16

)(DF

]Eq.(1.1)[using

spatial

joints-Rforjoints-Sfor

spatial

5)(23)(2

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16

1

1

j

j

n

i i

n

i iL

f

fn

Example Continued


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DOF2

)(DF

sconstrain8

)(DF

]Eq.(1.3)[using

spatial

joints-RforDOFjoints-SforDOF

spatial

1)(13)(3

86

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16

1

1

j

j

n

ii

n

iijL

f

fnn

Example Continued

Example RRRR Mechanism


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Example RRRR Mechanism

DOF25)4()(DF

)(DF

sconstraint51-6-6joint-Rforsconstraintof.

)(DF

spatial

spatial

spatial

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16

4

4

16

1

cL

i

j

L

n

iiL

nn

fNon

n

fnj

1

1

3

2

4

Statically indeterminant

structure

Planar Linkages (Mechanisms)


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Planar Linkages (Mechanisms)

Its a special case of the general one

(Spatial mechanisms)

The links move in same planeor in parallel planes

The axes of the revolute joints are parallel

D:\Courses\Machinery\lectures\Machinery\AnExample Quick Return Design.htm

Degrees of Freedoms (Mobility) for PLANAR Mechanism
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Degrees of Freedoms (Mobility) for PLANAR Mechanism

Each unconstrained rigid link has 3 - DF in plane motion

A fixed link has Zero DF

The presence of joints in a system reducesthe MOBILITY of Planar Mechanism by

jointtheofity)(Connectivfreedomofdegreesofnumbertheis:

jointby theproducedsconstraintofnumbertheis:

;

i

c

f

n

Where

ic fn 3

Examples


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Examples

sconstraint

areJointRevolutebyproducedsconstraintofnumberthe

ity)(connectivDOF-1hasJointRevoluteThe

2133

ic fn

Revolute Joint

If thePlanar Mechanismcontainsonly1-DF pairsor joint


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Dr. Hitham Tlilan 39

(1.4))(DFplanar jL nn 213

Where;

nj: is the number of joints

fi: is the number of DOF (connectivity) of joints

pairsDF-1ofnumberthe:

framethe(includinglinksofnumbertotalthe:Where;

j

L

n

n

If the Planar Mechanism contains only1-DF pairs or joint

(1.5)(DF

OR;

planar jn

i ijL

fnn1

13

Example Determine the Mobility (DF) for the following link


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Dr. Hitham Tlilan 40

DF1

1)11(11)-4-3(4

,)(DF)..(Eq

DF1

4)(2-1)-3(4)(DF)..(Eq

planar

planar

41351

21341

4

4

1

j

n

iijL

jL

j

L

nfnn

nn

n

n

j


1 1

2

3

4



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structurantindeterminstatically(DF1-

1)111(11)-5-3(4

,)(DF)..(Eq

DF1-

5)(2-1)-3(4

)(DF)..(Eq

planar

planar

51351

213415

4

1

j

n

iijL

jL

j

L

nfnn

nnn

n

j


3

1 1

2 4

1When the joint connect more than 2-

links the same joint counted by(Number of connected links-1)


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thenpairs)DF-(2andpairs)DF-(1

contains)(mechanismlinkageplanartheIf

jj nn

(1.6))(DFplanar jjL

nnn 213

DOF 0 structure

mechanismDOF > 0

Example


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joint)(ForkjointDF-2ofNumber

71(slider)revolute)or(pinjointDF-1ofNumber

1

6

7

j

j

L

n

n

n

Example

1

1

1

23

4

5

6

7

Fork Joint

Slider

Spring

DF31-7)(2-1)-3(7

)(DF planar

jjL nnn 213

Example


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contact)(CamjointDF-2ofNumber

revoluteor(pinjointDF-1ofNumber

1

2

3

j

j

L

n

n

n

Example

DF1

1-2)(2-1)-3(3

)(DF planar

jjL nnn 213

1

1

3

2

Common tangent

Higher pair

(cam contact)

2-DF

One Degree of Freedom Configurations


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One Degree of Freedom Configurations

Grblers Criterion

1-DF planar mechanism made up of lower pairs (1-DF joints)

must satisfy Grblers Criterion, which is

(1.70432 Lj nn

7046326

4044324

1

jjL

jjL

nnn

nnn

)(

)(

withmechanismplanarawantweif

jointDF-1ofnumderthefind)(

Example

criterionsGrubler'using

criterionsGrubler'using

th1 theory of machines ch1

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