Theory of - MechFamilymechfamilyhu.net/download/uploads/mech14374346381.pdf · Planer and Spatial...

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Dr. Hitham Tlilan 1

Theory of Theory of MachinesMachines 042341

Day and TimeDay and Time::Sun. ~ Th. 12:40-13:40

Instructor: Instructor: Dr. Dr. HithamHitham TlilanTlilan

Office: E3118 (Engineering Building) Tel.: 4463

Dr. Hitham Tlilan 2

Course DescriptionCourse Description

and, the static and dynamic forces required for the proper design of

A study ofA study oflinear and angularlinear and angular

DisplacementsDisplacements VelocitiesVelocities AccelerationsAccelerations

of points and bodiesof points and bodies

Mechanical linkages, Cams, and Geared systems.

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Dr. Hitham Tlilan 3

Chapter OneChapter OneMechanisms and Machine Mechanisms and Machine

Basic ConceptsBasic Concepts

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Mechanics

Statics Dynamics

Kinematics Kinetics

Mechanics of materials

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KinematicsKinematicsIs the study of bodies (mechanisms) on the basis of Is the study of bodies (mechanisms) on the basis of the motion requirements without referenced to the the motion requirements without referenced to the

force that act on the mechanism force that act on the mechanism

Kinematics DiagramKinematics DiagramIs the diagram that used to express the complex Is the diagram that used to express the complex

parts of machines for easy design process.parts of machines for easy design process.

Dr. Hitham Tlilan 6

KineticsKineticsIs the study of the motion in bodies (mechanisms) Is the study of the motion in bodies (mechanisms) under the force and torques that act on the body under the force and torques that act on the body

(mechanism) (mechanism)

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MechanismMechanismIt is a combination of rigid bodies or It is a combination of rigid bodies or

elements ( Linkages) elements ( Linkages) Formed and connected Formed and connected to transmit motionto transmit motion

The Linkages moved upon each other with definite The Linkages moved upon each other with definite relative motionrelative motion

Mechanism consists of linkages and jointsMechanism consists of linkages and joints

Dr. Hitham Tlilan 8

Planer and Spatial Mechanisms In a planar mechanisms, all of the relative motions of the rigid bodies are in one plane or in

parallel planes Motion of such mechanism is called Coplanar

If there is any relative motion that is not in the same If there is any relative motion that is not in the same plane or in parallel planes, the mechanism is called the plane or in parallel planes, the mechanism is called the

spatial mechanismspatial mechanism..••Motion of such mechanism is called spatial motionMotion of such mechanism is called spatial motion

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Example of Mechanisms

Can crusher Simple press

Rear-window wiper

Moves packages from an assembly bench to a conveyor

Dr. Hitham Tlilan 10

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)


The Slider-Crank Mechanism

1: Frame (fixed) 2: Crank (input Link)3: Connecting rod (coupler Link) 4: Output link (Slider)

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Machines Machines are 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 of transferring motion and forces from a power source to an output.

MachineMachine is is mechanism or a collection of mechanismsmechanism or a collection of mechanisms


Example of Machines

Internal Combustion EngineInternal Combustion Engine

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Types of MotionTypes of Motion

(1)(1) Plane Motion ( Planar Motion)Plane Motion ( Planar Motion)(1-1) Translation:TheThe motionmotion ofof aa rigidrigid bodybody thatthat thethe positionposition ofof eacheachstraightstraight lineline ofof thethe bodybody isis parallelparallel toto allall ofof itsits otherotherpositionspositions..

(1-1-1) Rectilinear TranslationAll points of the body moves in parallel straight line paths

In this Mechanism the piston moves between 2-positions


(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 at a constant distance from a fixed axis perpendicular to the plane of motion

(1-3) Rotation and Translation

(2) Spatial MotionWhen a body moves with rotation When a body moves with rotation

about about 33-- nonnon--parallel axes and parallel axes and translate in translate in 3 3 -- independent directions. independent directions.

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Translation to TranslationTranslation to Translation


Rotational to RotationalRotational to Rotational

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Rotation to Translation

D:\Courses\Machinery\lectures\Machinery\An Example Quick Return Design.htm


1.4 Terminology and DefinitionsLinkLink it is a rigid body (member) with provision at each end for

connection to two (more) other links When several links are moveable connected to each other by

joints, it is called kinematics chain.OR The combination of links and pairs without a fixed link is not

a mechanism but a kinematic chain

If NOT, the chain is said to be open kinematics chain If these links are connected in such a way that no motion

is possible then we have a locked chain ( structure)

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

the chain form one or more closed loopsthe chain form one or more closed loopsIf the link form a closed loops, it is called If the link form a closed loops, it is called

closed kinematic chainclosed kinematic chain

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Frame Frame is the fixed or stationary link in the mechanism

1 11 1

1

The engine block is considered as frame even if the automobile is moving

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Joint Joint Is the connection between links that permit Is the connection between links that permit constrained relative motionconstrained relative motion


Pairing Elements It occurs when two elements are joined together so that relative

motion between these 2-elements is consistent

Higher pair Higher pair ((HH))When the joint by which When the joint by which the links are connected the links are connected has point or line contacthas point or line contact

Lower pair Lower pair ((LL))When the joint by which When the joint by which the links are connected the links are connected

has surface contacthas surface contact

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InversionInversionIn 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 PeriodCycle and Period

•• CycleCycle is the complete sequence of position of links in a mechanismis the complete sequence of position of links in a mechanism( ( from some initial position back to the same initial positionfrom some initial position back to the same initial position))

•• PeriodPeriod is the time required to complete one cycle of motionis the time required to complete one cycle of motion


11..5 5 Degrees of freedom (Mobility) Degrees of freedom (Mobility) The definition of the degrees of freedom (DOF) of a

mechanism is the number of independent relative motions among the rigid bodies.

A body that is restricted to move in a plane (Planar) has A body that is restricted to move in a plane (Planar) has 33--DOFDOFTranslation in 2-directions

&Rotation within the same plane

In generalIn generalUnconstrained (Spatial) rigid body has 6-DOF

Translation in 3-directions&

Rotation about 3-coordinate axes

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Constraint due to JOINTSConstraint due to JOINTS

Each joint has a number Of degrees of freedom

(connectivity(connectivity))

The presence of joints in a system reduces the MOBILITY of Spatial Mechanism by

joint theof ity)(Connectiv freedom of degrees ofnumber theis : joint by the produced sconstraint ofnumber theis :

;

i

c

fnWhere

ic fn 6


Examples

sconstraint areJoint Revolute by produced sconstraint ofnumber the

ity)(connectiv DOF-1 hasJoint Revolute The

5166

ic f n

Revolute Joint

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Example Spherical Joint

sconstraint areJoint Spherical by produced sconstraint ofnumber the

ity)(connectiv DOF-3 hasJoint Spherical The

3366

ic f n


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

16

16


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

structureDF -1: the mechanism statically indeterminant

structure


Example gives RSSR Mechanism

11

3

24

33-6 -6joint-Sfor sconstraint of

51-6 -6joint-Rfor sconstraint of

)(DFspatial

i

i

L

n

iijL

f.No

f.Non

fnnj

4

161

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Example Continued

DOF 26 )(DF

sconstraint 16

)(DF

] Eq.(1.1) [using

spatial

joints-Rfor joints-Sfor

spatial

5)(23)(2

1146

16

1

1

j

j

n

ii

n

iiL

f

fn


DOF 2

)(DF

sconstraint 8

)(DF

] Eq.(1.3) [using

spatial

joints-Rfor DOFjoints-Sfor DOF

spatial

1)(13)(3

86

81446

16

1

1

j

j

n

ii

n

iijL

f

fnn

Example Continued

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Example RRRR Mechanism

DOF 25)4( )(DF

)(DFsconstraint 51-6 -6joint-Rfor sconstraint of .

)(DF

spatial

spatial

spatial

2018146

16

44

161

cL

i

j

L

n

iiL

nnfNo

nn

fnj

1

1

3

2

4

Statically indeterminant structure


Planar Linkages (Mechanisms)It’s a special case of the general one

(Spatial mechanisms)The links move in same plane or in parallel planes

The axes of the revolute joints are parallel

D:\Courses\Machinery\lectures\Machinery\An Example Quick Return Design.htm

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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 reduces the MOBILITY of Planar Mechanism by

joint theof ity)(Connectiv freedom of degrees ofnumber theis : joint by the produced sconstraint ofnumber theis :

;

i

c

fnWhere

ic fn 3


Examples

sconstraint areJoint Revolute by produced sconstraint ofnumber the

ity)(connectiv DOF-1 hasJoint Revolute The

2133

ic f n

Revolute Joint

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(1.4) )(DFplanar jL nn 213

Where;nj: is the number of jointsfi: is the number of DOF (connectivity) of joints

pairs DF-1 ofnumber the :frame) the (including links ofnumber total the :

Where;

j

L

nn

If the Planar Mechanism contains only 1-DF pairs or joint

(1.5) )(DF

OR;

planar

jn

iijL fnn

113


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

, )(DF)..(Eq

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

)(DF)..(Eq

planar

planar

41351

21341

44

1j

n

iijL

jL

j

L

nfnn

nnnn

j

Example Determine the Mobility (DF) for the following link

1 1

2

3

4

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structure)ant indetermin statically ( DF 1 - 1)111(11)-5-3(4

, )(DF)..(Eq

DF 1- 5)(2-1)-3(4

)(DF)..(Eq

planar

planar

51351

21341

54

1j

n

iijL

jL

j

L

nfnn

nn

nn

j

Example Determine the Mobility (DF) for the following link

3

1 1

2 4

1

When the joint connect more than 2-links the same joint counted by(Number of connected links-1)


then; pairs) DF-(2 and pairs) DF-(1 contains )(mechanism linkageplanar the If

jj nn

(1.6) )(DF planar jjL nnn 213

DOF ≤ 0 structure

mechanismDOF > 0

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joint) (Fork joint DF-2 ofNumber

71(slider)revolute)or (pin joint DF-1 ofNumber

1

67

j

j

L

n

nnExample

1

1

1

23

4

5

6

7

Fork Joint

SliderSpring

DF 31-7)(2-1)-3(7

)(DF planar

jjL nnn 213


contact) (Cam joint DF-2 ofNumber

revolute)or (pin joint DF-1 ofNumber

1

23

j

j

L

nn

n

•

•

Example

DF 11-2)(2-1)-3(3

)(DF planar

jjL nnn 213

1

1

3

2

Common tangent

Higher pair(cam contact)

2-DF

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One Degree of Freedom ConfigurationsGrübler’s Criterion

1-DF planar mechanism made up of lower pairs (1-DF joints)must satisfy Grübler’s Criterion, which is

(1.7) 0432 Lj nn

7046326

4044324

1

jjL

jjL

nnn

nnn

)(

)(

with mechanismplanar awant we if joint DF-1 ofnumder the find )(

Example

criterion sGrubler' using

criterion sGrubler' using

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