presentaion of fluid

8/13/2019 presentaion of fluid

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Machine DynamicsChapter 1

Dr. Dongming GanDr. Dongming Gan

Slides Adapted from

Prof. Kostass lectures


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Mechanism CategorizationMechanism Categorization

Based on the characteristics of the motionof the links:

Planar Mechanisms

Spherical Mechanisms

Spatial Mechanisms


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Mechanism Categorization:Mechanism Categorization: Planar Mechanism

All its particles move on planar curves

parallel to a single common plane

Their motion can be observed from

single direction i.e. from a single view The majority of practical mechanisms, e.g.

Planar four-bar linkage

Plate cam & followerSlide crank mechanism


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Mechanism Categorization:Mechanism Categorization: Planar Mechanism

Planar Linkages: Planar Mechanismsutilizing ONLY lower pairs i.e.

revolute pairs: axes normal to motion plane

prismatic pairs: axes parallel to motion plane


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Mechanism Categorization:Mechanism Categorization: Spherical Mechanisms

Have a stationary point as they move

The locus of each pt is on a spherical surface

All spherical surfaces are concentric

Example: Hookes Universal joint (or Cardan

joint)


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Mechanism Categorization:Mechanism Categorization: Spatial Mechanisms

No restrictions on the relative motions

Complex motion and simple techniques do

not suffice

Will be covered during the end of the

course in the context or Robotics


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Mechanism MobilityMechanism Mobility

The number of input parameters (pair

variables) that must be independentlydetermined to bring the device into a particular

position / orientation

Can be determined by its Number of links

Number & Type of joints


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Mechanism Mobility:Mechanism Mobility: Kutzbach Criterion

n: number of links, including the fixed

Each link has 3 DOF (except for the fixed

one) i.e. 3(n-1) in total

j1: number of 1 DOF pairs

j2: number of 2 DOF pairs

Kutzbach Criterion for mobility m :m=3(n-1)-2j1-j2


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m=3(n-1)-2j1-j2


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m=3(n-1)-2j1-j2


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m=3(n-1)-2j1-j2


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m=3(n-1)-2j1

-j2

Criterion failed because did not consider

dimensional properties of links. Good for early design considerations


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Mechanism Mobility:Mechanism Mobility: Grubler Criterion

From Kutzbach Criterion: m=3(n-1)-2j1-j2

which applies to Planar Mechanisms,

if

1 DOF joints (j2=0)

andm=1

thenGrubler Criterion3n-2j1-4=0

The simplest mechanism


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Mechanism Mobility:Mechanism Mobility: Grubler Criterion

The simplest mechanism satisfying 3n-

2j1-4=0 is forn=j1=4

Slider-crank 4-bar linkage


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Mechanism Mobility:Mechanism Mobility: 33--DDKutzbach & Grubler

Criteria

Kutzbach : m=6(n-1)-5j1-4j2-3j3-2j4-j5

Grubler: 6n-5j1-7=0

The simplest mechanism satisfying the 3-D

Grubler is for n=j1=7


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Mechanism Mobility:Mechanism Mobility: ExamplesExamples

n=5 j1=5 j2=1

m=3(n-1)-2j1-j2=1


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n=7 j1=9 j2=1

m=3(n-1)-2j1-j2=-1 wrong!!!! m=1 !


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n=5 j1

=5 j2

=1

m=3(n-1)-2j1-j2=1


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presentaion of fluid