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TotalReviewofComputer-aidedDesignandManufacturingScoreAssessmentAttendance(10%)Rollcall5times(2markseachtime)courseerercises(15%)Courseexerci

ses3times(5markseachtime)Termpaper(25%)Examination(50%)2-houropenbookpaper(CAD90%plusCAM10%),CalculationproblemsandnounsexplainExa

minationMaterialLecturenotesTutorialsandexercisesTeachingMaterial(MECHANICALENGINEERINGCAD/CAM)ReferencesbooksSurfacemodellingforCAD/CAM,Cha

pter1-5,7Geometricmodelling,chapter9-10.TheCNCWorkshop(ver2),chapter1Chapter1:InstructionWhatisCAD/CA

M/CAE/CAPP?Howistherelationshipamongthem?)WhatistheHISTORYofCAD/CAM?HardwareandsoftwareofCAD/CAMsystem?WhatisGeometricModellingan

ditstypicalapplications?Chapter2:CurvesFourcurvemodelsStandardpolynomialcurveFergusoncurveBeziercurveB-splinecurve

CurvefittingPolynomialCurveModelsCurveSegmentDefinition:Acubicpolynomialcurvemodel:r(u)=a+bu+cu2+du3usedinrepresentingacurvesegmentisspecifiedbyitse

ndconditions,e.g.,(a)4points(P0,P1,P2andP3)or(b)twoendpointsP0andP1;twoendtangentst0andt1.P0P1P2P3niiiar0u(u)Ingeneral,a

degree-npolynomialcurvecanbeusedtofit(n+1)datapoints.FergusonCurveModelConstructingacurvesegment:Joiningtwoendpoin

tsP0andP1;Havingspecifiedendtangentst0andt1i.e.,P0=r(0);P1=r(1);t0=r’(0);t1=r’(1)P1P0t1t0r(u)r(u)=UA=UMVwith0u1BezierCurveModel

with0u1OnevaluatingtheBezierequationanditsderivativeatu=0,1r(0)=V0r(1)=Vnr’(0)=n(V1–V0)r’(1)=n(Vn–Vn-1)BezierfoundafamilyoffunctionscalledB

ernsteinPolynomialsthatsatisfytheseconditions:BezierCurveModelCubic(n=3)BeziercurvemodelV0V1V2V3V3V2V1V0V2V1V0V3r(u)=(1–u)3V0+3u(1–u)2V

1+3u2(1–u)V2+u3V3r(u)==UMRr(0)=V0r’(0)=3(V1–V0)r(1)=V3r’(1)=3(V3–V2)Theshapeofthecurveresemblesthatofthecontrolpolygon.

B-splineModelwith0u1Ni,n(u)=TheprimaryfunctionB-splineModeldefinedbyn+1pointsViisgivenbytheWhereB-splineModelQuadrati

cuniformB-splinemodelwithcontrolpointsV0,V1,andV2r(t)=½[t2t1]=U3M3P30≤t≤1CubicuniformB-splinemodelwithcontrolpointsV0,V1,V2,andV3r

(t)=1/6[u3u2u1]=U4M4P40≤t≤1ParametricContinuityConditionTwocurvesegmentsra(u)andrb(u)ra(1)=P1=rb(0)(C0-

continuous)ra’(1)=t1=rb’(0)(C1-continuous)ra’’(1)=rb’’(0)(C2-continuous)CollectivelycalledaparametricC2-co

ndition.ThecompositecurvetopassthroughP0,P1,P2,andthetangentst0andt2areassumedtobegiven.Thus,theproblemhereistodetermineth

eunknownt1sothatthetwocurvesegmentsareC2-continuousatthecommonjoinP1.P0P1P2t2t0t1=?ra(u)rb(u)CubicSplineFitting(

FergusonModel)EmployingFergusoncurvemodelra(u)=UCSarb(u)=UCSbwith0u1U=[u3u2u1]C=1122123301000001

Sa=[P0P1t0t1]TSb=[P1P2t1t2]TApplyingC2continuity:ra’’(1)=6P0–6P1+2t0+4t1rb’’(0)=-6P1+6P2-4t1-2t2C0-c

ontinuityandC1-continuityalreadyappliedCubicSplineFitting（FergusonModel)ApplyingparametricC2-conditiont0+4t1+t2=3(P2–P0)N

ow,considerconstructingaC2-continuouscurvepassingthroughasequenceofn+1(P0toPn)pointsEndtangentst0andtnaregive

n,inadditiontothe(n+1)points{Pi}.(Howmanycurvesegments???)Therearetotallyncurvesegments.Foreachpairofneighbouringcurvesegmentsri-

1(u)andri(u),wehaveti-1+4ti+ti+1=3(Pi+1–Pi-1)fori=1,2,…,n–1B-splineModelOnevaluatingthecubicB-spline(k=4)anditsderivativeatt=1,0,r(

0)=[4V1+(V0+V2)]/6r(1)=[4V2+(V1+V3)]/6r’(0)=(V2–V0)/2r’(1)=(V3–V1)/2B-splinecurvesandBeziercurveshavemanyadvantagesincommonControlpointsinfluenc

ecurvesegmentshapeinapredictable,naturalway,makingthemgoodcandidatesforuseinaninteractivedesignenvironment.Bothtypesofcur

veareaxisindependent,multivalued,andbothexhibittheconvexhullproperty.B-splinecurveshaveadvantagesoverBe

ziercurves:Localcontrolofcurveshape.Theabilitytoaddcontrolpointswithoutincreasingthedegreeofthecurve.V0V1V3V2CubicSplineFittingEstimationofen

dtangents,t0andtnCircularendconditionPolynomialendconditionFreeendconditionChapter3:SurfacesFoursurfacepatchmodelsStandardpolynomialsurfacepa

tchFergusonsurfacepatchBeziersurfacepatchB-splinesurfacepatchThreeSurfaceConstructionMethodsTheFMILLmethodFergusonfitt

ingmethodB-splinefittingmethodCurvedBoundaryInterpolatingSurfacePatchesStandardPolynomialPatchModelConsideravector-valuedpolynomialfunc

tionr(u,v)whosedegreesarecubicinbothuandvwithcoefficientsdijfor(ui,vj).Thatisabi-cubic(standard)polynomialpatchdefinedasr(u

,v)=with0u,v1whichcanbeexpressedinamatrixformasr(u,v)=UDVTwhere,U=[u3u2u1],V=[v3v2v1],andthecoefficient

smatrixD=FergusonSurfacePatchModelSolvingthe16linearequationsfortheunknowncoefficientsdijgivesusaFergusonpatchequation:r(u,v)=UDVT=

UCQCTVTfor0u,v1C=Q=BezierSurfacePatchModelr(u,v)==UMBMTVT0u,v1WhereM=B=ThematrixMiscalleda(cubic)Beziercoeffic

ientmatrix,andBiscalledaBeziercontrolpointnetwhichformsacharacteristicpolyhedron.BezierSurfacePatchModelBezierpatchvs.FergusonPatchByevaluatingthec

ornerconditionsoftheBezierpatch,wehavethefollowingrelationships:Atu=0,v=0,r(0,0)=V00s00=3(V10–V00)t00=3(V01–V00)x00=9(V00–V01–V10+V11)B-

splineSurfacePatchModelConsidera44arrayofcontrolvertices{Vij}.r(u,v)==UNBNTVTfor0u,v1N=SurfaceConstru

ctionMethodsItisdesiredtouselowdegree(usuallycubic)polynomialpatchmodeltoformacompositesurface.Threemethodst

obeintroduced:TheFMILLmethodFergusonfittingmethodB-splinefittingmethodB-SplineSurfaceFittingComparisonbetweenFer

gusonfittingandB-splinefittingSamecompositesurfaceresultedWhenmakingfurtherchanges,localchangeforB-splinesurface,globalchangeforFergusonsu

rface.Question:Whenonecontrolpointischanged,howmanypatchesareaffected?CurvedBoundaryInterpolatingSurfacePatche

sMethodsofconstructingasurfacepatchinterpolatingtoasetofboundarycurves:RuledsurfacesLoftedsurfacesCoonssurfacesTwotypesofsweepsurfacepatches:Tr

anslationalsweeppatchesRotationalsweeppatchesRuledSurfacesConsidertwoparametriccurves,r0(u)andr1(u)with0u1(seefigure)

.Alinearblendingofthe2curvesdefinesasurfacepatchcalledaruledsurfacer(u,v)=r0(u)+v(r1(u)-r0(u));0u,v1Avectorinthedirectionofr1(u

)-r0(u)iscalledarulingvectort(u).TranslationalSweepSurfacePatchesInputSummaryTwoparametricspacecurves,g(u)andd(v).Atranslationalswe

epsurfaceisdefinedbythetrajectoryofthecurveg(u)sweptalongthesecondcurved(v).Themovingcurveg(u)iscalledageneratorcurveThegu

idingcurved(v)iscalledadirectorcurver(u,v)=g(u)+d(v)-d(0)0u,v1r(u,v)g(u)RotationalSweepSurfacePatchesAlsoknownassurf

aceofrevolutionConsiderasectioncurves(u)onthex-zplanes(u)=x(u)i+z(u)k=(x(u),0,z(u))Rotatethesectioncurves(u)aboutthez-a

xis,theresultingsweepsurfacecanbeexpressedasanparametricequationas:r(u,)=(x(u)cos,x(u)sin,z(u))r(u,)Chapter4:SolidModellingTwosolidmodelre

presentationschemesGraph-basedmodel(B-reps)Booleanmodel(CSG)EulerFormulaGraph-BasedModelsForsolidsrepresente

dasplanar-facedpolyhedron,manysimplerepresentationschemesareavailable,e.g.,connectivitymatrixforpolyhedron.Connectivit

ymatrix(oradjacencymatrix):Abinarymatrix0-elementindicatesnoconnectivityexists1-elementsindicateconnectivityexistsbetweenthepairofelements(vertices

,edges,orfaces).BooleanModelsThebinarytreeforthismodelTheleafnodesaretheprimitivesolids,withBooleanoperatorsateachinternalnodeandth

eroot.Eachinternalnodecombinesthetwoobjectsimmediatelybelowitinthetree,and,ifnecessary,transformstheresultinreadinessforthenextoperation.Basi

cConceptsofSolidModelEuler’slaw(orEuler’sformula)Foravalidsolid(polyhedron),thefollowingrelationshipmustbe

satisfied:V–E+F-(L–F)=2–2HV=NumberofverticesE=NumberofedgesF=NumberoffacesL=NumberofedgeloopsH=Numbero

fthroughholesThisexpressioncanalsobere-writtenas:V–E+F-R=2–2HWhereR=L–Fisthenumberofinterioredgeloops.ExternaledgeloopInterioredgelo

opChapter7:PartProgrammingandManufacturingWhatisCNC/NC?Howabouttheircharacteristics?)WhatisCNC/MC/FMS/CIMS?Howistherelation

shipamongthem?)WhatisthebasicconstructionforNCprogramming?HowtodeterminethecocrdinatesystemsofNCmachinetools?WhatisRP/RE

?Howabouttheircharacteristics?)TipYoushouldpreparesufficientmaterials.Youshouldbringyourscientificcalculator,notyouriPhon

e.Youmayneedaruler.Alloftheseformthescopeoftestinthefinalexam.ThefinaltipPractice,practice,andpractice…ThankyouWishyouforthebestgrad

es!