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

3times(5markseachtime)Termpaper(25%)Examination(50%)2-houropenbookpaper(CAD90%plusCAM10%),Calculationproblemsandnouns

explainExaminationMaterialLecturenotesTutorialsandexercisesTeachingMaterial(MECHANICALENGINEERINGCAD/CAM)ReferencesbooksSurfacem

odellingforCAD/CAM,Chapter1-5,7Geometricmodelling,chapter9-10.TheCNCWorkshop(ver2),chapter1Chapter1:InstructionWha

tisCAD/CAM/CAE/CAPP?Howistherelationshipamongthem?)WhatistheHISTORYofCAD/CAM?HardwareandsoftwareofCAD/CAMsystem?WhatisGeometricModellinganditstypi

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

odelsCurveSegmentDefinition:Acubicpolynomialcurvemodel:r(u)=a+bu+cu2+du3usedinrepresentingacurvesegment

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

ngeneral,adegree-npolynomialcurvecanbeusedtofit(n+1)datapoints.FergusonCurveModelConstructingacurvesegment:JoiningtwoendpointsP0andP1

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

Modelwith0u1OnevaluatingtheBezierequationanditsderivativeatu=0,1r(0)=V0r(1)=Vnr’(0)=n(V1–V0)r’(1)=n(Vn–Vn-1)Bezierfoundafamilyoffunct

ionscalledBernsteinPolynomialsthatsatisfytheseconditions:BezierCurveModelCubic(n=3)BeziercurvemodelV0V1V2V3V3V2V1V0V2V1V0V3r

(u)=(1–u)3V0+3u(1–u)2V1+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-spl

ineModelQuadraticuniformB-splinemodelwithcontrolpointsV0,V1,andV2r(t)=½[t2t1]=U3M3P30≤t≤1CubicuniformB-splinemodelwithcontrolpointsV

0,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)Collectivelycalledaparame

tricC2-condition.ThecompositecurvetopassthroughP0,P1,P2,andthetangentst0andt2areassumedtobegiven.Thus,theproblemhereistodeterminetheunknownt

1sothatthetwocurvesegmentsareC2-continuousatthecommonjoinP1.P0P1P2t2t0t1=?ra(u)rb(u)CubicSplineFitti

ng(FergusonModel)EmployingFergusoncurvemodelra(u)=UCSarb(u)=UCSbwith0u1U=[u3u2u1]C=1122123301000001Sa=[P0P1t0t1]TSb=[P1P2t1

t2]TApplyingC2continuity:ra’’(1)=6P0–6P1+2t0+4t1rb’’(0)=-6P1+6P2-4t1-2t2C0-continuityandC1-continuityalr

eadyappliedCubicSplineFitting（FergusonModel)ApplyingparametricC2-conditiont0+4t1+t2=3(P2–P0)Now,considerconstructingaC2-continuouscurvepassin

gthroughasequenceofn+1(P0toPn)pointsEndtangentst0andtnaregiven,inadditiontothe(n+1)points{Pi}.(Howmanycurvesegmen

ts???)Therearetotallyncurvesegments.Foreachpairofneighbouringcurvesegmentsri-1(u)andri(u),wehaveti-1+4ti+ti+1=3(P

i+1–Pi-1)fori=1,2,…,n–1B-splineModelOnevaluatingthecubicB-spline(k=4)anditsderivativeatt=1,0,r(0)=[4V1+(V0+V2)]/6

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

influencecurvesegmentshapeinapredictable,naturalway,makingthemgoodcandidatesforuseinaninteractivedesignenvironment.Bot

htypesofcurveareaxisindependent,multivalued,andbothexhibittheconvexhullproperty.B-splinecurveshaveadvantagesoverBe

ziercurves:Localcontrolofcurveshape.Theabilitytoaddcontrolpointswithoutincreasingthedegreeofthecurve.V0V1V3V

2CubicSplineFittingEstimationofendtangents,t0andtnCircularendconditionPolynomialendconditionFreeendconditionChapter3:S

urfacesFoursurfacepatchmodelsStandardpolynomialsurfacepatchFergusonsurfacepatchBeziersurfacepatchB-splinesurfa

cepatchThreeSurfaceConstructionMethodsTheFMILLmethodFergusonfittingmethodB-splinefittingmethodCurvedBoundaryInterpolati

ngSurfacePatchesStandardPolynomialPatchModelConsideravector-valuedpolynomialfunctionr(u,v)whosedegreesarecubic

inbothuandvwithcoefficientsdijfor(ui,vj).Thatisabi-cubic(standard)polynomialpatchdefinedasr(u,v)=with0u,v1whichcanbeexpressedinamatrixformasr(u

,v)=UDVTwhere,U=[u3u2u1],V=[v3v2v1],andthecoefficientsmatrixD=FergusonSurfacePatchModelSolvingthe16lineareq

uationsfortheunknowncoefficientsdijgivesusaFergusonpatchequation:r(u,v)=UDVT=UCQCTVTfor0u,v1C=Q=BezierSurfacePatchModelr(u,v)==UMBMTVT0u,v1

WhereM=B=ThematrixMiscalleda(cubic)Beziercoefficientmatrix,andBiscalledaBeziercontrolpointnetwhichformsacharacteristicpolyhedron.BezierSurfacePatchMo

delBezierpatchvs.FergusonPatchByevaluatingthecornerconditionsoftheBezierpatch,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)==UNB

NTVTfor0u,v1N=SurfaceConstructionMethodsItisdesiredtouselowdegree(usuallycubic)polynomialpatchmodeltoformac

ompositesurface.Threemethodstobeintroduced:TheFMILLmethodFergusonfittingmethodB-splinefittingmethodB-SplineSurfaceFitt

ingComparisonbetweenFergusonfittingandB-splinefittingSamecompositesurfaceresultedWhenmakingfurtherc

hanges,localchangeforB-splinesurface,globalchangeforFergusonsurface.Question:Whenonecontrolpointischanged,howmanypatchesareaffected?CurvedBoundaryI

nterpolatingSurfacePatchesMethodsofconstructingasurfacepatchinterpolatingtoasetofboundarycurves:RuledsurfacesLoftedsurface

sCoonssurfacesTwotypesofsweepsurfacepatches:TranslationalsweeppatchesRotationalsweeppatchesRuledSurfacesConsi

dertwoparametriccurves,r0(u)andr1(u)with0u1(seefigure).Alinearblendingofthe2curvesdefinesasurfacepatc

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

lingvectort(u).TranslationalSweepSurfacePatchesInputSummaryTwoparametricspacecurves,g(u)andd(v).Atranslationalsweepsurfaceisdef

inedbythetrajectoryofthecurveg(u)sweptalongthesecondcurved(v).Themovingcurveg(u)iscalledageneratorcurveTheguidingcurv

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

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

cecanbeexpressedasanparametricequationas:r(u,)=(x(u)cos,x(u)sin,z(u))r(u,)Chapter4:SolidModellingTwosolidmodelrepresentationschemesGraph-

basedmodel(B-reps)Booleanmodel(CSG)EulerFormulaGraph-BasedModelsForsolidsrepresentedasplanar-facedpolyhedron,manysimplereprese

ntationschemesareavailable,e.g.,connectivitymatrixforpolyhedron.Connectivitymatrix(oradjacencymatrix):Abinarymatrix0-elementin

dicatesnoconnectivityexists1-elementsindicateconnectivityexistsbetweenthepairofelements(vertices,edges,orfaces).BooleanModel

sThebinarytreeforthismodelTheleafnodesaretheprimitivesolids,withBooleanoperatorsateachinternalnodeandtheroot.Eachinternalnodecom

binesthetwoobjectsimmediatelybelowitinthetree,and,ifnecessary,transformstheresultinreadinessforthenextoperation.

BasicConceptsofSolidModelEuler’slaw(orEuler’sformula)Foravalidsolid(polyhedron),thefollowingrelationshipmustbesatisfied:V–E+F-(L–F)=2–2H

V=NumberofverticesE=NumberofedgesF=NumberoffacesL=NumberofedgeloopsH=NumberofthroughholesThisexpressi

oncanalsobere-writtenas:V–E+F-R=2–2HWhereR=L–Fisthenumberofinterioredgeloops.ExternaledgeloopInterioredgeloopChapter7:Part

ProgrammingandManufacturingWhatisCNC/NC?Howabouttheircharacteristics?)WhatisCNC/MC/FMS/CIMS?Howistherelationshipamongthem?)Whatisth

ebasicconstructionforNCprogramming?HowtodeterminethecocrdinatesystemsofNCmachinetools?WhatisRP/RE?Howaboutth

eircharacteristics?)TipYoushouldpreparesufficientmaterials.Youshouldbringyourscientificcalculator,notyouri

Phone.Youmayneedaruler.Alloftheseformthescopeoftestinthefinalexam.ThefinaltipPractice,practice,andpractice…ThankyouWishyouforthebestgrades

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