Geometric modeling

CAD/CAM Subject-Mechanical engineering

1. UNIT -2: Geometric Modeling
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By
Dr.D.Sreeramulu,
Professor,
AITAM, Tekkali.

2. ®Educational Purpose Only
Introduction
•Geometric modeling is the process in which a model of the given
design/drawing is created to represent the size and shape of the
component.
•The amount of time and effort a designer spends in creating a
geometric model cannot be justified unless the resulting database
is utilized by the applications module, i.e. Product Cycle for
Manufacturing.
Product Cycle in a Manufacturing Environment

3. Requirements
The functions that are expected of geometric modeling are:
•Design and Design Analysis
Evaluation of areas and volumes.
Evaluation of mass and inertia properties.
Interference checking in assemblies.
Analysis of tolerance build-up in assemblies.
Analysis of kinematics –mechanics, robotics.
Automatic mesh generation for finite element analysis.
•Drafting
Automatic planar cross sectioning
Automatic hidden line and surface removal.
Automatic production of shaded images.
Automatic dimensioning.
Automatic creation of exploded views for technical illustrations.
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4. •Manufacturing
Parts classification.
Process planning.
Numerical control data generation and verification.
Robot program generation.
•Production Engineering:
Bill of materials.
Material requirement.
Manufacturing resource requirement.
Scheduling.
•Inspection and Quality control
Program generation for inspection machines.
Comparison of produced part with design.
Requirements
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5. Geometric Models
In general, there are three types of models, namely
Wire frame models(Edge Model, Line Model, Skelton Model)
Surface models (Area Model)
Solid or Volume models
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6. WireFrameModels
•Awireframemodelofanobjectisthesimplest,butverbose,
geometricmodelthatcanbeusedtorepresentitmathematically
inthecomputer.
•Typically,awireframemodelconsistsentirelyofpoints,lines,
arcs,andcircles,conics,andcurves.
•Advantages:-
Wireframemodelsaresimpleandeasetocreate
Theyrequirerelativelylittlecomputertimeandmemory.
It’sconsideredasthenaturalextensionoftraditional
methodsdrafting.
Thesecanformsthebasisforthesurfacemodels.
•Disadvantage:-Theseareambiguousrepresentationsofthereal
objects
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7. Wireframe Models
These wire frame entities are divided into Analyticand Synthetic
entities.
•Analyticentitiesarepoints,lines,arcsandcircles,filletsand
chamfersandconics(ellipses,parabolasandhyperbolas).
•Syntheticentitiesincludevarioustypesofsplines(cubicspline,
B-spline,β(beta)-spline,γ(nu)-spline)andBeziercurves.
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8. Surface Models
•ASurfacemodelofanobjectcanbebuiltbydefiningthesurfaces
onthewireframemodel.Itrepresentsonlyanenvelopeofpart
geometry.(Hollow)
•Typically,asurfacemodelconsistsofanalyticandsyntheticentitieslike
Planesurface,Ruled(lofted)surface,Surfaceofrevolution,Tabulated
cylinder,Beziersurface,B-splinesurface,CoonspatchandOffsetsurface.
•Advantages:-
Thesearelessambiguousthanwireframemodels
SurfaceModelsarericherinitsassociatedgeometricconstraints,
whichmakesmoresuitableforengineeringanddesign
applications.
•Disadvantages:-
Thesedon’tlendthemselvestodraftingbackground.
Moretrainingandmathematicalbackgroundisneededby
theuser
MoreCPUtimeandmorestoragespacecomparedtowireframe.
Attimes,thereisascopeofconfusionforidentifyingbetween
surfaceandsolidmodels.
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9. Surface Models
•Different Analytic surface entities are :
1.PlaneSurface:Thisisthesimplestsurfaceandrequiresthreenon-
coincidentpointstodefineaninfiniteplane.Thisisusedtogenerate
c/sviewsbyintersectingasurfacemodelwithit,formassproperty
calculationswhereaplaneisneeded.
2.Ruledsurface(Loftedsurface):-Thisisalinearsurfacewhich
interpolateslinearlybetweentwoboundarycurvesthatdefinesthe
surface(rails).
3.Surfaceofrevolution:-Thisisanaxis-symmetricsurfacethatcan
modelaxi-symmetricobjects.It’sgeneratedbyrotatingorrevolvinga
planarwireframeentityinspaceabouttheaxisofsymmetryata
certainangle.
4.Tabulatedsurface:-It’sasurfacegeneratedbytranslatingaplanar
curveacertaindistancealongaspecifieddirection.It’susedto
generatesurfacesthathaveidenticalcurvedcrosssections.
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10. Surface Models
•Different Synthetic surface entities are :
1.Beziersurface:-It’sasurfacethatapproximatesgiveninputdataand
isdifferentfromthepreviousthatitisasyntheticcurve.It’sageneral
surfacethatcannotpassthroughallthedatapointsandpermits
twistsandkinks.Itallowsonlyglobalcontrolofthesurface.
2.B-Splinesurface:-It’sasurfacethatapproximateorinterpolate
giveninputdata.It’sasyntheticsurfaceandit’slikeaBeziersurface
butpermitslocalcontrol.
3.Coonspatch:-Thisisusedtocreateasurfaceusingcurvesthatform
closedboundaries.
4.Filletsurface:-It’saB-Splinesurfacethatblendstwosurfaces
together.Thetwooriginalsurfacesmayormaynotbetrimmed.
5.Offsetsurface:-It’sausefulsurfacetousetospeedupsurface
construction.Offsetcommandbecomesveryefficienttouseifthe
originalsurfaceisacompositeone.Forexample,tocreateahollow
cylinder,theoutercylindercanbecreatedbyusingcylinder
commandandtheinneronecreatedbyusingoffsetcommand.
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11. ®Educational Purpose Only
Surface Models
•Surface Models define only the geometry of their corresponding objects. They store
no information about the topology of the objects.
ForExample;iftherearetwosurfaceentitiesthatshareawireframeentity(edge),
neitherthesurfacesnortheentitywillstorewillstoresuchinformation.

12. •Thehighestlevelofsophisticationingeometricmodelingis3Dmodeling.
•Solidmodelsarebetter,inthesensethattheyallowthesolidnatureofan
objecttobedefinedinthecomputerandthushelptocalculatemass
properties.
•Advantages:-
1.Asolidmodelofanobjectisamorecompleterepresentationthanits
surfacemodel.
2.Asolidmodelconsistsofboththetopologicalandgeometricaldataof
itscorrespondingobject.
3.Solidmodelscanbequicklycreatedwithouthavingtodefineindividual
locationsaswithwireframes.(CSG)
4.Colorgraphicscapacityisanotherverypowerfultoolwhichhelpsto
classifycomponentsinanassemblyorhighlightdimensions.
Solid Models
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13. •Fortheconstructionofsolidmodelstwoapproachesareused:-
i)primitivemodelingii)boundarymodeling.
Inthefirstapproach,elementarygeometricshapesoftencalled
primitivesarecombinedtocreatecomplexsolidmodels.Thisapproachis
knownasbuildingblockmodeling(CSG).
The most commonly used solid primitives are the block, cylinder, cone and
sphere.
BLOCK:This is a box whose geometrical data is its Width, Height and
Depth. Its local coordinate system is X
L, Y
L, and Z
L as shown in figure. The
point P is its origin and W, H, D determines the location with respect to the
coordinate system.
CYLINDER:It’s a right circular cylinder whose geometry is defined by its
radius R and height H. The length of H is usually taken along the direction
of the Z
L–axis.
CONE:It’s a right circular cone whose base radius R and height H is user
defined.
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Solid Models

14. SPHERE: It’s defined by its radius or diameter and is centered about
origin of its local coordinate system.
WEDGE: It’s a right-angled wedge whose height H, width W and base
depth D from its geometric data.
TORUS: It’s a primitive that is generated by the revolution of a circle
about an axis lying in its plane. Its geometry can be defined either by the
body radius R1 and the torus body centerline radius R
2or by its inner
radius R
1and outer radius R
0.
InBoundaryModeling(B-Rep),whichisalsoknownasperimeter
modeling;elasticlinesarestretchedtoformtheoutlinestodefinethe
boundaryoftheparttobemodeled.Theprinciplebehindthis
modelingisthatpartgeometryisdifferentfromparttopologyandthat
theycanbedefinedseparately.
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Solid Models

15. Generallythetechnicaldrawingconsistsofalotofinformationbesidesthe
simplevieworthegeometricrepresentation.Thegeometricconstruction
methodsemployedtomakeuseofthenormalinformationavailableatthe
productdesignstageandalsobeassimpleaspossibleinconstruction.
The3Dgeometricconstructionmethods,whichextendfromthe
2D,are:
•LinearextrusionorTranslationalsweep,and
•Rotationalsweep.
Inlinearextrusion,initiallya2Dsurfaceisgeneratedandthen
sweptalongastraightlinethusgeneratingthirddimensionanditis
possibletorepeatthesametechniqueforgeneratingreasonablycomplex
geometry.Thesweepdirectioncanbeany3Dspacecurveandneednotto
beastraightline.
Geometric Construction methods
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16. Anothertypeofconstructiontechniqueistherotationalsweep,
whichcanbeutilizedonlyforaxi-symmetricjobs.Thistypeisused
forallaxi-symmetriccomponentssuchasbottlesusedforvarious
applications.
Therotationalsweepcanbeenhancedbytheadditionof
axialand/orradialoffsetwhilesweepingtogethelicalorspiral
objects.InCAM,sweepcanbeusedinthematerialremoval
operationstocalculatethetoolpaths.Thevolumesweptbythetool
whensubtractedfromtheblankwillgeneratethefinalshape
required.
Geometric Construction methods

17. CSG:isavolumetricrepresentationinwhichasolidobjectisexplicitly
representedbyanorderedbinarytree.Theleavesofthetreeareinstancesof
primitivesolids.TheintermediatenodescontainregularizedBooleanoperations
includingunion,intersection,anddifference
1. Constructive Solid Geometry

18. 2. Boundary Representation (B-rep)
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F3
F4
F5
F6
F1 F2 F3 F4 F5 F6
E1 E2 E3 E4

19. Thank you
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