Module 2 CAD Methods and Systems

•Product Design and CAD

•CAD Systems hardware

•Geometric Modeling

•Solid Modeling

•Data Exchange Standards

•Rapid Prototyping

Integrated CAD/CAM

• Kernel in figure 2.1 should contain the complete description of the part – in sufficient views and appropriate format – to convey the full intent of the designer– Geometric modeling is very important to

CAD/CAM integration – it is the basis for future automated processes e.g. mathematical analyses, CAPP, automated inspection, etc.

Part description

• A part is fully defined by:– Geometric entities – dimensions, surface

finish, definition of surfaces and edges, fit and function

– Materials of manufacture and– functionality

[Show samples of part drawings and review format]

Geometric Modeling

• Understanding of geometric modeling concepts is essential to understanding engineering design

• Geometric representation of a part (product) is a necessary first step in mechanical and/or discrete part manufacturing

Definitions

• Geometric Modeling – a technique that uses computational geometry to define geometric objects. It has three components: 1) part design 2) part representation and 3) rendering.– Rendering (realistic image generation) – goal

is to generate a lifelike picture i.e. close as possible to picture of object.

Definitions

• Solid geometric modeling – subset of geometric modeling where only solid objects are defined

• Geometric primitives – starting tool set for geometric modelers e.g. lines, points, and surfaces.

Geometric Modeling Methods

• Multi-view Representation– 2-D drawing – part is described in plan, front, and side

views; and elevations– 3-d drawing – is derived by simultaneously examining

the three views and an elevation

• Wire frame geometry – 3-D vertices are entered as x, y, z triplets and are joined to create the 3-dimensional object. Wire frame geometry contains only points and lines and does not fully describe the part because ….???– Show wire frame figures

Geometric Modeling Methods

• Surface Modeling – adds surfaces to wire frame representations. Though an important improvement over wire frames, it does not contain a complete description of part entities to allow for important engineering calculations – like volume and mass properties

Geometric Modeling Methods

• Solid Modeling – data structure contain all vital data for use in design analyses and manufacturing planning programs:– Its introduction met an important mfg

requirement for fully automated and integrated design and mfg planning

– It also overcomes the difficulties of multi-view orthographic, wire frame, and surface modelers

Design Process-Figure

CAD Procedure•Fig 24.2(b)

•Geometric modeling – Create, Manipulate and/or Display a Mathematical model (database) of the geometry “graphics”

•Engineering analysis - more complicated and thorough analysis - Computer Aided Engineering e.g Finite Element and Tolerance analysis (Communicate with database).

•Design review and evaluation •Automatic dimensioning•Error Checking•Animation and Simulations•Rapid prototyping (Stereo-lithography and Virtual)

•Automated drafting (500% productivity improvement)

Typical CAD System

Computer

Graphics Terminal

Input Devices

SecondaryStorage

OutputDevice

Workstation

CAD System Hardware

ElectronicTablet

Input

DrumPlotter

Output

ComputerGraphics Terminal

Secondary StorageWorkstation

Other CAD Configurations

a) Host and Workstation –Fig 24.6(a)• Host is Mainframe or Minicomputer (Time –sharing)• For large data bases (automotive industry, weather

forecast)

b) Engineering Workstation – Fig 24.6(b)• Stand alone minicomputer • Share data between users and data storage (server)• High performance (3D)/Expensive

c) A PC-based system – Fig 24.6(c)

Other CAD configurations

Output Devices

• PlottersTypically, produce paper copies of large format (C-, D- and E-sizes and nonstandard sizes) finished drawings.

• PrintersProduce a small format (A- or B-size) hardcopy of geometric models, sketches and drawings.

Reported Benefits of CAD• Increased the productivity of the designer (CAD

improves conceptualization) • Enhanced design quality (variety of design and

analysis)• Improved design documentation (legibility, fewer

errors, standardization)• Development of manufacturing data base

ANSI Y14.xXStandard

ISO Standard

Engineering Drawing - Fig 2.2

Datum

Dimensional TolerancesGeometric Characteristic

Geometric Modeling Techniques

• Representation Techniques

2D Multiple Views (projections)3D Wire Frame Model3D Surface Model3D Solid Model

2D Multiple Views (example)

Orthographic Projection Isometric View

More projections maybe needed for more complicated objects

Top

Front Right Side

Convention?

2D Multiple Views (projections)

– 2D views of 3D geometry (Fig 2.3)

– Objects are represented by points (vertices), lines (edges) and curves (primitives)

– Drafting oriented (limited use in design)

– No relations between points and lines (connectivity) in the different views (not 3D part?)

–Used for NC sheet metal

3-D Wire frames (Fig 2.5)

3-D Wire frames (Fig 2.6 & 2.7)

3-D Wire frames

• Stick or wire diagrams represent objects (connect dots – no information about surfaces ‘meaningless objects’)

• Points and lines (vertices and edges) are the primitives and are defined in 3D

• Ambiguous and incomplete representation

• Hidden lines can be removed to improve visualization of shape (colors?)

• Simple to create and manipulate

3-D Surface Model• Include information about surfaces

•Data (vertices & edges) is entered in an ordered manner to define surfaces.

• The modeler does not recognize inside or outside of an object (does not store topology – relationship between primitives)

• The modeler can not determine the physical properties of the object

•Adequate for NC machining

3-D Solid Models• Offer complete and unambiguous definition of

solids – construct a realizable solid • Six methods are available to construct models,

the following are the most used– Pure Primitive Instancing (PPI)– Sweeping (S)– Constructive Solid Geometry (CSG)– Boundary Representation (BREP)

Pure Primitive Instancing (PPI)

PPI involves recalling the already stored primitive solids (Fig 2.24) . Primitive solids include cubes, spheres, cylinders, and others

Sweeping (S)

•Sweeping refers to generation of volumes by moving polygon or polyhedron into space (Fig 2.26)

Fig 2.26 Sweeping Examples

Constructive Solid Geometry (CSG)•CSG uses Boolean operations on solids (PPI and others)

Boolean Operations addition (+ or ) subtraction (-) intersection (* or )

Fig 2.27

2-D

3-D

Boundary Representation (BREP)

•BREP enters all bounding edges (in a specific order) for all surfaces to create valid volume (realizable volume)

•BREP stores the actual part (vertices, edges, faces, dimensions, topology,etc-)

3D Solid Modeler: Storage of Data Base

•Two forms of data base storage CSG and BREP (similar in concepts to construction techniques) (Fig 2.30)

CSG stores the instruction for how to make the part (implicit)

BREP stores the actual part data (vertices, edges, and faces); geometry and topology (explicit)

BREP database is Larger than CSG

Efficiency of data structure is measured by ?

•Example (Fig 2.31 )

• BREP of cylinder (what about sphere or cone?)

F1E1

E2

E3

Most modern modelers provide several types of construction techniques, but immediately convert each type to an internal B-Rep data structure.

Validity Check

• A solid modeler must guarantee that the object created is, in fact, a real (valid) solid object.

• Euler's equation can be used on B-Rep data (available directly or extracted from CSG models) to validate that a model represents a real polyhedron.For simple polyhedron

V – E + F = 2

For multiple polyhedra

V – E + F – H + 2P – 2S = 0

V = No. of vertices E = No. of edges F = No. of faces H = No. interior loops (connected edges) P= No. of passage ways

S = No. exterior shell (connected surfaces)

Validity Check: Examples

Cube

Hole

•Cylinder with thru hole

a) Apply to the whole objectRule: V – E + F – H + 2P – 2 S = 0 Total 10 – 15 + 7 – 2 + 2(1) – 2(1) = 0

b) Apply to individual objectsRule: V – E + F – H + 2P – 2 S = 0Cube: 8 – 12 + 6 – 0 + 2(0) – 2(1) Hole: 2 – 3 + 1 – 2 + 2(1) – 2(0) Total 10 – 15 + 7 – 2 + 2(1) – 2(1) = 0

F1E1

E2

E3

V1

V2

• Solid cube

Validity Check: Revisited

Euler Formula V – E + F – H + 2P – 2 S = 0

• Can be applied successfully to combined geometries of an object

• Caution should be exercised when applied to individual geometries of

an object (it does not add up for objects with protrusions!)

• Subface (sub-surface) implicitly indicates an inner loop (H=1) and it

it does not hold significant volume

• Study Example in handout (p 22) and validate the geometry (Fig 2.28)

Part Feature Recognition

• Definitions:– Feature - a general term applied to a

physical portion of a part, such as a surface, hole, or slot.

– feature-of-size - is one cylindrical or spherical surface or a set of parallel surfaces, each of which is associated with a size dimension.

Feature-Based Design

• because of non-unique feature construction process between designers, part design and process/manufacturing planning have become two distinct activities with slightly different emphases:– design - fit, form and function– manufacturing planner - feature

recognition, process selection and sequence definition.

CAD Data Transfer Standards• Standard exchange formats (neutral format) permit the sharing

of CAD databases across different systems.

System AStandardFormat

System B

System K

System Z

• Why use a standard exchange format?• To transfer CAD files without loss of information• To ease reuse of data internally (applications) or externally

(suppliers)• To archive data for future use despite changes in systems• Minimize transmission and processing costs (encoding)

CAD Data Transfer Standards:Proprietary and De-facto Standards

• IGES (Initial Graphics Exchange Specification): It is an ISO standard for the majority of 2D and 3D systems.

• PDES(Product Definition Exchange Specification) More comprehensive (primitives, material type, and process plan)

• DXF (Drawing eXchange File): Originally developed by AutoCAD. Creates ASCII data files. Very common .Many applications

Selecting a Solid Modeler

•Flexibility - Multiple construction techniques.

•Robustness - consistency (minimal errors) in creating realizable objects

•Simplicity - Pull down menus

•Performance - ?

•Cost

Rapid Prototyping:Stereolithography with Acrylic Resin

• The CAD solid model is converted into a vertical stack of slices as thin as 0.0025”(STL file) for up to 20”x20” objects.

• The slices are used to guide a laser beam and solidify the cor-responding layers in the photo-polymer.

Photocurableliquid polymer (Acrylate Resin)

Ultravioletlaser beam

Object is builtup layer by layer

• The cured acrylic prototypes are not as strong mechanically as the real parts, but have high dimensional accuracy (about 200 inches) suitable for checking space requirements and verifying design concepts.

Geometric Transformation

Modify display (modify data structure)

Transformations: Definitions• Translation

a' = T aa b

c Ta' b'

c'

• Rotation

a' = Rz ab

c

a

Rzb'

c'

a'

x

y

a

a'

• Scaling

a' = S a a b

cS

a' b'

c'

Transformations: Rotation

x

y

p

p

Rz

p (x,y) =xy

x

y

x'

y'p'(x',y') =y'

x'

x' = p cos (p coscosp sinsiny' = p sin (p cossinpsincos

but p cos (xand p sin= y or x'

y' =x cos ysinx siny cos

x'

y'

1=

xy1

cos -sin sin cos 0 0 1

p'(x',y') = Rz p (x,y)The transformation matrix Rz transforms any point having a rotation about the z-axis at the origin.

Replace with x and y

Transformations: Translation

x

y

x

y p (x,y) =xy

T ?y'

x'

x'

y'p'(x',y') =

The transformation matrix Ttransforms any point, giving itplanar displacements x and yalong the x- and y-axis respectively.

x

y

x' = x + xy' = y + y

algebraicform

orx'

y' = xy

+ xy

vectorform

homogeneouscoordinates

p'(x',y') = T p (x,y)matrix form

x'

y'

1

=xy1

1 0 x 0 1 y0 0 1

Matrix Addition to Multiplication (homogeneous coordinates)

Must Equal ‘1’

Transformations: Scaling

x

yp (x,y)

x

y

p'(x',y')

x'

y'S

p

p'

Scaling operation simply requires multiplying each coordinate with its corresponding scale factor sx or sy.Thus x' = sx x and y' = sy y

or x'

y' =sx xsy y

Non-uniformscaling

x'

y'

1=

xy1

sx 0 0 sy 0 0 1

For uniform scaling, sx = sy = s = scale factor

s = p'/p

1 0 0 1

0 0 1/s

S =

The transformation matrix Stransforms any point beingscaled by a factor s = sx = sy

with respect to the origin.

Negative Scaling?

p'(x',y') = S p (x,y)

2D Transformation Formulas

x'

y'

1=

xy1

sx 0 0 sy 0 0 1

Scaling

p'(x',y') = S p (x,y)

=xy1

cos -sin sin cos 0 0 1

x'

y'

1

Rotation

p'(x',y') = R p (x,y)

Translation x'

y'

1

=xy1

1 0 x 0 1 y0 0 1p'(x',y') = T p (x,y)

Translation ExampleThe corner a of the triangle moved from (4,1) to(1,3), what is the translation transformation matrixT? If points b and c where initially at points (5,3)and (6,1) respectively, determine the new coord-inates c' and b' using T.

0 x

y

1 2 3 4 5 6

2

3

4

1

5

6

(4,1)a

b

c(6,1)

(5,3)

(1,3)

a'

b'

c'

T ?

Solution:the displacements x and y arex = final coord. initial coord. = x' x = 1 4 = 3y = final coord. initial coord. = y' y = 3 1 = 2

Thus, T = 1 0 x 0 1 y0 0 1

1 0 0 1 0 0 1

=

Check point a , a' = T a = 1 0 0 1 0 0 1

1

= 1

which is ok.

b' = T b = 1 0 0 1 0 0 1

1

= 2 1

and c' = T c = 1 0 0 1 0 0 1

1

=

1

Rotation ExampleThe corner a of the triangle is initially at point (4,1). If the triangle is rotated 60o about the z-axis at the origin, what is the rotation matrix R? What is the new position of point a? If points b and c were initially at points (5,3) and (6,1) respectively, what are the new coordinates of c' and b' using R?

0x

y

1 2 3 4 5 6

2

3

4

1

5

6

(4,1)a

b

c (6,1)

(5,3)

60o

a'b'

c'

R ?Solution:

R = cos -sin sin cos 0 0 1

=1/2 -

1/2 0 0 1

a' = R a = 1

1/2 1/2 0 0 1

=

2 1

=

1

b' = R b = 1

1/2 1/2 0 0 1

=0.098 5.830

1c' = R c =

1

=2.1345.696

1

1/2 1/2 0 0 1

Scaling ExampleThe vertex (corner) a of the polygon is initially positioned atpoint (3,1). If the polygon is scaled uniformly by 50% (0.50) about the origin, what is the scaling matrix S? What is the new position of vertex a? If points b and c where initially at points (3,3) and (0,2) respectively, determine the new coordinates c' and b' using S.

x1 2 3-1-2 0

y

2

3

1

-1

-2

a

b

c

a'

b'c'

Solution:For a scale factor s= 0.5, the scaling matrix S is

1 0 0 1

0 0 1/s

S = =1 0 0 1

0 0 1/0.5

= 1 0 0 1 0 0 2

a' = S a = 1

1 0 0 1 0 0 2

= 3 1 2

= 1.5 0.5 1

The transformed vector must be normalized so that the homogeneous coordinate is 1, thus the division by 2.

b' = S b = 1

1 0 0 1 0 0 2

= 3 3 2

= 1.5 1.5 1

c' = S c = 1

1 0 0 1 0 0 2

= 0 2 2

= 0 1 1

Combined Transformations• Different transformations can be combined

by forming the product of their respective transformation matrices in a proper order.

• Rotating an object about a point other than the origin requires the following sequence: a translation T1 to the origin

followed by a rotation R at the origin

a trip T2 to bring the object back to its original location.

Effective rotationabout a point otherthan the origin.

x1 2 3-1-2 0

y

2

3

1

-1

-2

T1

R

T2

• The combined operations are represented by the matrix M:

M = T2 RT1

• Note that the right most transformation is always the first one applied and the left most is the transformation applied last. Similar procedure should be

followed for scaling

3D Transformation Matrices

• The 2D transformations discussed so far can be generalized into 3D by adding the z-coordinate which requires 4x4 matrices instead of the 3x3 matrices used for 2D.

• 3D translation, rotation and scaling matrices are

T (x, y, z) = 1 0 0 x

1 y0 1 z

0 0 0 1

S (s) = 1 0 0

1 0 1

0 0 0 1/s

Rx () = 1 0 0 0

cos sin sin cos 0 0 0 1

Ry () = cos sin

0 1 sin 0 cos 0

0 0 0 1

Rz () = cos sin sin cos 0 0 1 0

0 0 0 1