from manual drafting to cadbctill/20007/vickers/a8.pdf08/03/2001 from manual drafting to cad –...
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08/03/2001
From Manual Drafting to CAD
– Electronic drafting using a Computer-Aided Drafting (CAD) system
– Computer graphics and geometric modeling
– Design modeling using an advanced CAD/CAE/CAM system
– Finite element analysis– Engineering optimization– Virtual (Soft) prototyping
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Questions• What are the basic CAD techniques?
– Geometric representation and transformation– Solid and surface modeling– Parametric modeling and parameter optimization– Pre- and post- processors for Finite Element Analysis– Design and Mfg. database management
• What are the differences between a conventional 2D electronic drafting package and a full-scale CAD/CAE/CAM system? (Computer-Aided Design, Engineering and Manufacturing)
• What do we need to know to be a better user of the CAD system?– The basic CAD techniques– The capabilities and limitations of various CAD systems
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08/03/2001
Development of CAD• In 1960's
– mechanism design satisfying several geometric constraints– design parameter optimization– simple 2-D graphics
• In 1970's– wireframe modeling– free-form surface modeling – mainframe computers
• Late 1970's– solid modeling
• Early 1980's– CAD/CAM integration– mechanical feature recognition from a CAD database
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08/03/2001
• Middle 1980's– feature-based CAD system – mini and micro computers,– parametric design – PC's & Turnkey systems
(Pro/ENGINEER Products)
• Late 1980's– design for manufacturing– design for automated assembly
• 1990's– concurrent engineering design– integrated design, analysis and optimization– virtual-prototyping – workstations and high-end PCs
• 2000’s– robust concurrent design optimization– virtual engineering & enterprise
Development of CAD
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Unique Characteristics of A CAD System
Precision of Precision of Electronic Electronic GraphicsGraphics
Mathematical Mathematical Processing Power Processing Power of A Digital of A Digital ComputerComputer++
ProductProductDesign KnowledgeDesign Knowledge
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How are these models generated?
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How is Geometry represented in a CAD system?• Wireframe Model (low-level entities)
Points and Lines
• Solid Model (middle to high-level entities)Points, Primitives and Boolean Operations
• Surface Model (middle-level entities)Points, Boundary and Control Curves; Surface Patches
Representation of Low-level Geometry Entities:• Points: A 2D point – [x y]; and A 3D point – [x y z]
A vector representation of a 3D point: p = x i + y j + z k• Lines: two points• Planes: a collection of boundary lines• Components: a collection of boundary planes
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Why geometry transformation?• Better understanding of the design
• Communication with customers
• Generating various outputs
Common transformations:• Translation• Rotation• Scaling
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Applications of geometry transformation?
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3-D Transformation
TranslationTranslate point V(x, y, z) by (dx, dy, dz) to point V’(x’, y’, z’)
+
=
z
y
x
ddd
zyx
zyx
'''
y
z
o
xdx
dy
dzVV’
}
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3-D Transformation
Scaling
=
zyx
ss
s
zyx
z
y
x
000000
'''
o y
x
z
VV’
yy’
z z’
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3-D Transformation
Rotation
x
yV’(x’, y’)
V(x, y)θ
φ
o
y
zx
o
About z
θθθθ
cossin'sincos'
'
yxyyxx
zz
+=−=
=
−=
zyx
zyx
1000cossin0sincos
'''
θθθθ
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3-D Transformation
y
zV’(y’, z’)
V(y, z)θ
φ
o
Rotation
y
z
x oθθθθ
cossin'sincos'
'
zyzzyy
xx
+=−=
=
−=
zyx
zyx
θθθθ
cossin0sincos0
001
'''
About x
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3-D Transformation
z
x V’(z’, x’)
V(z, x)θ
φ
o
Rotation
y
z
x
o
θθθθ
sincos'cossin'
'
xzzxzx
yy
−=+=
=
−=
zyx
zyx
θθ
θθ
cos0sin010
sin0cos
'''
About y
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Homogeneous Representation
The representation is introduced to express all geometric transformations in the from of matrix multiplication for the convenience of manipulation.
Dummy (n+1)th coordinate to facilitate multiplication
=
11000100010001
1'''
zyx
ddd
zyx
z
y
x
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Homogeneous Representations
=
1000000000000
][z
y
x
ss
s
HScaling
Rotation
−=
10000cos0sin00100sin0cos
][θθ
θθ
yH
VHHHV nn ][]][[' 11 �−=
Composition of Transformation