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COMPUTER AIDED DESIGN
Dr. Maqsood Ahmed Khanmaqsoodahmed@neduet.edu.pk
Course PlanTopic Lectures
Fundamentals of CAD 02
Geometric Modeling
1. Representation of Curves 02
2. Representation of Surfaces 02
3. Geometric Modeling Systems 01
4. Manipulation of Curves and Surfaces 02
5. Modeling Techniques (Solid, Surface, Wireframe) 02
CAD/CAM Software
Transformations (2D and 3D) 02
Concurrent Engineering 02
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Course Plan
Software : CATIA V5 (R18) ; Matlab R2008a
Marks Distribution :
1. Final theory paper = 60 Marks2. Sessional Marks
i. Attendance = 16ii. Project = 14 iii. Midterm Exam = 10
40 Marks
Books
Mastering CAD/CAM by Ibrahim Zeid
Principles of CAD/CAM/CAE Systems
by Kunwoo Lee
CAD/CAM Principles and Applications
by P N Rao
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Introduction
� CAD/CAM is a term which means computer-aided design andcomputer-aided manufacturing.
� It is the technology concerned with the use of digital computersto perform certain functions in design and production.
� It is a bridge between design and manufacturing.
� Definition-CAD
Computer-aided design (CAD) can be defined as the use ofcomputer systems to assist in the creation, modification,analysis, and optimization of a design.
Computer System
The computer system consists of the hardware and software to perform
the specialized design functions.
The CAD hardware
Typically consists of the computer, one or more graphic display
terminals, keyboards, and other peripheral devices.
The CAD software
Consists of the computer graphic programs to implement computer
graphics on the system plus application programs to facilitate the
engineering functions (stress-strain analysis, dynamic response of
mechanisms, heat-transfer calculations etc.) of the company
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The Product Cycle and CAD/CAM
Product Cycle: Various activities and functions that must beaccomplished in the design and manufacture of a product is termedas the product cycle.
Product Cycle without CAD/CAM
Product Cycle with CAD/CAM
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Reasons of Using CAD
To increase the productivity of the designer
This is accomplished by helping the designer to visualize the
product and its component subassemblies and parts; and by
reducing the time required in synthesizing, analyzing, and
documenting the design.
To improve the quality of design
A CAD system permits a more thorough engineering analysis using
different analysis software (ANSYS, ABAQUS, and Nastran) and
larger number of design alternatives can be investigated.
Reasons of Using CAD
To improve communication
Use of a CAD system provides better engineering drawings, more
standardization in the drawings, better communication of the
design, fewer drawing errors, and greater legibility.
To create a data base for manufacturing
In the process of creating the documentation for the product design
(geometries and dimensions of the product and its components,
material specifications, BOM etc.), much of the required data base
to manufacture the product is also created.
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Analysis Tools
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Injection Molding - Moldflow by Autodesk
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Plastic injection molding simulation software provides toolsthat help manufacturers validate and optimize the design ofplastic parts and injection molds by accurately predictingthe plastic injection molding process
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Sheet Metal Design-NX by Siemens
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The Conventional Design Process
The process of designing is characterized as an iterative procedure,
which consists of six identifiable steps
Recognition of need
It involves the realization by someone that a problem exists for
which some corrective action should be taken.
Definition of problem
It involves a thorough specification (physical and functional
characteristics, cost, quality, and operating performance) of the
item to be designed
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The Conventional Design Process
Synthesis
Conceptualization of a product
Analysis and optimization
Evaluation
Measuring the design against the specifications
Presentation
The Application of Computers for Design
The various design-related
tasks which are performed by
a modern computer-aided
design system can be grouped
into four functional areas:
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Geometric Modeling
It is concerned with the computer compatible mathematical
description of the geometry of an object.
To use the geometric modeling, the designer constructs the image
of the object on the monitor screen by three types of commands.
1. The first type of command generates the basic geometric
elements (e.g., points, lines, and circles).
2. The second command type is used to accomplish scaling,
rotation, or other transformations of the elements.
3. The third type causes these elements to be joined into the
desired shape of the object.
Geometric Modeling
During this geometric modeling process, the computer
� Converts the commands into mathematical model.
� Stores it in the computer data files.
� Display it as an image on the monitor screen.
Different methods of displaying object in geometric modeling:
� Wire frame modeling.
� Surface modeling.
� Solid modeling.
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Engineering Analysis
In any engineering design project, some type of analysis is
required. The analysis may involve:
� Stress-strain calculations
� Heat-transfer computations
� Vibration etc.
Turnkey CAD/CAM systems often include or can be interfaced to
engineering analysis software.
Design Review and Evaluation
� Interference checking
� Kinematics packages
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Automated Drafting
� Automated drafting involves the creation of hard-copy
engineering drawings directly from the CAD data base.
� CAD systems can increase productivity in the drafting function by
roughly five times over manual drafting.
� Some favorable features are:
1. Automatic dimensioning
2. Generation of crosshatched areas
3. Scaling of the drawing
4. Develop sectional views
5. Enlarged views of particular part details.
Creating the Manufacturing Data Base
� Conventionally, a two step procedure, designing and then
manufacturing was employed.
� This was both time consuming and involved duplication of efforts.
� It is the goal of CAD/CAM not only to automate certain phases of
design and certain phases of manufacturing, but also to
automate the transition from design to manufacturing.
� Much of the data and documentation is generated during design
phase which is required to plan and manage the manufacturing
operations (e.g., geometry data, bill of materials, parts list,
material specification, etc.)
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Benefits of CAD
1. Productivity improvement in design
2. Shorter lead time
3. Design analysis
4. Fewer design errors
5. Standardization of design, drafting, and documentationprocedure
6. Drawings are more understandable
7. Improved procedures for engineering changes
8. Benefits in manufacturing
Techniques for Geometrical Modeling
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Curves Representation
Explicit function
It is a function in which the dependent variable is expressed in
terms of some independent variables.
It is denoted by:
Example:
where a , n and b are constant.
ny ax bx= +
( )y f x y mx c= ⇒ = +
Curves Representation
Implicit function
It is a function in which the dependent variable is not expressed in
terms of some independent variables.
The implicit equation of a curve lying in the xy plane has the form.
For a given curve the equation is unique up to a multiplicative
constant.
( , ) 0f x y =
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Implicit Equations
An example is the circle of unit radius centered at the origin,
specified by the equation:
2 2 1 0x y+ − =
4 3 17 0y x+ + =
Problems with Implicit and Explicit Representations
1. They represent unbounded geometry
2. Curves are often multi-valued
3. With implicit representation it is not possible to generate orderly
sequence of points
The difficulties in using the implicit or explicit representations might
be overcome by the appropriate programming of the CAD system.
There are some other attractive alternative representations of
geometries which do not posses these problems.
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Parametric Equations
� In parametric form, each of the coordinates of a point on the
curve is represented separately as an explicit equation function
of an independent parameter
� Thus, C(u) is a vector-valued function of the independent
variable, u.
� Although the interval [a, b] is arbitrary, it is usually normalized to
[0, 1].
( )( )
( )
x uu a u b
y u
= ≤ ≤
C
Parametric Equations
� The first quadrant of the circle is defined by the parametric
functions
� Setting , one can derive the alternate representation
� Thus, the parametric representation of a curve is not unique
( ) cos( )
( ) sin( ) 02
x u u
y u u uπ
=
= ≤ ≤
tan( 2)t u=2
2
2
1( )
12
( ) 0 t 11
tx t
tt
y tt
−=+
= ≤ ≤+
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Advantages
� By adding a z-coordinate, the parametric model is easily
extended to represent arbitrary curves in three- dimensional
space.
� It is difficult to represent bounded curve segments (or surface
patches) with implicit form. However, boundedness is built into
the parametric form through the bounds on the parameter
interval.
� Parametric curves possess a natural direction of traversal (from
C(a) to C(b) if a ≤ u ≤ b); implicit curves do not. Hence, it is easy
to generate ordered sequence of points along a parametric
curve.
Advantages
� The parametric form is more natural for designing and
representing shapes in a computer. The coefficient of many
parametric functions, e.g., Bezier and B-spline curves, possess
considerable geometric significance. This translates into
interactive design methods and numerically stable algorithms.
� Compute a point on a curve or surface is difficult in the implicit
form.
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Types of Curve Representations
Parametric
Analytical Synthetic
Analytical Curves
1. Point
2. Line
3. Circle
4. Ellipse
5. Parabola
6. Hyperbola
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Synthetic Curves
1. Analytical curves are usually not sufficient to meet the
geometric design requirements of mechanical parts.
2. Products such as car bodies, ship hulls, airplane fuselage and
wings, propeller blades, shoe insoles, and bottles are a few
examples that require free-form, or synthetic curves and
surfaces.
3. The need for synthetic curves in design arises when a curve is
represented by a collection of measured points.
4. The typical form of these curves is a polynomial.
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Synthetic Curves
5. Various continuity requirements can be specified at the data
points to impose various degree of smoothness on the resulting
curves.
6. The order of continuity becomes important when a complex
curve is modeled by several curve segments pieced together
end-to-end.
7. Zero-order continuity yields a position-continuous curve. First
and second order continuities imply slope and curvature
continuous curves respectively.
Types of ContinuityThere are two ways of describing smoothness of ��� order.
� Geometric or visual continuity, ��
The ��� order derivatives are same
� Parametric continuity ��
The ��� order derivatives along with their magnitudes are same
For example,
� ��continuity means continuity of the tangent vector, while G�
continuity means continuity of slope.
� � continuity means continuity of the acceleration vector, while G
continuity means continuity of the curvature.
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Types of Continuity
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Types of ContinuityGeometric Continuity� �
�: Curves are joined at common point� �
�: First derivatives are proportional at the join point. (Thecurve tangents have the same direction, but not necessarilythe same magnitude i.e., C1’(1) = (a,b,c) and C2’(0) =(ka,kb,kc)).
� �: First and second derivatives are proportional at joint point.
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�� Continuity
Aesthetical Impression
You need to move the end points to join.
Curves will be continuous but will
probably have a visible crease
Curves will appear smooth, their reflection
could have sudden changes
Reflection will change smoothly as, ambient
shadows will be gradual.
Math. analysis
f(x) = g(x).
f(x) = g(x)
f’(x) = g’(x)
f’’(x) = g’’(x)
Curves Continuity
� It may be obvious that a curve would require G1 continuity to
appear smooth.
� For good aesthetics, such as those aspired to in architecture
and sports car design, higher levels of geometric continuity
are required. For example, reflections in a car body will not
appear smooth unless the body has G2 continuity.
� A rounded rectangle (with ninety degree circular arcs at the
four corners) has G1 continuity, but does not have G2
continuity.
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Go Check in CATIA
1. Go to Start > Shape > FreeStyle
2. Click on 3D curve and draw following two curves using
control point option.
3. To verify it click on Connect Checker Analysis and select
the two curves.
The curves have only Zero order continuity
G1 Continuity Check in CATIA
1. Click on 3D curve and draw following two curves using
Through point option.
2. To verify it click on Connect Checker Analysis and select
the two curves.
The curves have only First order continuity
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G2 Continuity Check in CATIA
1. Click on 3D curve and draw following single curve.
2. Using split to break the curve
3. To verify it click on Connect Checker Analysis and select
the two curves.
The broken curve segments have Second order continuity
Curvature Analysis in CATIA
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Radius of Curvature Analysis
Observe:
1. The location of Point of Inflection
2. Direction of Radius of Curvature
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Curvature Analysis in CATIA
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Types of Synthetic Curves
Major CAD/CAM systems provide following types of synthetic
curves:
1. Cubic polynomial curves
2. Hermite curve
3. Bezier curve
4. Cubic spline curve
5. B-spline curve and
6. NURBS curve
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Cubic polynomial curves
In three dimensional modeling a geometric representation is
required that will:
1. Describe non-planar curve.
2. Avoid computational difficulties and unwanted undulations
(oscillations) that might be introduced by high-order polynomial
curves.
These requirements are satisfied by the Cubic Polynomial Curves
therefore, it has become very popular as a basis for computational
geometry.
Cubic polynomial curves
1. A cubic polynomial is the minimum-order polynomial that can
guarantee the generation of curves.
2. In addition, the cubic polynomial is the lowest-degree
polynomial that permits inflection within a curve segment and
that allows representation of non-planar (twisted) 3D curves in
space.
3. Higher order polynomials are not commonly used in CAD
because they tend to oscillate , are computationally
inconvenient, and are uneconomical of storing curve and
surfaces in the computer.
0 1 2, , or G G G
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Cubic polynomial curves
Just as two information are required to define a line, and three
information for an arc of a circle, four information are required to
define the boundary conditions for a cubic polynomial.
If the four information are points, the fitting of a curve through these
points is known as Lagrange interpolation, shown in the following
figure.
0P
1P
2P
3P
[ ]3
2 30 1 2 3
0
( ) ( ) ( ) ( ) 0 1ii
i
u u x u y u z u u u u u=
= = = + + + ≤ ≤∑P a a a a a
Cubic polynomial curves
Find a cubic polynomial curve equation which satisfy following
boundary conditions.
P(u = 0) = [0 0]
P(u = 0.25) = [2 2]
P(u = 0.5) = [4 0]
P(u = 1) = [6 2]
0P
1P
2P
3P
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Polynomials (Curves)
� Linear:
� Quadratic:
� Cubic:
We usually define the curve for 0 ≤ t ≤ 1
( )
( )
( ) dcbaf
cbaf
baf
+++=
++=
+=
tttt
ttt
tt
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2
Hermite Curve
If two end points of a curve and the tangent vectors
at the end points are used to define a cubic polynomial, it is called
Hermite interpolation , shown in the following figure.
0 1P , P ' '0 1P , P
1 0 2 1 3 0 4 1( ) ( ) ( ) ( ) ( )u f u f u f u f u′ ′= + + +P P P P P
Basis Functions
0P
1P
0′P
1′P
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Derivation of Hermite Curve
0 0
1 0 1 2 3
0 1
1 1 2 3
(0)
(1)
(0)
(1) 2 3
= == = + + + ⇒
′ ′= =′ ′= = + +
P P a
P P a a a a
P P a
P P a a a
0 0
1 1
2 0 1 0 1
3 0 1 0 1
3 3 2
2 2
==
′ ′= − + − −′ ′= − + +
a P
a P
a P P P P
a P P P P
[ ] 2 30 1 2 3( ) ( ) ( ) ( ) 0 1 (1)u x u y u z u u u u u= = + + + ≤ ≤ − − −P a a a a
3
0
( ) (0 1)ii
i
u u u=
= ≤ ≤∑P a
Hermite Curve
Thus, by substituting in equation-1, we obtain:
2 3 2 3 2 3 2 30 1 0 1( ) (1 3 2 ) (3 2 ) ( 2 ) ( )u u u u u u u u u u′ ′= − + + − + − + + − +P P P P P
0
12 3 2 3 2 3 2 3
0
1
( ) 1 3 2 3 2 2u u u u u u u u u u
= − + − − + − + ′ ′
P
PP
P
P
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Hermite Curve
Or, in matrix notation P = UCS where
0
12 3
0
1
( )
1 0 0 0
0 0 1 0( ) 1
3 3 2 1
2 2 1 1
u
u u u u
= ′ − − − ′−
P = U C S
P
PP
P
P
Plot Hermite Curve using Matlab
0
1
0
1
1 1
6 5
8 0
2 30
=
′ − ′ −
P
P
P
P
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Effect of Tangent Vectors on the Shape of the Curve
0 1 2 3 4 5 61
2
3
4
5
6
7
8
9
S = [1 1;6 5;-8 0;2 -30]
-2 -1 0 1 2 3 4 5 61
2
3
4
5
6
7
8
9
S = [1 1;6 5;-8 0;30 -30]
0 1 2 3 4 5 61
2
3
4
5
6
7
8
9
S = [1 1;6 5;8 0;30 -30]
-2 -1 0 1 2 3 4 5 61
1.5
2
2.5
3
3.5
4
4.5
5
S = [1 1;6 5;-8 0;30 8]
Effect of Tangent Vectors on the Shape of the Curve
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Four Hermite Basis Functions
2 31
2 32
2 33
2 34
( ) 1 3 2
( ) 3 2
( ) 2
( )
f u u u
f u u u
f u u u u
f u u u
= − +
= −
= − +
= − +
Hermite Curve
Hermite curve can be represented as:
are its geometric coefficients.
Equation-2 gives the general form of a cubic polynomial in the
Hermite basis.
1 0 2 1 3 0 4 1( ) ( ) ( ) ( ) ( ) (2)u f u f u f u f u′ ′= + + + − − −P P P P P
0 1 0 1, , ,′ ′P P P P
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Properties
� The curve passes through the end points (u = 0, u = 1)
� The curve shape can be controlled by changing its end points or its tangent vectors
� If the two end points P0 and P1 are fixed in space, the designer can control the shape of the spline by changing either the magnitudes or the directions of the tangent vectors
� The use of Hermite curve in design applications is not very popular due to the need for tangent vectors or slopes to define the curve.
� It is not easy to predict curve shape according to changes in magnitude of tangent vectors
Properties
� Control of the curve shape is not easy because of its global control characteristics. For example, changing the position of a data point or end slope changes the entire shape of the curve, which does not provide the intuitive feel required for design.
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Example
Calculate the mid-point of the Hermite curve that fits the pointsand the tangent vectors0 1(1,1), (6,5)= =P P 0 1(0,4), (4,0) ′ ′= =P P