Geometric Modelling
Prof. Janakarajan Ramkumar Professor Department of Mechanical & Design Program IIT Kanpur, India.
• Understand the various requirements for the information that is generated during the geometric modelling stage.
• Study various types of geometric models possible and their applications
• Develop various methodologies used for geometric construction such as sweep, surface models, solid models, etc.
• Recognize the various types of surfaces and their application as used in geometric modelling
• • Understand the solid construction methods including b-rep and CSG
methods
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• The computer compatible mathematical description of the geometry of the object is called as geometric modeling.
• The CAD software allows the mathematical description of the object to be displayed as the image on the monitor of the computer.
• A geometric model contains description of the modelled object’s shape. Since geometric shapes are described by surfaces, curves are used to construct them.
• Computer geometric modelling uses curves to control the object’s surfaces as they are easy to manipulate. The curves may be constructed using analytic functions, a set of points, or other curves and surfaces.
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https://www.coroflot.com/MJFellis/Mouse-Design-CAD-Nov-2011
Geometric modelling of a computer mouse
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There are three steps in which the designer can create geometric models by using CAD software, these are:
1) Creation of basic geometric objects: In the first step the designer creates basic geometric elements by using commands like points, lines, and circles.
2) Transformations of the elements: In the second step the designer uses commands like achieve scaling, rotation and other related transformations of the geometric elements.
3) Creation of the geometric model: During the final step the designer uses various commands to that cause integration of the objects or elements of the geometric model to form the desired shape.
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https://in.pinterest.com/pin/753860425103945294/?lp=true 6
Geometric modelling is the central part of product design
Rao, CAD/CAM Principles and Applications, 2010, TMH
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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.
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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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Manufacturing • Parts classification.
• Process planning.
• Numerical control data generation and verification.
• Robot program generation.
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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.
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Two-dimensional
Three-dimensional
The three principal classifications can be
• The line model (wireframe modelling),
• The surface model, and
• The solid or volume model
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1. Wire frame geometry
User enters 3D vertices and joins the vertices to create a 3D object called a wire frame.
The wire frame models lack the surface definition.
2. Surface model
User enters the vertices and edges in an ordered manner. outlining or bounding one face at a time so that surfaces are defined.
It can not relocation the volume of the part.
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Rao, CAD/CAM Principles and Applications, 2010, TMH Rao, CAD/CAM Principles and Applications, 2010, TMH
Rao, CAD/CAM Principles and Applications, 2010, TMH Rao, CAD/CAM Principles and Applications, 2010, TMH
wireframe
Rao, CAD/CAM Principles and Applications, 2010, TMH Rao, CAD/CAM Principles and Applications, 2010, TMH
surface model
Features Line model Surface model Volume model Automatic view generation (perspective and orthographic)
Impossible Impossible Possible
Cross-sectioning Manually guided Manually guided Possible, even automated cross-hatching is possible
Elimination of hidden details
Manually guided May be possible Possible
Analysis functions (Geometric calculations)
Difficult or impossible
Difficult or impossible
Possible
Numerical control application
Difficult or impossible
Automatic possible Automatic possible
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Point definitions
Line definitions
Circle definitions
Arc definitions
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Rao, CAD/CAM Principles and Applications, 2010, TMH
Point Definitions
Rao, CAD/CAM Principles and Applications, 2010, TMH
Line Definitions
Rao, CAD/CAM Principles and Applications, 2010, TMH
Circle Definitions
Rao, CAD/CAM Principles and Applications, 2010, TMH
Arc Definitions
Vertex number X coordinate Y coordinate Z coordinate
1 0 0 0
2 10 0 0
3 10 10 0
4 0 10 0
5 0 0 15
6 10 0 15
7 10 10 15
8 0 10 15
Edge number Start point End point
1 1 2
2 2 3
3 3 4
4 4 1
5 5 6
6 6 7
7 7 8
8 8 5
9 1 5
10 1 6
11 1 7
12 1 8
1 2
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5 6
78
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10
11
12
1
2
3
4
5
6
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8Wireframe Data representation for a Cube
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The three-dimensional geometric construction methods which extend from the 2D that is normally used are: Linear extrusion or
translational sweep, and
Rotational sweep etc.
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Rao, CAD/CAM Principles and Applications, 2010, TMH Rao, CAD/CAM Principles and Applications, 2010, TMH
Extrusion
Geometric Construction Methods
Linear sweep between two cross sections
Zeid, Mastering CAD/CAM, 2004, TMH
Sweep two cross sections along a guide curve
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Geometric Construction Methods
Rao, CAD/CAM Principles and Applications, 2010, TMH Rao, CAD/CAM Principles and Applications, 2010, TMH
Component Model by Rotational Sweep
Geometric Construction Methods
Various Solid-Modelling Primitives
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Geometric Construction Methods
Rao, CAD/CAM Principles and Applications, 2010, TMH
Boolean Operators and their effect on Model Construction
Geometric Construction Methods
Rao, CAD/CAM Principles and Applications, 2010, TMH
Boolean examples
Rao, CAD/CAM Principles and Applications, 2010, TMH
Constructive Solid Geometry (CSG)
• It is a technique used in solid modeling. • Constructive solid geometry allows a modeler to create a complex
surface or object by using Boolean operators to combine simpler objects.
• potentially generating visually complex objects by combining a few primitive ones.
https://en.wikipedia.org/wiki/Constructive_solid_geometry
Geometric Construction Methods
Zeid, Mastering CAD/CAM, 2004, TMH
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Geometric Constraints
Zeid, Mastering CAD/CAM, 2004, TMH
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Geometric Constraints
Zeid, Mastering CAD/CAM, 2004, TMH
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Geometric Constraints
Zeid, Mastering CAD/CAM, 2004, TMH
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Geometric Constraints
Geometric Modelling
Function of Geometric Modelling
Comparison of different modelling methods
Free form curves
Geometric Construction Methods
Geometric Constraints
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To recapitulate
References
1. Rao, P.N., 2004. CAD/CAM: principles and applications. Tata McGraw-Hill Education.
2. Zeid, I., 1991. CAD/CAM theory and practice. McGraw-Hill Higher Education.
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