CAD/CAM Principles and Applicationshome.iitk.ac.in/~jrkumar/download/ME761A/Lecture 4 Geometric Modelling.pdf · Zeid, Mastering CAD/CAM, 2004, TMH Sweep two cross sections along

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


wireframe


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


Possible

Numerical control application


Automatic possible Automatic possible

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Point definitions

Line definitions

Circle definitions

Arc definitions

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Point Definitions


Line Definitions


Circle Definitions


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

9

10

11

12

1

2

3

4

5

6

7

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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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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Component Model by Rotational Sweep


Various Solid-Modelling Primitives

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Boolean Operators and their effect on Model Construction



Boolean examples


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



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Geometric Constraints


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Geometric Modelling

Function of Geometric Modelling

Comparison of different modelling methods

Free form curves



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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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Documents

CAD/CAM Principles and Applicationshome.iitk.ac.in/~jrkumar/download/ME761A/Lecture 4 Geometric Modelling.pdf · Zeid, Mastering CAD/CAM, 2004, TMH Sweep two cross sections along