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KP3213 CAD/CAM. Lecture 3 snap shot Objective of Lecture 4 Lecture 4: Curve representation and solid modelling Book review of week 2 & 3. Curve Representation. Curve Representation. Curve Representation. Coordinates are given by continuous parameter single valued

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kp3213 cad cam
KP3213 CAD/CAM
  • Lecture 3 snap shot
  • Objective of Lecture 4
  • Lecture 4: Curve representation and solid modelling
  • Book review of week 2 & 3
slide4

Curve Representation

Coordinates are given by continuous parameter single valued

polynomial X=x(u), Y=y(u) and Z=z(u). Variable u is constraint

By Closed interval such as [0,1]

rapid prototyping rp
Rapid Prototyping (RP)
  • Physical model that directly represents component.
  • Based upon layered manufacturing concept
  • 3D CAD decomposed into cross-sectional representations of small thickness
  • Sequence
  • A CAD model constructed and converted to STL (standard triangular language)
  • Model sliced.
  • First layer created, model lowered by one layer until completion
  • Model and supports removed. Surface is cleaned.
slide9

Technologies Involved

  • Stereolithography / photolithography
  • Selective Laser Sintering
  • 3-D Printing
  • Laminated Object Manufactruing (LOM)
  • Fused Deposition Model
3 d solid model
3-D SOLID MODEL

3-D solid model captured complete geometry of an object

-inside and outside of the object

-volume and intersection of the object can be calculated

-Hidden-surface/line removal and a shaded image can be produced

Internal representation vs external representation

Internal representation is how computer stores the model.

External representation is how picture or image is displayed

approaches
Approaches
  • Constructive Solid Geometry (CSG)
  • Boundary Representation (B-rep)
  • Pure Primitive Instancing - Parametric model
  • Spatial Occupancy Enumeration - model of fixed size spatial cells
  • Cell Decomposition - model of variable spatial cells
  • Hybrid (feature-based modellers)
constructive solid geometry csg
Constructive Solid Geometry (CSG)
  • Based on simple geometric primitives
    • boxes, cones, spheres, etc.
  • Primitives are positioned and combined using boolean operations
    • union (addition)
    • difference (subtraction)
    • intersection
  • Represented as a boolean tree
csg example

C

A

(A-B)  C

B

A-B

CSG Example
boundary representation b rep
Boundary Representation (B-Rep)
  • Solids represented by faces, edges and vertices
  • Topological rules must be satisfied to ensure valid objects
    • faces bounded by loop of edges
    • each edge shared by exactly two faces
    • each edge has a vertex at each end
    • at least 3 edges meet at each vertex
  • Euler’s rule applies: V-E+F=2
  • Surface must be closed
b rep example

Edges

Vertices

Faces

B-Rep Example
slide19

BOUNDARY MODEL

12

Geometry and Topology

8

13

6

7

1

2

4

object

9

5

3

10

11

14

Face

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

F14

face

equation

Loop

L1

L3 L4

. . .

E5 E6 E7 E8 E10

E1 E2 E3 E4

. . .

Edge

V5 V6 V7 V8 V10

V1 V2 V3 V4

Vertices

. . .

csg vs b rep
CSG

Simple representation

Limited to simple objects

Stored as binary tree

Difficult to calculate

Rarely used anymore

B-Rep

Flexible and powerful representation

Stored explicitly

Can be generated from CSG representation

Used in current CAD systems

CSG vs. B-Rep
feature based modelling
Feature-Based Modelling
  • Parts modelled by adding features to a base part
  • Features represent manufacturing “operations”
    • holes, ribs, fillets, chamfers, slots, pockets, etc.
  • Material can be added or subtracted, similar to CSG
  • Features are not limited to simple primitives, and can be created by extrusion, sweeping, revolving, etc.
  • A history tree is created, similar to a CSG boolean tree
example
Example

Slot

Fillets

Shell

Hole

history tree
History Tree

Final Part

Increasing

part

complexity

Part3

Shell

Part2

Hole

Part1

Fillets

Features

added

Base

Slot

modifying parts
Modifying Parts
  • The part is created from the history tree
  • Features can be added, deleted and re-ordered
  • Feature dimensions can be changed
  • Feature parameters can be changed
    • eg. From protrusion to cutout
book review for week 2
Book Review for Week 2
  • CAD/CAM Principles and Application 2nd edition by PN Rao Published by Mc Graw Hill
    • Chapter 2: 2.1  2.9
    • Chapter 3: 3.1  3.4
    • Chapter 4: 4.1  4.4

Book Review for Week 3

  • Chapter 5: 5.1  5.44