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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. Curve Representation. Curve Representation. Curve Representation. Coordinates are given by continuous parameter single valued

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KP3213 CAD/CAM

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  1. KP3213 CAD/CAM • Lecture 3 snap shot • Objective of Lecture 4 • Lecture 4: Curve representation and solid modelling • Book review of week 2 & 3

  2. Curve Representation

  3. Curve Representation

  4. 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]

  5. Bezier Curve

  6. Bezier Curve

  7. Bezier Curve

  8. 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.

  9. Technologies Involved • Stereolithography / photolithography • Selective Laser Sintering • 3-D Printing • Laminated Object Manufactruing (LOM) • Fused Deposition Model

  10. Summary and Comparison of Rapid Prototyping Technologies

  11. Solid Modelling

  12. 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

  13. 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)

  14. 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

  15. CSG Primitives

  16. C A (A-B)  C B A-B CSG Example

  17. 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

  18. Edges Vertices Faces B-Rep Example

  19. 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 . . .

  20. 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

  21. 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

  22. Example Slot Fillets Shell Hole

  23. History Tree Final Part Increasing part complexity Part3 Shell Part2 Hole Part1 Fillets Features added Base Slot

  24. 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

  25. 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

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