Development of Oblique Prisms, Pyramids, and Cones in Mechanical Engineering Drawing

1. Lecture #8 Chapter 22 Dr. John Cheung Mechanical Engineering DrawingMECH 211/M

2. Quiz - Intersection • Complete the missing view and show the intersection of two cylinders.

3. Quiz - Intersection • Missing view.

4. Quiz - Intersection • Intersection of two cylinders.

5. Developments Construction of an unfolded or unrolled surface of a form Commonly used in Sheet metal Packaging / Containers Pipes / ducts Pattern making

6. Developable Surfaces Parallel edge Vertex

7. Sheet Metal Hems & Joints Marking and folding done from inside

8. Parallel-Line Developments Find T.S of base – use its perimeter as stretch line. Seam line – shortest lateral edge Top and bottom attached to longer edge.

9. Development of Oblique Prism Find true length of lateral edges. Find true shape of section – hence the stretch-out line.

10. Development of Oblique Prism Find true length of lateral edges.

11. Development of Oblique Prism Stretch-out line

12. Development of Right Cylinder Divide the cylinder periphery into number of equal segments. Base –stretch out line = 3.142 x Dia.

13. Development of Oblique Cylinder – FIG-22-7 Both ends – Not TL Find TL of lateral edges. Find true shape of cylinder cross section. Divide section perimeter – number of segments.

14. True length by revolution method

15. Development of a Pyramid – FIG 22-8 Point 0 located at base centre – use as the centre of lateral edge radius. Top becomes true shape viewing perp. to point views BC and AD. Use revolution method to obtain the TL. For line 0-3, Rotate line 0-3 to intersect horizontal line in TV. The intersection = 3R. Project P3R to FV to intersect horizontal line. Intersection = P3R in FV. Line 0_#R = TL of Line 0-3. Pyramid base = True shape, hence edges = TL.

16. Development of a Pyramid – FIG 22-8

17. Development of oblique pyramid – FIG 22-9 • Use Point 0 as centre of development. • Use revolution method. If views become too messy, use True Length diagram. • Pyramid base and top– true shape, hence chord – true length.

18. Development of oblique pyramid – FIG 22-9

19. Development of right circular cone – Fig 22-10 Radial line developments. S = Slant height, R = radius of cone base.

20. Development of oblique cone – Fig 22-11 • Find True length of cone base. • Rotate P4 to intersect horizontal line at P4’ in FV. • Project P4’ to intersect the horizontal line from P4 in TV at P4’. • Repeat for others. • Chord P4’-P5’ (R) = True length for base from P4 to P5.

21. Development of oblique cone – Fig 22-11 – Transition piece • Extend contour elements – Point A. • Find TL of lateral edges. • Line A-4 – Rotate P4 to intersect horizontal line at P4” in TV. • Project P4” to FV to intersect extended horizontal line from P4 – yielding corresponding P4”. • Line A-P4” = True length of Line A-4. • Repeat method to cone top.

22. Development of oblique cone – Fig 22-11 – Transition piece

23. Triangulation A process of dividing a surface into triangles Often used as an approximation Commonly used in transitional pieces

24. Transition piece – Rectangular ends- FIG 22-13 Draw P9 and P10 to ease development. Draw true length diagram. One for lateral edges and other for diagonal lengths. Base and top = True shape. Chords in base and top – true length.

25. Transition piece – Rectangular ends- FIG 22-13

26. Transition piece connecting two circular ducts – FIG 22-14 • Elements do not intersect at a common vertex. • Circular intersection with larger pipe – true shape in TV. • Other end – true shape in Auxiliary view. • Planes in cone not parallel – Approximate development by triangulation method.

27. Transition piece connecting two circular ducts – FIG 22-14 TL diagram – edges. TL diagram – diagonal lines. Diagonal Edges

28. Square to Round Transition Piece

29. In Class Assignment Page 661 Figure 22.20 Problem 2 Using revolution method.