This document discusses the development of surfaces for various geometric shapes used in engineering. It provides instruction on how to construct parallel line and radial line developments of prisms, cylinders, pyramids and cones. It also covers how to construct developments of transition pieces using triangulation. The document contains 35 figures illustrating examples of developments for shapes including prisms, cylinders, pyramids, cones and various transition pieces.

1. Development of surfaces
1
After studying this topic and working through the problems you
should be able to do the following:
• constant parallel line developments of prisms and cylinders
• construct radial line developments of pyramids and cones
• construct the development of transition pieces using
triangulation

2. 2
Figure 1 –
Regular right prism

3. 3
Figure 2 –
Truncated right prism

4. 4
Figure 3 –
Rectangular prism pipe elbow

5. 5
Figure 4 –
Hexagonal prism

6. 6
Figure 5 – Truncated
hexagonal right prism

7. 7
Figure 6 –
Oblique hexagonal prism

8. 8
Figure 7 – Line of intersection of
cylinder and cone—element method

9. 9
Figure 8 – Line of intersection of cylinder
and cone—cutting plane method

10. 10
Figure 9 – Line of intersection of cylinder
and cone—common sphere method
Excelsior High School-GMED -UNIT 1- D. Hall

11. 11
Figure 10 –
Right cylinder
Excelsior High School-GMED -UNIT 1- D. Hall

12. 12
Figure 11 –
Truncated right cylinder

13. 13
Figure 12 –
Oblique cylinder

14. 14
Figure 14 –
Oblique T
piece—equal
diameter
cylinders

15. 15
Figure 15 –
Offset T piece
—unequal
diameter
cylinders

16. 16
Figure 16 – Oblique
cylindrical connecting pipe

17. Figure 17 – Alternative method of
determining the line of intersection

18. 18
Figure 18 – Right pyramid

19. 19
Figure 19 – Oblique pyramid
—whole and truncated

20. 20
Figure 20 – Right cone

21. 21
Figure 21 – Right cone
truncated parallel to the base

22. 22
Figure 22 – Right cone truncated
at an angle to the base

23. 23
Figure 23 – Right cone-vertical
cylinder intersection

24. 24
Figure 24 – Truncated right
cone-right cylinder intersection

25. Figure 25 – Right cone-right
cylinder oblique intersection
25

26. 26
Figure 26 – Oblique cone
—whole and truncated

27. 27
Figure 27 – Oblique cone-
oblique cylinder intersection

28. 28
Figure 28 – Breeches piece
—equal angle, equal diameters

29. 29
Figure 29 – Breeches piece
—unequal angle, equal diameters

30. 30
Figure 30 – Breeches piece
—cylinder and two cones, equal angle

31. Figure 31 – Square-to-rectangle
transition piece

32. 32
Figure 32 – Round-to-round
transition piece

33. 33
Figure 33 – Square-to-round
transition piece

34. 34
Figure 34 – Oblique hood

35. 35
Figure 35 –
Rectangle-to-
rectangle,
angular offset
transition
piece