EG_Unit_3_Development of surfaces.pptx

Unit 3rd of engineering graphics of Savitribai Phule pune university. First year engineering syllabus of engineering graphics.

1. UNIT - III DEVELOPMENT OF LATERAL SURFACES OF SIMPLE AND SECTIONED SOLIDS Dr. Somnath Kolgiri P. G. Moze College of Engineering Pune

2. Definitions Development of Surfaces of the solid : Suppose an object like a square prism is wrapped around by using paper. When the wrapper is opened and spread out on a plane surface, the resulting figure is called the development of the surfaces of the solid. Note : The development of any solid shows the true shape of all the surfaces of the solid.

3. Methods of Development Parallel line method Radial line method Approximate method Note : Th e d e v elopme n t of the l a t e r al sur f aces of the objects only are shown. Th e bas e a n d t o p a r e cut t o t h e r equi r ed geometrical shape and fastened suitably.

4. PRISMS & CYLINDERS – Parallel Line Development Method http://www.youtube.com/watch?v=IwlrJOHgOB8

5. Development of Prism End Lateral Surface Lateral Sides

6. Problem 1 Draw the development of the lateral surfaces of a right square prism of edge of base 30 mm and axis 50 mm long.

7. P r o b l e m 1 50 30 a (a 1 ) b (b 1 ) c (c 1 ) d (d 1 ) a’ 1 (d’ 1 ) b’ 1 (c’ 1 ) b’(c’) a’ ( d’) Draw a line equal to the length of the perimeter of the base of the prism. A 1 B 1 C 1 120 D 1 A 1 A B C D A

8. Development of Cylinder End Lateral Sides Lateral Surface

9. Problem 2 Draw the development of the complete surface of a cylindrical drum . Diameter is 40 mm and height 60 mm.

10. P r o b l e m 2 60 p’ q’ (w’) r’ (v’) s’ (u’) t’ e’ q(b) r (c ) s(d) t ( e) c ’ ( g ’ ) a’ b’(h’) u( f ) w ( h) v(g) d’(f’)  40 p(a) Draw a line equal to the length of the circumference of the base circle (  D). A B C D P R Q S T E 125.6 U V W P F G H A

11. Problem 3 A hexagonal prism , edge of base 20 mm and a xi s 5 m m lon g , r e s ts with its bas e on HP suc h th a t pa r allel to one of V P . It its r e c t an g ula r f aces is i s cut b y a p lane perpendicular to VP, inclined at 45° to HP and passing through the right corner of the top face of the prism. Draw the sectional top view. Develop the lateral surfaces of the truncated prism.

12. P r o b l e m 3 1’ 4’ 3’ 2’ a( a 1 ) 45  20 ( 5 ’ ) 50 (6’) 45  b( b 1 ) c(c 1 ) d( d 1 ) e(e 1 ) f(f 1 ) a ’ 1 b’ 1 (f’ 1 ) c’ 1 (e’ 1 ) d’ 1 a’ b’(f’) c’(e’) d’ 20 A 1 A B 1 B C D E F A C 1 D 1 E 1 F 1 A 1 1 2 3 4 5 6 1 Draw six equal rectangles to represent the development of the lateral surfaces of the hexagonal prism in thin lines.

13. Problem 4 A hexagonal prism of base side 20 mm and height 45 mm is resting on one of its ends on the HP with two of its lateral faces parallel to the VP. It is cut by a plane perpendicular to the VP and inclined at 30° to the HP . The plane meets the axis at a distance of 20 mm above the base . Draw the development of the lateral surfaces of the lower portion of the prism. Page no 300

14. P r o b l e m 4

15. Problem 5 A pentagonal prism , side of base 25 mm and altitude 50 mm, rests on its base on the HP such that an edge of the base is parallel to VP and nearer to the observer. It is cut by a plane inclined at 45° to HP , perpendicular to VP and passing through the center of the axis . (i) Draw the development of the complete surfaces of the truncated prism.

16. P r o b l e m 5 50 3’ 1 1’ 2’ 45 ° 4 5 25 a( a 1 ) b (b 1 ) c( c 1 ) d( d 1 ) d ’ 1 a ’ 1 b ’ 1 c’ 1 e(e 1 ) ( e ’ 1 ) a’ b’ ( e’) c’ d’ 3 2 ( 5 ’ ) 4’ 25 1 A 1 A B 1 B C 1 C D 1 D E 1 E A 1 A 2 3 4 5 1

17. Problem 6 A pentagonal prism of side of base 30 mm and altitude 60 mm stands on its base on HP such that a vertical face is parallel to VP and away from observer. It is cut by a plane perpendicular to VP, inclined at an angle of 50° to HP and passing through the axis 35 mm above the base . Draw the development of the lower portion of the prism. Page no 15.4 (Exercise)

18. PYRAMIDS & CONES – Radial Line Development Method

19. Development of Pyramid

20. Problem 7 Draw the development of the lateral surfaces of a square pyramid , side of base 25 mm and height 50 mm, resting with its base on HP and an edge of the base parallel to VP.

21. P r o b l e m 7 a o 25 b c d 50 a’ ( d’) b’(c’) o’ If the top view of a slant edge of a pyramid is parallel to XY, then the front view of that edge will give its true length. To obtain the true length of a slant edge make “ ob” parallel to XY. O as center and ob as radius draw an arc to cut the horizontal drawn from o at a1. a 1 a ’ 1 True length of slant edge O A B C D A 25

22. Development of Cone Ci r c u m f e r e n c e of base circle End Slant length

23. Problem 8 Draw the development of the lateral surface of a cone of base diameter 48 mm and altitude 55 mm.

24. P r o b l e m 8 o  48 a b c d 55 a’ c’ o’ True length (L) of slant generator O A B C D A b’(d’) 144 °  = (Base circle radius/True slant length)*360 °  = (24/60)*360 °  =144 ° Divide 144 ° into 4 equal parts. Per division 36 ° 36 °

25. Problem 9 A square pyramid of base side 25 mm and altitude 50 mm rests on it base on the HP with two sides of the base parallel to the VP. It is cut by a plane bisecting the axis and inclined a 30° to the base . Draw the development of the lateral surfaces of the lower part of the cut pyramid.

26. P r o b l e m 9 a o 25 b c d 50 a’ ( d’) b’(c’) o’ o’a’ 1 gives the true length of the slant edge. O1=O4=o’1” , similarly O2=O3=o’2” T o o b t ain the true l e n g th o f a s l a n t edge make “ ob” parallel to XY. O as center and ob as radius draw an arc to cut the horizontal drawn from o at a1. a 1 a ’ 1 True length of slant edge O A B C D A 25 30 ° 1’ ( 4 ’ ) 1’’(4’’) (3’) 2’ 2’’(3’’) 1 2 3 4 1

27. Problem 10 A square pyramid base 35 mm side axis 70 mm long rests on its base on HP such that two adjacent sides of the base are equally inclined to VP. It is sectioned by a plane perpendicular to VP inclined a 30° to HP and passing through the mid-point of the axis. Draw the sectional top view and develop the lateral surfaces of the truncated pyramid.

28. P r o b l e m 1

29. Problem 1 1 A regular hexagonal pyramid of side of base 30 mm and height 60 mm is resting vertically on its base on HP such that two of the sides of the base are perpendicular to VP. It is cut by a plane inclined at 40° to HP and perpendicular to VP. The cutting plane bisects the axis of the pyramid. Obtain the development of the lateral surface of the truncated pyramid.

30. P r o b l e m 1 1 p 2 q s p’(u’) 60 3’ ( 4’) q’(t’) 1 1 ’ ( 6 ’ ) 2 ’( 5 ’ ) r 30 40 ° 3 5 S e cti o n al t op view 30 o o’ a’ t u 4 a 6 1 ’ ’( 6 ’’ ) 2’’(5’’) 3’’(4’’) r ’(s ’ ) a ’ 1 P a 1 O 1 Q R S T U P 2 3 4 5 6 1

31. Problem 1 2 A hexagonal pyramid of base of side 25 mm and altitude 50 mm is resting vertically on its base on the ground with two of the sides of the base perpendicular to the VP. It is cut by a plane perpendicular to the VP and inclined at 40° to the HP , The plane bisects the axis of the pyramid. Draw the development of the lateral surfaces of the pyramid. Page no 313

32. P r o b l e m 1 2

33. Problem 1 3 A pentagonal pyramid side of base 30 mm and height 52 mm stands with its base on HP and an edge of the base is parallel to VP and nearer to it. It is cut by a plane perpendicular to VP, inclined at 40° to HP and passing through a point on the axis 32 mm above the base . Draw the sectional top view. Develop the lateral surface of the truncated pyramid. Page no 15.12

34. P r o b l e m 1 3 30 a b c d e a’ ( e’) b’ 52 o’ 32  2’ 3’ (4 ’ ) 1’ (5’) 1 2 o 3 4 5 a 1 (d’) c’ a’ 1 O 1 B C D E A 2 3 4 5 6 A 1” 2” 3” 40 4” 5”

35. Problem 1 4 A pentagonal pyramid of base side 25 mm and height 60 mm is resting vertically on its base on the ground with one of the sides of the base parallel to the VP. It is cut by a plane perpendicular to the VP and parallel to the HP at a distance of 25 mm above the base . Draw the development of the lateral surfaces of the frustum of the pyramid . Also show the top view of the cut surface. Page no 311

36. P r o b l e m 1 4

37. Problem 1 5 A Cone of base diameter 60 mm and height 70 mm is resting on its base on HP. It is cut by a plane perpendicular to VP and inclined at 30° to HP . The plane bisects the axis of the cone. Draw the development of its lateral surface.

38. P r o b l e m 1 5 X Y V.P. H . P . 70 o’ a’ e’ 30  b c d e d’ ( f ’ ) c ’ ( g ’ ) b’(h’) f h g  60 a 35 1’ 2 ’ ( 8 ’ ) 3 ’ ( 7 ’ ) o 1” 5 ” 4 ’ ( 6 ’ ) 5’ ( 6 ”) 4” ( 7 ” ) 3” (8”) 2” oa is parallel to XY. So o’a’ = OA = True length of the generator (slant height) A B C D E 14 2 °  = (r/L)*360 °  = (30/76)*360 °  =14 2 ° Divide 142 ° into 8 equal parts. Per division 17.75 ° O 17. 8 ° F G H A 1 2 3 4 5 6 7 8 1

39. Problem 1 6 A Cone of base 50 mm diameter and 60 mm height, rests with its base on HP. It is cut by a section plane perpendicular to VP, parallel to one of the generators and passing through a point on the axis at a distance of 22 mm from the apex . Draw the sectional top view and develop the lateral surface of the remaining portion of the cone.

40. P r o b l e m 1 6 X H . P . 60 o’ p’ Y t’ V.P. b c d e s’( u’) q’(w ’) r’(v’) f h g  50 a 22 1 ’ (7 ’ ) 2 ’ (6 ’ ) 3’(5’) 4’ 1 2 3 5 6 7 o 4 a’ a 2”(6 ” ) 3”(5 ” ) 4” O A B C D E 17.3 ° F G H A 1 2 3 138.5 ° 4 5 6 7 Measure in top view b to 1. b1=B1 ; g7=G7

41. Best of Luck