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Projections of Solids

Projections of Solids. Mohammed Umair Hamid Assistant Professor (NSAKCET) Mechanical Department Engineering Graphics 1 Year 1 Semester. PROJECTIONS OF SOLIDS. Definition of Solid :.

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Projections of Solids

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  1. Projections of Solids Mohammed Umair Hamid Assistant Professor (NSAKCET) Mechanical Department Engineering Graphics 1 Year 1 Semester

  2. PROJECTIONS OF SOLIDS Definition of Solid: A solid is a three dimensional object having length, breadth and thickness and it is completely bounded by either plane or curved, or combination of the two, is called as 3-Dimensional Solid. -The shape of the solid is described by drawing its two orthographic views usually on the two principle planes i.e. H.P. & V.P. -For some complicated solids, in addition to the above principle views, side view is also required. -A solid is an aggregate of points, lines and planes and all problems on projections of solids would resolve themselves into projections of points, lines and planes.

  3. Classification of Solids: Solids may be divided into two main groups (A) Polyhedra APolyhedrais defined as a solidbounded by planes calledfaceswhichmeet in straight lines callededges. (B) Solids of revolution When a solid is generated by revolutions of a plane figure about a fixed line (Axis) then such solids are named as solids of revolution.

  4. There are seven regular Polyhedra which may be defined as stated above Solids of revolutions may be of following types

  5. (1) Prism: Faces Edge Axis It is a polyhedra having two equal and similar faces called its ends or bases, parallel to each other and joined by other faces which are rectangles. The imaginary line joining the Centres of the bases or faces is called Axis of Prism.

  6. According to the shape of its base, prism can be sub classified into following types: (c) Pentagonal Prism (b) Square Prism (a) Triangular Prism (d) Hexagonal Prism

  7. Edge Axis Base (2) Pyramid: This is a polyhedra having plane surface as a base and a number of triangular faces meeting at apoint called theVertexor Apex. The imaginary line joining the Apex with the Centre of the base is calledAxisof pyramid.

  8. According to the shape of its base, pyramid can be sub classified into following types: (a) Triangular Pyramid: (c) Pentagonal Pyramid: (b) Square Pyramid: (d) Hexagonal Pyramid:

  9. Rectangle Axis Base (1) Cylinder: A right regular cylinder is a solid generated by the revolution of a rectangle about its vertical side which remains fixed.

  10. Generators Right angle triangle Axis Base (2) Cone: A right circular cone is a solid generated by the revolution of a right angle triangle about its vertical side which remains fixed.

  11. Important Terms Used in Projections of Solids: (1) Edge or generator: For Pyramids & Prisms, edges are the lines separating the triangular faces or rectangular faces from each other. For Cylinder, generators are the straight lines joining different points on the circumference of the bases with each other

  12. Important Terms Used in Projections of Solids: Apex Edges Apex PYRAMID Generators CONE (2) Apex of solids: ForCone and Pyramids, Apex is the point where all the generators or the edges meet.

  13. Rectangle Axis Generators Faces Base Edge Axis CYLINDER PRISM

  14. Important Terms Used in Projections of Solids: (3) Axis of Solid: For Cone and Pyramids, Axis is an imaginary line joining centre of the base to the Apex. For Cylinder and Prism, Axis is an imaginary line joining centres of ends or bases.

  15. Axis Base (4) Right Solid: A solid is said to be a Right Solid if its axis is perpendicular to its base. Axis Base (5) Oblique Solid: A solid is said to be aOblique Solidif its axis is inclined at an angle other than 90° to its base.

  16. (6) Regular Solid: A solid is said to be a Regular Solid if all the edges of the base or the end faces of a solid are equal in length and form regular plane figures

  17. CUTTING PLANE PARALLEL TO BASE FRUSTUM OF A PYRAMID (7) Frustum of Solid: When a Pyramid or a Cone is cut by a Plane parallel to its base, thus removing the top portion, the remaining lower portion is called its frustum.

  18. Important Terms Used in Projections of Solids: (8) Truncated Solid : When a Pyramid or a Cone is cut by a Plane inclined to its base, thus removing the top portion, the remaining lower portion is said to be truncated.

  19. Class A(1): Axis perpendicular to H. P. and hence parallel to both V.P. & P.P. Y X o’ Axis a’,b’ c’,d’ a d o b c

  20. Class A(2): Axis perpendicular to V.P. and hence parallel to both H.P. & P.P. X Y f’,6’ e’,5’ d’,4’ a’,1’ b’,2’ c’,3’ 4 1 2,6 3,5 H d a c,e b,f

  21. Class A(3): Axis perpendicular to P.P. and hence parallel to both H.P. & V.P. X Y L 3’ c”3” c’ a’,b’ b”2” 1’2’ a”1” 1 a c 3 2 b

  22. a’(b’) c’ PROBLEM NO: 1 Draw the projections of a triangular prism, base 40mm side and axis 50mm long, resting on one of its bases on the ground with a vertical face perpendicular to the V.P. O’ 50 1’ ( 2’) O’ 3’ Y X b(2) c(3) O 40 a(1)

  23. PROBLEM NO: 2 Draw the projections of a pentagonal pyramid, base 30mm edge and axis 50mm long, having its base on the ground and an edge of the base parallel to V.P. o‘ 50 a’ e‘ b’ e‘ d‘ X Y e d c o a 30 b

  24. PROBLEM NO: 3 Draw the projections of i) a cylinder, base 40mm dia and axis 50mm long, ii) a cone, base 40mm dia and axis 50mm long, resting on the ground on their respective bases. a’ c’ o‘ b’ d’ 50 50 a’ c’ b’ d’ 2’ 4’ 1’ 3’ X X Y Y d d 4 1 3 a a c c o o 2 b b 40 40

  25. b’(d‘) a’ c’ d(4) c(3) a(1) b(2) PROBLEM NO : 4 A cube of 50mm long edges is resting on the H.P with its vertical faces equally inclined to the V.P. Draw its projections. 50 X Y 2’(4’) 3’ 1’ 45⁰ 50

  26. PROBLEM NO: 5 A hexagonal prism has one of its rectangular faces parallel to the ground, its axis is perpendicular to the VP and 3.5cm above the ground. Draw its projections when the nearer end is 2cm in front of VP. Side of the base is 2.5cm, axis 5cm long. 2.5 f (6) e (5) d (4) a (1) c (3) b (2) 3.5 Y X 2 5 (3) 2 (6) 4 1 50 c (e) d a b (f)

  27. PROBLEM NO : 6. A hexagonal pyramid, base on the ground and a side of the base parallel to and 25mm in front of the VP. Draw the projections taking a side of the base 40mm and axis 65mm long. O’ 65 b’ (f’) c’ (e’) d’ a’ Y X 25 f e a d O c b 40

  28. PROBLEM NO: 8. A triangular pyramid base on the ground and an edge of the base inclined at 450 to the VP, the apex 40mm in front of the VP. Draw the projections taking a side of the base 40mm long and axis 65mm long. o’ 65 c’ a’ o’ b’ Y X c 45⁰ 40 o a 40 b

  29. 4 d’’ 3’ c’ 1’ a’ 2’ b’ PROBLEM NO: 9 A cylinder, axis perpendicular to the VP and 40mm above HP, one end 20mm in front of the VP. Draw the projections taking diameter of the base 50mm and the axis 65mm long. (Home work). ⌽50 40 Y X 20 a b d c 65 1 2 4 3

  30. PROBLEM NO: 10 A pentagonal prism, rectangular face parallel to and 10mm above the HP, axis perpendicular to the VP and one base in the VP. Draw the projections taking side of the base 40mm long and axis 65mm long. e’ 40 2’ 1’ 3’ a’ o d’ 4’ 5’ c’ b’ 10 5 3 4 2 1 Y X 65 a e c d b

  31. PROBLEM NO: 11 A square pyramid, all edges of the base equally inclined to the HP and the axis parallel to and 50mm away from both HP and VP. Draw the projections taking a side of the base 40mm and axis 65mm long. 65 d’’ d’ 40 a’’ a’(c’) o’’ o’ c’’ 50 b’ b’’ 45⁰ X Y 45⁰ 50 a d(b) o c

  32. PROBLEM NO: 12 A cone, apex in the HP. Axis vertical and 40mm in front of VP. Draw its projections taking dia of the base 50mm and axis 65mm long. (Home work). a’ b’ d’ c‘ 65 o‘ X Y d 40 a o c ⌽50 b

  33. PROBLEM NO: 13 A pentagonal pyramid, base in the VP and an edge of the base in the HP. Draw its projections taking a side of the base 40mm and axis 65mm long. e’ 40 a’ o’ d’ c’ b’ X Y a e c b d 65 o

  34. INCLINED TO ONE PLANE PROBLEM NO:1 Draw the projections of a pentagonal prism, base 25mm side and axis 50mm long, resting on one of its rectangular faces on the ground with the axis inclined at 450 to the VP.

  35. 25mm • d’(i’) • d1’ • i1’ B’ • j1’ • e1’ • c1’ • e’(j’) • c’(h’) • h1’ • X • g1’ • Y • f1’ • a’(f’) • b’(g’) • a1’ • b1’ • 45o • c1 • b • e • a • d • c • b1 • d1 • a1 • e1 • 50mm • h1 • g1 • i1 • f1 • g • j • h • f • i • j1

  36. PROBLEM NO:2 Draw the projections of a cylinder 75mm dia. and 100mm long, lying on the ground with its axis inclined at 300 to the VP and parallel to the ground.

  37. g’ • g1’(71’) • 7’ • h1’(81’) • f1’(61’) • f’ • 6’ • h’ • 8’ • e1’(51’) • a1’(11’) • a’ • 1’ • e’ • 5’ • Ф75mm • Y • X • d1’(41’) • b1’(21’) • d’ • 4’ • b’ • 2’ • c1’(31’) • c’ • 3’ • 45o • e • f (d) • g(c) • e1 • g1 (c1) • f1 (d1) • a1 • h1 (b1) • h (b) • a • 5 • Ф100mm • 6 (4) • 7 (3) • 8 (2) • 1 • 51 • 71 (31) • 61 (41) • 11 • 81 (21)

  38. PROBLEM NO:3 A hexagonal pyramid, base 25mm side and axis 50mm long, has an edge of the base on the ground. Its axis inclined at 300 to the ground and parallel to the VP. Draw its projections.

  39. o’ • o’1 • 50mm • b’1(a’1) • c’1(f’1) • Y • X • b‘(a‘) • d’(e’) • c‘(f‘) • d’1(e’1) • 300 • f1 • f • e • e1 • a • a1 • o • o1 • 25mm • d • b1 • b • d1 • c1 • c

  40. PROBLEM NO:4 Draw the projections of a cone, base 75mm dia. and axis 100mm long lying on the HP on one of its generators with the axis parallel to the VP.

  41. o’ • a’1 • b’1(d’1) • a’ • b’(d’) • c’ • c’1 • o’1 • d • Y • Ф100mm • X • d1 • o1 • o • c1 • a1 • a • c • Ф75mm • b • b1

  42. INCLINED TO BOTH PLANES PROBLEM NO:5 A square prism, base 40mm. side and height 65mm,has its axis inclined at 45˚to the H.P and has an edge of its base on the H.P and inclined at 30˚ to the VP draw its projections.

  43. f’(e’) • g’(h’) • f’1(e’1) • h’2 • e’2 • g’1(h’1) • g’2 • f’2 • 65mm • b’1(a’1) • a’2 • d’2 • c’1(d’1) • 450 • c’2 • X • b’(a’) • c’(d’) • b’2 • Y • 300 • d2 • a(e) • d(h) • a1 • e1 • d1 • h1 • c2 • a2 • 40mm • b2 • h2 • g1 • f1 • b(f) • c(g) • b1 • c1 • g2 • e2 • o • f2

  44. PROBLEM NO:6 Draw the projections of a hexagonal pyramid edge of the base 30mm and height 65mm. standing on one of its edges in the HP. The edge making an angle of 45˚ to the VP, and the slant face containing this edge makes an angle of 60˚ to the HP.

  45. o’ • o’1 • o’2 • b’1(a’1) • a’2 • f’2 • 65mm • e’2 • c’1(f’1) • b’2 • 600 • c’2 • d’2 • d’1(e’1) • b‘(a‘) • d’(e’) • c‘(f‘) • Y • X • 450 • f2 • e2 • f1 • f • a2 • a1 • e1 • d2 • e • a • o1 • 35mm • c2 • b2 • b • b1 • d1 • d • c • c1 • o2

  46. PROBLEM NO:7 Draw the projections of a cone , base 45mm. diameter and axis 50mm. long , when it is resting on the ground on a point on its base circle, with the axis making an angle of 30˚ to the HP and 45˚ with the VP.

  47. o’ • o’1 • o’2Y • 50mm • a2’ • a’1 • d2’ • b1’(d1’) • b2’ • b’(d’) • c’ • c’1 • c2’ • a’ • β • 45o • d • d2 • d1 • a2 • o • a1 • c1 • c2 • c • a • o1 • b2 • Ф45mm • b • b1 • o2

  48. THANK YOU

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