ENGINEERING DRAWING (CHAPTER-9)


๐Ÿ“˜ ENGINEERING DRAWING

Chapter 9 – Projection of Solids

9.1 Introduction

  • A solid is a 3D object having length, breadth, and thickness.

  • In engineering drawing, we represent these solids on 2D planes (HP & VP) using orthographic projection.

  • Solids are used in machine design, civil structures, tools, models, and construction drawings.

9.2 Classification of Solids

(A) Polyhedra (bounded by plane surfaces)

  1. Regular Polyhedra – All faces are equal regular polygons

    • Tetrahedron (4 faces)

    • Cube (6 square faces)

    • Octahedron (8 triangular faces)

  2. Prism – Two bases are equal polygons, joined by rectangular faces

    • Triangular prism, Square prism, Hexagonal prism, etc.

  3. Pyramid – A polygonal base with triangular faces meeting at a point (apex)

    • Triangular pyramid, Square pyramid, Pentagonal pyramid, etc.

(B) Solids of Revolution (formed by revolving a plane figure)

  • Cylinder → rectangle revolved about one side

  • Cone → right-angled triangle revolved about one side

  • Sphere → semicircle revolved about diameter

(C) Frustum & Truncated Solids

  • Frustum → solid cut by a plane parallel to base

  • Truncated → solid cut by a plane inclined to base

9.3 Position of Solids in Projection

The projection of a solid depends on its position with respect to HP & VP.

Cases:

  1. Axis perpendicular to HP, parallel to VP

    • FV = true shape & size of solid

    • TV = true shape of base

  2. Axis perpendicular to VP, parallel to HP

    • TV = true shape

    • FV = projection (distorted)

  3. Axis parallel to both HP & VP

    • Both FV and TV show projections (elongated).

  4. Axis inclined to one plane and parallel to other

    • One view shows inclination, other view is distorted.

  5. Axis inclined to both HP and VP

    • Auxiliary projection is required.

9.4 Projection of Specific Solids

(A) Cube (Hexahedron)

  • Given: Cube of side 40 mm, resting on HP with one face parallel to VP.

  • Steps:

    1. Draw TV → square of 40 mm.

    2. Project FV → square.

    3. If cube is tilted, use auxiliary projection.

(B) Prism

  • Example: Hexagonal Prism, base side 25 mm, axis 50 mm long, resting on HP with base edge parallel to VP.

  • Steps:

    1. TV → Hexagon (true shape of base).

    2. Project FV → rectangle with edges showing vertical edges.

    3. Show hidden edges by dashed lines.

(C) Pyramid

  • Example: Square Pyramid, base side 30 mm, axis 60 mm, resting on HP.

  • Steps:

    1. TV → Square base.

    2. Project FV → Triangle (apex above center of base).

    3. Join apex to all base corners.

(D) Cylinder

  • Example: Cylinder, base ⌀40 mm, height 60 mm, axis vertical.

  • Steps:

    1. TV → Circle (true base).

    2. Project FV → Rectangle (height = 60, width = diameter).

    3. Show axis with chain line.

(E) Cone

  • Example: Cone, base ⌀50 mm, height 70 mm, resting on HP.

  • Steps:

    1. TV → Circle of ⌀50 mm.

    2. Project FV → Triangle (apex above center of base).

(F) Sphere

  • Always projects as a circle in any view.

  • FV, TV, Side view → all circles.

9.5 Truncated and Frustum Solids

When a solid is cut by a plane:

  • Truncated Solid → cut by an inclined plane.

  • Frustum → cut by a plane parallel to base.

Example: A cone, base ⌀60 mm, height 80 mm, cut by a plane parallel to base at half height.

  • FV → Trapezium (showing frustum).

  • TV → Circle (smaller circle for cut section).

๐Ÿ‘‰ These are very important for sectional views and development of surfaces (next chapters).

9.6 Practical Applications of Solid Projections

  • Mechanical Engineering → Nuts, bolts, gears, shafts, machine blocks.

  • Civil Engineering → Buildings, water tanks, piers, domes.

  • Architecture → Roofs, cones, spheres, cylinders.

  • Manufacturing → Patterns, casting designs, sheet-metal works.

9.7 Summary of Chapter

  • Solids are classified into Polyhedra, Solids of Revolution, Frustums & Truncated Solids.

  • Projection depends on axis position (perpendicular, parallel, inclined).

  • Cube, Prism, Pyramid, Cylinder, Cone, and Sphere are projected step by step.

  • Truncated & Frustum solids are important in sectional views and developments.


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