ENGINEERING DRAWING (CHAPTER -11)


๐Ÿ“˜ ENGINEERING DRAWING

Chapter 11 – Development of Surfaces

11.1 Introduction

  • Development of a surface means unfolding or spreading out the surface of a 3D solid on a 2D plane.

  • This gives the true size and shape of every face of the solid.

  • It is essential in sheet-metal work (fabrication of pipes, hoppers, tanks, ducts, chimneys).

Example:

  • A cylinder can be developed into a rectangle.

  • A cone can be developed into a sector of a circle.

11.2 Methods of Development

  1. Parallel Line Method

    • Used for prisms and cylinders (since their sides are parallel).

  2. Radial Line Method

    • Used for pyramids and cones (since their faces meet at a point).

  3. Triangulation Method

    • Used for transition pieces (objects connecting different shapes, like square-to-round ducts).

11.3 Development of Specific Solids

(A) Cube

  • Development = 6 equal squares arranged in the shape of a cross.

  • Applications: Packaging boxes.

(B) Prism

  • Example: Hexagonal prism, base side 25 mm, axis 60 mm.

  • Development:

    • Draw a rectangle of length = perimeter of base, height = axis.

    • Subdivide length into sides (25 mm × 6).

    • Draw two hexagons for top and bottom faces.

๐Ÿ‘‰ Used in ducts, ventilation shafts.

(C) Cylinder

  • Development = Rectangle.

    • Length = Circumference of base (ฯ€d).

    • Height = axis length.

  • Two circles added for top and bottom covers.

๐Ÿ‘‰ Applications: Pipes, boilers, cans, drums.

(D) Pyramid

  • Development = Apex connected to base edges.

  • Draw base (polygon), then from apex draw radial lines equal to slant edges.

  • Connect points → triangular faces obtained.

๐Ÿ‘‰ Applications: Roofs, hoppers.

(E) Cone

  • Development = Sector of a circle.

    • Radius of sector = slant height (l).

    • Arc length = Circumference of base (ฯ€d).

  • Angle of sector (ฮธ):

    ฮธ=Arc length2ฯ€l×360°ฮธ = \frac{\text{Arc length}}{2ฯ€l} \times 360°

๐Ÿ‘‰ Applications: Funnels, lampshades, chimneys.

(F) Truncated Solids

  • When a solid is cut by a plane (section), the cut surface must also appear in development.

  • Example: A truncated cone → development includes arc for the cut.

(G) Transition Pieces

  • Connect two different shapes (e.g., round pipe to square duct).

  • Developed using triangulation method.

๐Ÿ‘‰ Applications: Air-conditioning ducts, exhaust hoods, pipelines.

11.4 Practical Applications

  • Mechanical Engineering → Boiler shells, tanks, machine covers.

  • Civil Engineering → Layout of ducts, pipes, hoppers.

  • Architecture → Roof coverings, sheet-metal works.

  • Sheet Metal Industry → Manufacturing funnels, trays, drums, cans.

11.5 Summary of Chapter

  • Development = unfolding surface of a solid into a 2D plane.

  • Methods: Parallel line (cylinders, prisms), Radial line (cones, pyramids), Triangulation (transition pieces).

  • Developments are widely used in sheet-metal, fabrication, ducts, tanks, and chimneys.


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