ENGINEERING DRAWING (CHAPTER-8)


๐Ÿ“˜ ENGINEERING DRAWING

Chapter 8 – Projection of Points, Lines, and Planes

8.1 Introduction

Orthographic projection is based on projecting points, lines, and planes onto the principal reference planes:

  • Horizontal Plane (HP) → Top view (plan)

  • Vertical Plane (VP) → Front view (elevation)

  • Profile Plane (PP) → Side views

๐Ÿ‘‰ Any complex object is made up of points, lines, and planes.
So, to understand projection of solids, we must first master these basics.

8.2 Projection of Points

A point in space is defined by its distance from HP and VP.

Quadrants

The space around the reference planes is divided into four quadrants:

  1. First Quadrant → Point above HP and in front of VP

  2. Second Quadrant → Point above HP and behind VP

  3. Third Quadrant → Point below HP and behind VP

  4. Fourth Quadrant → Point below HP and in front of VP

๐Ÿ‘‰ In First Angle Projection (India/Europe), the object lies in the first quadrant.

Example

Point P is 25 mm above HP and 35 mm in front of VP.

  • FV (Front View) → 25 mm above XY line (on VP).

  • TV (Top View) → 35 mm below XY line (on HP).

8.3 Projection of Straight Lines

A line is defined by its position with respect to HP and VP.

Cases:

(A) Line Parallel to One Plane, Perpendicular to Other

  1. Parallel to HP, perpendicular to VP →

    • FV = Point (line projects as a point on VP).

    • TV = True length (parallel to XY).

  2. Parallel to VP, perpendicular to HP →

    • FV = True length (parallel to XY).

    • TV = Point.

(B) Line Parallel to Both HP and VP

  • Both FV and TV = True length, parallel to XY.

(C) Line Inclined to One Plane, Parallel to Other

  1. Inclined to HP, parallel to VP →

    • FV = Inclined at ฮธ to XY, true length.

    • TV = Parallel to XY, shorter length.

  2. Inclined to VP, parallel to HP →

    • FV = Parallel to XY, shorter length.

    • TV = Inclined at ฮธ, true length.

(D) Line Inclined to Both HP and VP

  • Neither view shows true length.

  • Auxiliary projection is used to find true length and angles of inclination.

8.4 Traces of a Line

  • Horizontal Trace (HT): Point where line (or its extension) meets HP.

  • Vertical Trace (VT): Point where line (or its extension) meets VP.

๐Ÿ‘‰ Important for locating lines in space (used in civil/structural engineering).

8.5 Projection of Planes

A plane is a flat surface like a sheet of paper.
It can be square, rectangle, triangle, circle, polygon, etc.

Cases:

(A) Plane Parallel to One Plane, Perpendicular to Other

  1. Parallel to HP → TV = True shape; FV = Line.

  2. Parallel to VP → FV = True shape; TV = Line.

(B) Plane Perpendicular to Both HP and VP

  • Both views → Lines.

(C) Plane Inclined to One Plane, Perpendicular to Other

  • True shape seen only in auxiliary view.

(D) Plane Inclined to Both HP and VP

  • Neither FV nor TV shows true shape.

  • Auxiliary projection used.

8.6 Examples of Plane Figures

  1. Circular Plane → Projects as ellipse when inclined.

  2. Square Plane → Appears as rectangle or line depending on orientation.

  3. Polygonal Plane → Used in nuts, bolts, plates.

8.7 Auxiliary Projections

  • Definition: An additional view taken on an auxiliary plane, inclined to HP or VP, to show the true shape and size of an object.

  • Steps:

    1. Draw regular FV and TV.

    2. Draw auxiliary plane parallel to the inclined surface.

    3. Project perpendiculars to auxiliary plane.

    4. Transfer distances → obtain true shape.

๐Ÿ‘‰ Auxiliary projection is essential whenever object is inclined.

8.8 Practical Applications

  • Locating positions of points (surveying, site plans).

  • Representing beams, trusses, shafts (lines).

  • Representing slabs, gusset plates, walls, machine covers (planes).

  • Finding true shapes of inclined surfaces (auxiliary view).

8.9 Summary of Chapter

  • A point is located by distances from HP and VP.

  • A line may be parallel, perpendicular, or inclined to HP/VP.

  • Traces (HT, VT) locate lines in space.

  • A plane may be parallel, perpendicular, or inclined to reference planes.

  • Auxiliary projection helps in finding true shape and size.


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