Projection of Regular Solids and Sectional View (6 hrs) · Engineering Graphics and Design

Orthographic Projections of Regular Solids

1. Classification of Engineering Solids

An engineering solid is a 3-dimensional object bounded by surfaces, classified into two major categories:

                          ENGINEERING SOLIDS
                                  |
         +------------------------+------------------------+
         |                                                 |
     POLYHEDRA                                    SOLIDS OF REVOLUTION
 (Bounded by flat plane faces)                (Generated by rotating a plane curve)
   - Prisms (Triangular, Square, Hexagonal)      - Cylinder (Rectangle rotated about side)
   - Pyramids (Square, Pentagonal, Hexagonal)    - Cone (Right triangle rotated about side)
   - Regular (Tetrahedron, Cube, Octahedron)     - Sphere (Semicircle rotated about diameter)

Type of Solid	Base Geometry	Lateral Surfaces	Apex / Top End
Prism	Polygon (two identical parallel bases)	Rectangles connecting corresponding sides	Identical parallel top base
Pyramid	Polygon (single base)	Isosceles triangles meeting at a point	Apex ( $O$ )
Cylinder	Circle	Continuous curved surface	Identical circular top base
Cone	Circle	Curved surface formed by generators	Apex ( $O$ )

2. Right and Regular Solids

Right Solid: A solid whose central axis is perpendicular to its base.
Regular Solid: A solid whose base is a regular polygon (all sides and angles equal).
Frustum: When a pyramid or cone is cut by a cutting plane parallel to its base, the remaining lower portion is called a frustum.
Truncated Solid: When a solid is cut by a cutting plane inclined to its base, the remaining lower portion is termed truncated.

3. The Initial Position Principle (Which View to Draw First?)

The golden rule of projecting solids is determining the Initial (True Shape of Base) Position:

If the solid rests on its base on HP (or axis is perpendicular to HP):
- Draw the Top View first (shows the true shape of the base).
- Project upward to draw the Front View.
If the solid rests on its base on VP (or axis is perpendicular to VP):
- Draw the Front View first (shows the true shape of the base).
- Project downward to draw the Top View.
If the axis is inclined to HP (by $\theta$ ):
- Stage 1: Assume axis is perpendicular to HP. Draw TV first, then FV.
- Stage 2: Tilt the Front View so that its axis (or base) makes angle $\theta$ with $XY$ . Project downward to construct the final Top View.

4. Solid Orientation Scenarios (Resting Conditions)

Resting on a Base Edge:                   Resting on a Corner:
Top view drawn with one edge              Top view drawn with the corner
PERPENDICULAR to XY                       lying on the horizontal centerline
      +----+                                   /\
      |    |                                  /  \
  ----+----+---- XY                       ---+----+--- XY
      |    |                                  \  /
      +----+                                   \/

Essential Positioning Rules:

Resting on an Edge of Base: The base must be oriented in the true-shape view such that the resting edge is perpendicular to the reference line $XY$ .
Resting on a Corner of Base: The base must be oriented such that the line joining the center to the resting corner is parallel to $XY$ (or the corner lies on the horizontal centerline).
Freely Suspended Solid: The line joining the point of suspension to the center of gravity ( $CG$ $C G$ ) of the solid is always strictly vertical (perpendicular to $XY$ $X Y$ in the front view):
- Cylinder / Prism: $CG$ is at height $H/2$ from the base along the axis.
- Cone / Pyramid: $CG$ is at height $H/4$ from the base along the axis.

5. Universal Rules of Visibility for Projections of Solids

When drawing the tilted views in Stage 2 or Stage 3:

The Outermost Boundary: All lines forming the exterior boundary of any view are always visible (drawn with continuous thick lines, Type A).
Nearest Face Rule: The face or base closest to the observer is fully visible; all its edges are drawn as solid visible lines.
Farthest Face Rule: The face or base farthest from the observer is hidden; its internal edges are drawn as dashed lines (Type E/F).
Non-Crossing Rule: Two visible lines can never cross each other without meeting at a real corner or vertex.
Generators of Cylinders/Cones: Only the two extreme bounding generators are drawn as solid outlines; intermediate surface generators are not physical edges and should not be drawn as outlines.

6. Summary of Key Exam Points

Center of Gravity Heights:
- Prism / Cylinder: $h_{CG} = \frac{H}{2}$ from base.
- Pyramid / Cone: $h_{CG} = \frac{H}{4}$ from base.
Axis Representation: Axis is always drawn as a chain thin line (Type G) with long dashes and single dots.
Base vs Axis Angle: If a base makes angle $\alpha$ with HP, the axis makes angle $\theta = 90^\circ - \alpha$ with HP.
Apparent Length of Axis: When a solid is tilted, the axis is foreshortened in the projected view; it only shows true length when parallel to the plane of projection.

Orthographic Projections of regular solids