Projections and Pyramid Problem

Jun 14, 2024

Lecture Notes: Projections and Pyramid Problem

Overview

  • Covered topics: Projections, isometric projection, projection of straight lines, points, planes, etc.
  • Recommended to review previous videos for foundational concepts.
  • Today's focus: Square pyramid problem.

Problem Statement

  • **Square Pyramid Details:
    • Base side: 40mm
    • Axis length: 80mm
    • Axis inclined at 30° to the Horizontal Plane (HP)
    • Find auxiliary view when axis is inclined at 45° to the Vertical Plane (VP).

Steps to Solve the Problem

Drawing the True Shape of the Base

  1. Base Type: Draw a square with a 40mm side on HP.
  2. Positioning: Place the base with the side on HP on the right side.
  3. Naming Corners: Label corners as A, B, C, D and the apex as O' P.
  4. Height: Show height 80mm from the base.

True Shape of the Solid

  1. Projection of Points: Project all points up from the base.
  2. Drawing the Edges: Draw all vertices and edges (O to A, O to B, O to C, O to D).
  3. Drawing Axis: Show axis as a dotted or dashed line.

Tilted Solid (Inclined to 30° HP)

  1. Base Angle: Use 60° for the base since 90 - 30 = 60.
  2. Position the Base: Incline the base at 60° to meet axis at 30°.
  3. Projection Lines: Extend all lines to create the inclination.
  4. Naming: Re-labeled points as A, B, C, and D.
  5. Final Edges and Axis: Show the base and apex edges correctly inclined.
  6. Top View: Project the vertices down.

Adding the Second Tilt (45° to VP)

  1. Auxiliary Plane Method: Use auxiliary plane to show second inclination:
    • Draw extended axis at 45° angle.
    • Create reference lines for height and axis.
  2. Projection: Project points into new axis.
  3. Draw Final Edges of the Solid: Use same rules - outer points, edges and axis show clear representation.
  4. Final Front View: Using auxiliary method for correct projection.

Key Rules

  1. True Shape of Base: Establish a clear base with proper dimensions and height.
  2. Outer Points: Always darken outer points for clarity.
  3. Base Visibility: Show base either dark if visible, dotted if hidden.
  4. Axis Draw: Dashed lines for axis, dotted lines for hidden lines.
  5. Projections: Ensure all projections follow clear, perpendicular lines from reference points.
  6. Angles and Inclination: Correct application for inclined angles - convert axis to base angles and vice versa as needed.
  7. Crossings: Dark lines only cross with dotted lines, dotted lines don't cross others.
  8. Review for Errors: Double-check each step for correct application of rules and angles.

Final Notes

  • Practice converting different shapes and projections scenarios.
  • Review errors made in previous problems and correct them using the above rules.
  • Use these guidelines across all projection-related problems. Practice with various angles and shapes for proficiency.