Unit 2: Projection of Points and Lines

1. Introduction to Orthographic Projections

Orthographic projection is a method of representing three-dimensional objects on a two-dimensional plane using parallel lines of sight perpendicular to the plane of projection.

Key Terminology

• Projectors: Parallel lines drawn from the object to the plane.
• Plane of Projection: The flat surface on which the image is formed.
• Reference Line (XY Line): The intersection line between the two principal planes.
• Principal Planes:
  • Vertical Plane (VP): The plane standing vertically (like a wall). The view projected here is the Front View (FV) or Elevation.
  • Horizontal Plane (HP): The plane aligned horizontally (like a floor). The view projected here is the Top View (TV) or Plan.

2. Principles of Quadrants

The intersection of the HP and VP creates four quadrants. The position of an object is defined relative to these planes.

The Pattern of Rotation

To convert the 3D quadrant system into a 2D drawing sheet:

1. The Vertical Plane (VP) remains fixed.
2. The Horizontal Plane (HP) is rotated clockwise.

The Four Quadrants

Note: Engineering drawings primarily use First Angle Projection (Europe/Asia) or Third Angle Projection (USA).

3. Projection of Points

A point has no dimensions; it only has a position.

Notation Standard

• Actual Point in Space: Capital Letter (e.g., A)
• Top View (on HP): Lower case letter (e.g., a)
• Front View (on VP): Lower case letter with a prime (e.g., a')

Projection Scenarios

1. Point A (Above HP, In front of VP): is above XY; is below XY.
2. Point B (Above HP, Behind VP): is above XY; is above XY.
3. Point C (Below HP, Behind VP): is below XY; is above XY.
4. Point D (Below HP, In front of VP): is below XY; is below XY.
5. Point on HP: Elevation () lies on the XY line.
6. Point on VP: Plan () lies on the XY line.
7. Point on both HP and VP: Both views lie on the XY line.

4. Projection of Lines

A line is the shortest distance between two points. Its projection depends on its orientation relative to the HP and VP.

True Length vs. Apparent Length

• True Length (TL): The actual length of the line. Visible when the line is parallel to the plane of projection.
• Apparent Length: The shortened length seen when a line is inclined to the plane of projection.

Case 1: Line Parallel to Both HP and VP

• Front View: Parallel to XY line. Shows True Length.
• Top View: Parallel to XY line. Shows True Length.

Case 2: Line Perpendicular to One Plane and Parallel to the Other

• Perpendicular to HP (Parallel to VP):
  • Front View: Vertical line perpendicular to XY (True Length).
  • Top View: A point.
• Perpendicular to VP (Parallel to HP):
  • Front View: A point.
  • Top View: Vertical line perpendicular to XY (True Length).

Case 3: Line Inclined to One Plane and Parallel to the Other

• Inclined to HP, Parallel to VP:
  • Front View: Inclined line showing True Length and true inclination angle ().
  • Top View: Line parallel to XY (Apparent length/shorter).
• Inclined to VP, Parallel to HP:
  • Front View: Line parallel to XY (Apparent length/shorter).
  • Top View: Inclined line showing True Length and true inclination angle ().

5. Concept of Traces of Lines

Traces are the points where a line intersects the reference planes (HP or VP) if extended.

• Horizontal Trace (HT): The point where the line (or its extension) meets the Horizontal Plane. In the Front View, this occurs where the projection line meets the XY axis.
• Vertical Trace (VT): The point where the line (or its extension) meets the Vertical Plane. In the Top View, this occurs where the projection line meets the XY axis.

Rule of thumb:

• To find HT: Extend the Front View to meet the XY line, then drop a perpendicular to intersect the Top View.
• To find VT: Extend the Top View to meet the XY line, then erect a perpendicular to intersect the Front View.

6. Projections of Plane Figures (2D Shapes)

Rectangle & Polygon

When drawing plane figures using instruments or AutoCAD:

1. Axis Perpendicular to Plane: If a plate is perpendicular to the HP, its Top View is a line.
2. Axis Inclined: If the surface is inclined to a plane, the view on that plane will be compressed (foreshortened).

Ellipse

An ellipse is a conic section or the view of a circle rotated relative to the viewing plane.

• Major Axis: The longest diameter.
• Minor Axis: The shortest diameter perpendicular to the major axis.

7. AutoCAD Commands

AutoCAD is a vector-based drafting software. Commands can be entered via the Command Line or Ribbon.

A. Coordinate Systems

1. Absolute: x,y (Relative to origin 0,0).
2. Relative: @dx,dy (Relative to the last point).
3. Polar: @length<angle (Distance and angle from the last point).

B. Drawing Commands

1. LINE (L)

Creates individual line segments.

• Command: L or LINE
• Process: Specify start point Specify next point.
• Note: Each segment is a separate object.

2. CIRCLE (C)

Creates circles using various methods.

• Center, Radius: Default method. Pick center, type radius.
• 2P (Two Point): Define diameter by two endpoints.
• 3P (Three Point): Define circle passing through 3 points.
• TTR (Tan, Tan, Radius): Tangent to two objects with a specific radius.

3. ARC (A)

Creates an arc (part of a circle).

• 3-Point: Start, point on arc, end.
• Start, Center, End: Useful for engineering curves.
• Note: Arcs are always drawn counter-clockwise by default in AutoCAD.

4. POLYLINE (PL)

Creates a connected sequence of segments as a single object.

• Advantages: Can have width, can include arc segments within the command, and calculates total area/perimeter easily.
• Command: PL Start point Next points.

5. ELLIPSE (EL)

• Center Method: Specify center Endpoint of axis 1 Distance to other axis.
• Axis, End Method: Specify two endpoints of an axis Distance to other axis.

8. Dimensioning Style (DIMSTYLE)

Proper dimensioning is critical for engineering drawings.

Accessing Dimension Style Manager

• Command: D or DIMSTYLE .

Key Settings in DIMSTYLE

1. Lines: Control color, linetype, and extend beyond ticks of dimension lines and extension lines.
2. Symbols and Arrows: Change arrowheads (e.g., Closed Filled for mechanical, Architectural Tick for civil).
3. Text: Set text height, placement (Centered/Above), and alignment (Aligned with dimension line).
4. Primary Units: Set precision (e.g., 0.00) and decimal separator.

Dimensioning Commands

• DIMLINEAR (DLI): Horizontal or vertical dimensions.
• DIMALIGNED (DAL): Dimensions parallel to an inclined line.
• DIMANGULAR (DAN): Angle between two lines.
• DIMRADIUS (DRA): Radius of circle/arc.
• DIMDIAMETER (DDI): Diameter of circle.

9. Hands-on Practice on AutoCAD

To successfully execute Unit 2 topics in AutoCAD, follow this workflow:

Step 1: Setup

1. Start Command: Type STARTUP set to 1 for advanced wizard, or just open a new acadiso.dwt (Metric) file.
2. Units: Type UN . Set to "Decimal" and Precision to "0.00". Set Insertion Scale to "Millimeters".
3. Limits: Type LIMITS. Set lower-left (0,0) and upper-right (e.g., 297,210 for A4).
4. Zoom: Type Z then A (Zoom All).

Step 2: Object Settings (Layers)

Use LA (Layer Properties) to create layers:

• XY Axis: Red color, continuous line.
• Object/Projection: White/Black, continuous, lineweight 0.30mm.
• Projectors: Grey, continuous, default weight.
• Dimensions: Blue, continuous.

Step 3: Drafting Projection of a Line (Example Workflow)

Problem: Line AB 50mm long, parallel to HP and VP.

1. Draw XY Line: Turn ORTHO mode ON (F8). Draw a horizontal line using L.
2. Draw Top View:
   • Command: L
   • Start point: Click somewhere below XY.
   • Next point: Move mouse right, type 50 .
3. Draw Projectors:
   • Use Object Snap (F3) to catch endpoints.
   • Draw vertical lines upward from the Top View past the XY line.
4. Draw Front View:
   • Draw a line connecting the vertical projectors above the XY line.
5. Dimension:
   • Command: DLI. Select endpoints of the line.

Step 4: Drawing Polygons

• Command: POL .
• Enter number of sides (e.g., 6 for Hexagon).
• Specify Center.
• Choose option:
  • Inscribed in circle (I): Polygon fits inside the imaginary radius (Corner to Center).
  • Circumscribed about circle (C): Polygon fits outside the imaginary radius (Flat edge to Center).

Step 5: Output

• Command: PLOT or Ctrl+P.
• Select "DWG to PDF".
• Paper size: ISO A4.
• Plot area: Extents or Window.
• Center the plot.