2 Projection of Lines
2.1 Introduction
Projection of lines is a fundamental topic in engineering graphics. It involves representing a line in different planes (such as the horizontal plane and vertical plane) to understand its true length and inclination.
2.2 Objectives
- Understand the concept of projection of lines.
- Learn to draw projections of lines inclined to one or both reference planes.
- Solve typical problems related to projection of lines.
2.3 Basic Concepts
- Projection: The representation of an object on a plane.
- Reference Planes: Usually the Horizontal Plane (HP) and Vertical Plane (VP).
- True Length: The actual length of the line in 3D space.
- Apparent Length: The length of the line as seen in the projection.
2.4 Types of Line Positions
2.4.1 Line parallel to both HP and VP.
- In this scenario, the projections on both the V.P. (front view) and H.P. (top view) will display the true length of the line.
2.4.2 Line parallel to one plane and perpendicular to the other.
When the line is parallel to the V.P., its projection on the V.P. (front view) shows the true length, while its projection on the H.P. (top view) appears as a point.
When the line is parallel to the H.P., its projection on the H.P. (top view) shows the true length, while its projection on the V.P. (front view) appears as a point.
2.4.3 Line parallel to one plane and inclined to the other.
If the line is parallel to the V.P. and inclined to the H.P., the front view (on V.P.) will show the true length (TL), while the top view (on H.P.) will display an apparent length (shorter than the TL).
If the line is parallel to the H.P. and inclined to the V.P., the top view (on H.P.) will show the true length (TL), while the front view (on V.P.) will display an apparent length (shorter than the TL).
2.4.4 Line inclined to both HP and VP.
When a line is inclined to both the HP and VP, neither projection (front view or top view) shows the true length. Both projections appear shorter than the actual length of the line.
The true length and true inclinations can be determined using auxiliary views or by rotating the projections.
2.4.4.1 Rotating Line AB to AB₁ (Making it Parallel to VP)
To determine the true length and inclination of a line inclined to both HP and VP, we often use the rotation method. In this method, the line AB is rotated about one of its ends (say, point A) until it becomes parallel to the VP, resulting in a new position AB₁.
- Front View (Projection on VP): When AB is rotated to AB₁ (parallel to VP), the front view shows the true length of the line.
- Top View (Projection on HP): The top view during this rotation will show the apparent length, which is shorter than the true length.
2.4.4.2 Rotating Line AB to AB₂ (Making it Parallel to HP)
Similarly, to find the true length and inclination of a line, the line AB can be rotated about one of its ends (say, point A) until it becomes parallel to the HP, resulting in a new position AB₂.
- Top View (Projection on HP): When AB is rotated to AB₂ (parallel to HP), the top view shows the true length of the line.
- Front View (Projection on VP): The front view during this rotation will show the apparent length, which is shorter than the true length.