Problem No 21 |Given TL,a',a,θ,Φ, B is in 3rd Q | KTU Engineering Graphics 2024,2019 & 2015 Scheme

Introduction

In this tutorial, we will guide you through the process of drawing the projections of a line AB, given its true length and its inclinations to the Horizontal Plane (HP) and Vertical Plane (VP). This exercise is particularly relevant for engineering graphics, helping you understand the spatial relationships of lines in different quadrants, specifically in the third quadrant.

Step 1: Understand the Given Parameters

Before starting the drawing, familiarize yourself with the provided data:

• True length of line AB: 100 mm
• Height of point A above HP: 10 mm
• Distance of point A in front of VP: 20 mm
• Inclination of line AB to HP: 30 degrees
• Inclination of line AB to VP: 20 degrees

Practical Tips

• Sketch a rough diagram to visualize the parameters.
• Label the line AB and its points (A and B) clearly.

Step 2: Draw the Initial Setup

1. Draw the HP and VP: Start by drawing the Horizontal Plane (HP) and the Vertical Plane (VP) on your drawing surface.
2. Locate Point A:
   • Mark point A, which is 10 mm above the HP and 20 mm in front of the VP.
   • This will be your reference point for further projections.

Common Pitfalls

• Ensure the distances are accurately measured to maintain the integrity of the geometric relationships.

Step 3: Project Line AB

1. Determine the projection of line AB onto the HP:

   • Use the inclination of 30 degrees to HP to project the line downwards from point A.
   • Calculate the horizontal and vertical components using trigonometric functions:
     • Horizontal component (x): 100 mm * cos(30°)
     • Vertical component (y): 100 mm * sin(30°)

2. Mark Point B:

   • From point A, measure the horizontal component to find the projection on HP.
   • Since point B is in the third quadrant, place point B accordingly.

Step 4: Draw the Projection onto the VP

1. Determine the projection of line AB onto the VP:

   • Use the inclination of 20 degrees to VP.
   • Calculate the components:
     • Horizontal component (x): 100 mm * cos(20°)
     • Vertical component (z): 100 mm * sin(20°)

2. Mark the projected position:

   • From point A, measure the horizontal component to position point B on VP.

Practical Advice

• Ensure the lines are drawn lightly first so you can adjust them as necessary.

Step 5: Mark Traces

1. Identify the Traces:

   • The trace on the HP is where line AB meets the HP.
   • The trace on the VP is where line AB meets the VP.

2. Draw the traces:

   • Clearly mark these points on your diagram for reference.

Conclusion

By following these steps, you have successfully projected the line AB given its true length and inclinations, with point B located in the third quadrant. Remember to double-check all measurements and projections for accuracy. This exercise reinforces your understanding of spatial visualization in engineering graphics, preparing you for more complex scenarios in your studies. If you have further queries about projections or engineering graphics, consider reviewing additional tutorials or practicing similar problems.