A Lesson on Principal Lines

1. Principal Lines

2. Rule 4: True length of line
• A line will appear in its true
length in a view taken such
that that the fold line is
parallel to the current
projection.

3. Principal lines
• Principal lines are parallel
to at least one of the
principal projection planes.
• A principal line appears in
true length in the principal
projection plane to which it
is parallel, and appears
parallel to the folding line
in the adjacent views.

4. Types of Principal Lines
• There are three basic types of principal lines:
• Horizontal line
• Frontal line
• Profile line
4

5. Horizontal lines
• A horizontal principal line is
parallel to the horizontal
(top) projection plane.
• A horizontal principal line
appears in true length in
the horizontal (top) view.
• A horizontal principal line
appears
• parallel to the TF folding
line in the front view and
parallel to the TR folding
line in the right side view.

6. Frontal lines
• A frontal line is parallel to
the frontal projection
plane, and appears in true
length in the frontal view.
• A frontal line appears
parallel to the TF folding
line in the top view and
parallel to the FR folding
line in the right side view.

7. Profile lines
• A profile line is parallel to
the profile (right side)
projection plane, and
appears in true length in
the right side view.
• A frontal line appears
parallel to the FR folding
line in the front view and
parallel to the TR folding
line in the top view.

8. SAMPLE PROBLEMS 8

9. Sample Problem #1
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
9

10. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 1:
• Since the front view of line
1-2 in the F-plane is
parallel to the H-plane, it
means that horizontal view
of line 1-2 will be in true
length. 10

11. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 2:
• Since point 2 should align
vertically between H and F
plane, projecting the
position of point 2 to the H
plane shows the possible
location of point 2. 11

12. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 3:
• Since the true length is in
H-plane, make a 70mm line
from point 1 and rotate it
until it hits the possible
location of pt. 2.
12

13. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 4:
• Note that there are two
possible locations of pt. 2,
but the problem describes
it to be behind point 1.
13

14. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 5:
• Having located pt. 2 in the
H-plane, simply project its
position to the P-plane to
locate its position in that
plane.
14

15. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 6:
• Since line 1-3 is a frontal
line, point 3 should be
aligned with point 1 at a
position parallel to the F-
plane.
15

16. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 7:
• Since line 2-3 is a profile
line, pt. 3 should be
aligned with pt. 2 at a
position parallel to the P-
plane. This locates the
position of pt. 3 in H-plane. 16

17. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 8:
• Since line 1-3 is a frontal
line, draw a 80mm line
from pt. 1 then rotate it
until it hits the possible
location of pt. 3. This
completes the front view. 17

18. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 9:
• The profile view can easily
be completed by projecting
the locations of pt. 3 in the
P-plane.
18

19. Sample Problem #1 (Answer)
• Line 1( 20,15,25) - 2(75, ?,
25) is 70mm long (2 behind
1). Line 1-3 is a 80mm
frontal line, and line 2-3 is
a profile line. Find the true
length of line 2-3.
• Step 10:
• Since line 2-3 is a profile
line, simply measure line 2-
3 in the P-plane to get its
true length.
19

20. Sample Problem #2
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
20

21. Sample Problem #2(Answer)
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
• Step 1:
• Since pt. 5 is 35mm below
pt. 1 on line 1-2, we can
easily locate pt. 5 in the F-
plane.
21

22. Sample Problem #2(Answer)
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
• Step 2:
• Projecting pt. 5 from the F-
plane to the H-plane helps
us locate pt. 5 in the H-
plane, which should also
be on line 1-2. 22

23. Sample Problem #2(Answer)
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
• Step 3:
• Since line 5-6 is a frontal
line, it follows that line 5-6
in the H-plane should be
parallel to the F-plane. Pt.
6 is also on line 3-4. 23

24. Sample Problem #2(Answer)
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
• Step 4:
• Projecting pt. 6 from H-
plane to F-plane helps us
locate pt. 6 on the F-plane,
which should be on line 3-4
24

25. Sample Problem #2(Answer)
• Point 5 is on line
1(20,65,90) – 2(60,15,25),
35mm below point 1. Point
6 is on line 3(90,5,25) –
4(140,80,80). Line 5-6 if
frontal. Find the true
length of line 5-6.
• Step 5:
• Since frontal view of line 5-
6 is now complete, the
true length can now be
determined.
25

26. SEATWORK PROBLEMS 26

27. Seatwork Instructions:
• Use a short bond paper.
• Place margin all around at
10mm from edge of paper.
• Draw a horizontal line
20mm below top margin to
create a panel where you
will write the word
problem.
• Divide the rest of the space
in equal parts depending
on the requirement of the
problem
27

28. Seatwork Problem #3-1
• Line 1(10, ?, 80) - 2(10, 20,
25) is 70mm long. The
front view of line 2 - 3(70,
?, 25) is true length as
indicated. Complete the
views of triangle 1-2-3
28

29. Seatwork Problem #3-2
• Line 2(60,15,80) –
3(60,55,?) is 60mm long.
Line 3 - 1(20,15,?) is
horizontal. How long is line
1-2?
29