Principal Lines

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.

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.

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

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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.

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.

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.

SAMPLE PROBLEMS 8

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.

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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

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

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.

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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.

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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.

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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.

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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

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

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.

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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.

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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.

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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.

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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

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

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

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.

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SEATWORK PROBLEMS 26

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

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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

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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?

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