Projections of Lines
The projections of a straight line in various positions in the first quadrant are grouped based on its orientation with reference to the vertical and horizontal planes. They are:1. Parallel to both the planes 2. Perpendicular to one plane 3. Parallel to
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Projections of Lines
The projections of a straight line in various positions in the first quadrant are grouped based on its orientation with reference to the vertical and horizontal planes. They are: 1. 2. 3. 4. 5. 6. 7. 8. 9.
Parallel to both the planes Perpendicular to one plane Parallel to one plane and inclined to the other plane Lying in one plane Lying in the reference line xy (intersection of the VP and the HP) Inclined to both the planes Inclined to both the planes with an end in the reference line xy Inclined to both the planes with ends in both the planes Perpendicular to the reference line xy The methods of obtaining the projections are classified under three categories.
Type I The straight line and its projection on a plane have the same length when the line is parallel to that plane. Hence, it is straight-forward to obtain one of the projections. When the straight line is parallel to both the planes, the projections have the same length. After marking the projections of one end of the line, the projections of the line are completed. There are six problems (nos. 1–6) that belong to this category. Type II The projections of a straight line inclined to both the planes will be given or stated. The true length, inclinations to the planes of projection and the meeting points of extension of the line with the planes (traces) are obtained by constructing trapeziums on the projections of the line itself. Following this method, the solutions to nine problems (nos. 7–15) are obtained.
© Springer Nature Singapore Pte Ltd. 2018 K. Rathnam, A First Course in Engineering Drawing, DOI 10.1007/978-981-10-5358-0_7
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Type III The method of obtaining the projections of a straight line inclined to both the planes is explained. This method is reversed to get the true length and inclinations to the reference planes from the projections of the line inclined to both the planes. An easy method of locating the traces alone from the projections of the line is also given with a caution that this simple procedure poses a problem when the projections of the line are perpendicular to the reference line xy. The remaining problems in this chapter are solved by following the method detailed in this type or by some combinations.
Solved Problems 1. Draw the projections of a line 40 mm long when it is parallel to both the HP and the VP. The line is 20 mm from both the planes. Consider the pictorial representation of the line AB in the first quadrant as shown in Fig. 7.1. The line is 20 mm above the HP and 20 mm in front of the VP. Horizontal projectors are drawn from A and B to meet the vertical plane at a0 and b0 . Since the line is parallel to the VP, a0 b0 will be parallel to AB. The elevation a0 b0 will be equal to the true length of the line AB (i.e. a0 b0 ¼ 40 mm). Vertical projectors are drawn from A and B to meet the horizontal plane at a and b. Since the line is parallel to the HP, the plan ab will be equal to the true length
Fig. 7.1 Pictorial representation
Solved Problems
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