STRAIGHT LINE DEVELOPMENT

This term refers to the development of an object that has surfaces on a flat plane of projection. The true size of each side of the object is known and the sides can be laid out in successive order. Figure 8-6 shows the development of a simple rectangular box with a bottom and four sides. There is an allowance for lap seams at the corners and for a folded edge. The fold lines are shown as thin unbroken lines. Note that all lines for each surface are straight.

Figure 8-7 shows a development drawing with a complete set of folding instructions. Figure 8-8 shows a letter box development drawing where the back is higher than the front surface.

RADIAL-LINE DEVELOPMENT

In radial-line development, the slanting lines of pyramids and cones do not always appear in their true lengths in an orthographic view. The draftsman must find other means, as we will discuss in the following paragraphs on the development of right, oblique, and truncated pyramids.

Figure 8-8.-Development drawing of a letter box.

Figure 8-9.-Development of a right pyramid with true length-of-edge lines shown.

Figure 8-10.-Development of an oblique pyramid by triangulation.

Right Pyramid

Construct a radial-line development of a triangle with a true length-of-edge line (fig. 8-9) and a right pyramid having all the lateral edges (from vertex to the base) of equal length. Since the true length of the lateral edges is shown in the front view (line (0-1 or 0-3) and the top view shows the true lengths of the edges of the base (lines 1-2, 2-3, and so on), the development may be constructed as follows:

With 0 as center (corresponding to the apex) and with a radius equal to the true length of the lateral edges (line 0-1 in the front view), draw an arc as shown. Drop a perpendicular line from 0 to intersect the arc at point 3. With a radius equal to the length of the edge of the base (line 1-2 on the top view), start at point 3 and step off the distances 3-2, 2-1, 3-4, and 4-1 on the large arc. Join these points with straight lines. Then connect the points to point 0 by a straight line to complete the development. Lines 0-2, 0-3, and 0-4 are the fold lines on which the development is folded to shape the pyramid The base and seam allowance have been omitted for clarity.

Oblique Pyramid

The oblique pyramid in figure 8-10 has all its lateral edges of unequal length. The true length of each of these edges must first be found as shown in the true-length diagram. The development may now be constructed as follows:

Lay out base line 1-2 in the development view equal in length to base line 1-2 found in the top view. With point 1 as center and a radius equal in length to line 0-1 in the true diagram, swing an arc. With point 2 as center and a radius equal in length to line 0-2 in the true-length diagram, swing an arc intersecting the first arc at 0. With point 0 as center and a radius equal in length to line 0-3 in the true-length diagram, swing an arc. With point 2 as center and radius equal in length to base line 2-3 found in the top view, swing an arc intersecting the first arc at point 3. Locate points 4 and 1 in a similar manner, and join those points, as shown, with straight lines. The base and seam lines have been omitted on the development drawing.

Truncated Pyramid

Figure 8-11 shows a truncated pyramid that is developed in the following manner: Look at the views in figure 8-11 as you read the explanation.

Draw the orthographic views, extending the lines of the sides to the apex at the top in view A. Draw three horizontal construction lines on the right side of the orthographic view (view B), one from the center of the top view; one from the top of the front view; and one from the bottom of the front view. With the point of the compass in the center of the top view, scribe two arcs (view C). Draw one from the inside corner of the top view to the horizontal line (point W), and the other from the outside corner of the top view to the horizontal line (point X). Draw two vertical lines, one from point W in

Figure 5-11.-Development of a truncated pyramid.

view D to the upper horizontal line on the front view (point Y), and the other from X to the lower horizontal line of the front view (point 2). Draw a line from the apex through points Y and 2 in view D. The distance between points Y and Z equals the true length of the truncated pyramid With the compass point at the apex of view E, find any convenient point to the right of the orthographic view, scribe an are with a radius equal to the distance between the apex and point Y in view D, and a second arc with a radius equal to the distance between the apex and point Z in view D. The two arcs are shown in view E. Draw a radial line beginning at the apex and cutting across arcs Y and Z in view E. Step off lengths along these arcs equal to the length of the sides of the pyramid: MN for the inside arc and OP for the outside arc (view E); the lengths MN and OP are taken from the orthographic view in view D. Connect the points along each arc with heavy lines (for example, points MN along the inner arc and points OP along the outer arc); Also use light lines to connect the apex with points M and 0, and the apex with points N and P, and so on, as shown in view F.

View G is the completed stretchout of a truncated pyramid complete with bend lines, which are marked (X).

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