TRIANGULAR DEVELOPMENT

Triangulation is slower and more difficult than parallel line or radial line development, but it is more practical for many types of figures. Additionally, it is the only method by which the developments of warped surfaces may be estimated. In development by triangulation, the piece is divided into a series of

Figure 2-52.-Radial line development of a frustum of a cone.

triangles as in radial Line development. However, there is no one single apex for the triangles. The problem becomes one of finding the true lengths of the varying oblique lines. This is usually done by drawing a true, length diagram.

An example of layout using triangulation is the development of a transition piece.

The steps in the triangulation of a warped transition piece joining a large, square duct and a small, round duct are shown in figure 2-53. The steps are as follows:

1. Draw the top and front orthographic views (view A, fig. 2-53).

2. Divide the circle in the top view into a number of equal spaces and connect the division points with AD (taken from the top part of view D, fig. 2-53) from point A. This completes one fourth of the development. Since the piece is symmetrical, the remainder of the development may be constructed using the lengths from the first part.

It is difficult to keep the entire development perfectly symmetrical when it is built up from small triangles. Therefore, you may check the overall symmetry by constructing perpendicular bisectors of AB, BC, CD, and DA (view E, fig. 2-53) and converging at point O. From point O, swing arcs a and b. Arc a should pass through the numbered points, and arc b should pass through the lettered points.

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