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84. Square to Round Transition.—The sheet metal worker is often called upon to make square to round transitions. In heating and ventilation, square and rectangular pipes are changed to round pipes, and ventilators with round shafts are mounted on rectangular bases. Wherever the cross-section of a pipe is changed to another shape the transformation should be gradual in order to avoid excessive friction.

Figure 268 is a pictorial view of a square to round transition. The transition may be considered as being made up of a rectangular prism, having a portion of a scalene cone at each corner, the spaces between these being filled by triangular-faced pieces.

Figure 269 shows one-quarter of the transition removed and the triangles that are to be used in the development of the pattern drawn in their respective positions.

The Plan.—The plan, Fig. 271, is the first view to be drawn. The plan may be divided into four equal parts. It is necessary to treat but one part. The center points of two sides of the square are first determined as shown by points 1 and 3. That part of the circumference between the horizontal and vertical diameters is now divided into four equal parts as shown by points A, B, C, and D.

The base lines are now drawn in, but before drawing them the draftsman must determine the order in which he intends to develop the pattern. It will simplify the study of triangulation if a standard method of development is adopted. Every line should be considered as running in but one direction; for instance, the line AB should be considered as running from point A to point B and not from point B to point A. Furthermore, this line should always be read as A to B, and not simply AB. By pursuing this method the draftsman is enabled to leave his drawing at any time and pick up the "thread" where he left off, upon his return. The letters should be confined to one base and the figures to the other. Thus in Fig. 271, the order would be 1–A, 2–A, 2–B, 2–C, 2–D, and D–3.

The elevation, Fig. 270, may now be drawn, but since the only added information it contains is the altitude of the triangles the experienced draftsman rarely draws this view.