In Fig. 612 are shown the plan and elevations of an offset or transition piece to form a connection between two pipes of oblong profile which will be spoken of in the demonstration as the upper and the lower pipes. M N O P Q L of the plan is the section or profile of the upper pipe which begins at the line A B of the elevation and extends upward, while F I H I J K of the plan is the section of lower pipe which begins at the line D C of the elevation and extends downward, A B C D being one view of the offset. At the right the same plan is shown turned one-quarter way around, from which, and the front elevation, are projected a side elevation of the offset. Corresponding points in the two plans arc indicated by the same letters, capitals being used in the one and italics in the other.
An inspection of the plan will show that the long diameter O L of the upper pipe cuts the profile of the lower pipe nearer one end than the other, from which it must be concluded that the pattern cannot be composed of symmetrical halves or quarters and that therefore the entire pattern must be developed at one operation.
Fig. 612. - Plan and Elevations of an Offset between Two Pipes of Oblong Profile.
As the sections of both pipes may be said to consist of four quarter circles joined to the straight side, the pattern will consist principally of four rounded corners joining the quarter circles which occupy the same relative position in the two pipes. Thus lines joining the quarter circles F G of the bottom and L M of the top would form one corner of the envelope of the offset. Lines from G H of the bottom to N O of the top would form another corner, lines from I J up to O P a third corner and lines from J K up to Q L the fourth. Lying between these corner pieces are the two triangular end pieces K L F and I H O and the side pieces M N G and Q P J. For convenience in describing the pattern the joint will be assumed through one of the ends at the line E L.
Preparatory to obtaining the pattern, first divide each of the four quarter circles of the lower pipe into the same number of equal parts; also divide the profile of the upper pipe in the same manner. To avoid confusion of lines two separate plans arc shown in Figs. 613 and 614 for obtaining these divisions. In Fig. 613 are shown the divisions of what may be called the back end, while Fig. 614 shows those of the front end. As will be seen by these plans, the points have been numbered alternately in the bottom and the top. Solid lines are first drawn, as shown, connecting points 1 2, 3 4, 5 6, etc., after which the four-sided figures thus produced are divided diagonally by the dotted lines 1 4, 3 6, 5 8, etc.
The next operation is the construction of a series of right angled triangles whose bases shall be equal to the several solid and dotted lines which have just been drawn, and whose altitudes shall equal the straight hight of the offset. These have been arranged in four groups, shown in Figs. 615 to 618, corresponding to the four corner pieces above mentioned. In Fig. 615, draw the right angle EST, making R S equal to the straight hight of the article, as indicated by A Z of front elevation. Measuring from S, set off on S T the lengths of solid lines in F G M L of the plan Fig. 613, including L E, which will give the slant hight Corresponding with b c of the side elevation. Connect the points in S T with R, as shown by the solid lines. These hypothenuses represent the distances from points between F and G in the lower pipe to points between M and L of upper pipe, as indicated by the solid line in plan. For the diagram of triangles representing the dotted lines in F G M L of the plan, draw the right angle R1 S1 T1, as shown at the right in Fig. 615, making R1 S1 equal to the straight hight of the article, as derived from A Z of front elevation. Measuring in each instance horn S1, set off on S1 T1 the lengths of dotted lines in F G M L, and from the points thus obtained draw lines to R1. The diagrams shown in Fig. 616 are constructed in the same manner and correspond to the solid and dotted lines in the corner G H O N, shown in Fig. 614. The diagrams of triangles in Fig. 617 are derived from the solid and dotted lines in I J P O of Fig.
Duplicates of Plan in Fig. 612. Showing System of Triangulation.
Fig. 616 - Diagrams of Triangles in G H O N of Fig. 6I4.
Fig. 615. - Diagrams of Triangles in F G M L of Fig. 613.
614, and in Fig. 618 an shown the diagrams of triangles derived from the solid and dotted lines in Q L K J of Fig. 613.
Fig. 617. - Diagrams of Triangles in I J P O of Fig. 614.
To develop the pattern draw any line, as E L of Fig. 619, in length equal to R E of Fig. 615, which gives the actual distance from E in the base to L in the top, as also shown by b c of side elevation and indicated in corresponding plan by le. With E of pattern as center, and E F of plan as radius, strike a small arc, F, which intersect with one struck from L of pattern as center, and R T of Pig. 615 as radius, thus establishing point F of pattern. With point F of pattern as center, and R1 1 of Fig. 615 as radius, strike a small are, 4, which intersect with one struck from point L of pattern as center, and L 4 of Fig. 613 as radius, thus establishing point 4 of pattern. With point 4 of pattern as center, and R 4 of Fig. 615 as radius, strike a small are, 3, which intersect with one struck from point F of pattern as center, and F 3 of the plan as radius, thus establishing point 3 of pattern. Proceed in this manner, as above described, and as indicated by the solid and dotted lines, until the points G and M of pattern arc located. With M of pattern as center, and M N of the plan as radius, strike a small arc, N, which intersect with one struck from G of pattern as center, and U W of Fig. 616 as radius, thus establishing point N of pattern. Proceed in the manner indicated until the remaining points in the pattern are located. It will be observed that the letters and figures in pattern designate points similarly indicated in Figs. 613 and 614. Lines traced through the points obtained as directed, and as shown from E to E' and L' to L, will produce the desired pattern.
619. - Pattern of Offset Shown in Fig. 612.
Fig. 618. - Diagrams of Triangles in Q L K J of Fig. 613
354. The New Metal Worker Pattern Book.