In Fig. 569 are shown the plan and elevations of an article in which the conditions are exactly the same as in the preceding problem. The article here shown differs from that shown in Fig. 566 only in the fact that the diameter of the round end or top is greater than the width of the base, while in Fig. 566 it is less, but the method of obtaining the pattern is exactly the same.
In this case, as in the preceding one, the article consists of four flat triangular pieces (two ends and two sides) and four equal rounded corners, each of which is a quarter of an oblique cone. As the entire envelope consists of four symmetrical quarters, one-quarter of the plan O P N J has been reproduced in Fig. 570 from which to obtain the patterns in the simplest manner.
Divide J I of plan into any convenient number of equal parts, and from the points thus obtained draw lines to N, which represents the apex of an inverted oblique cone. The object is to construct triangles whose altitudes will be equal to the straight hight of the article, and whose bases will be equal to the length of lines in I J N of plan, and whose hypothenuses will give the distance from points in I J of top to N in the base.
To construct this diagram, proceed as follows: From N of Fig. 570 as center, and radii equal to the lengths of the several lines drawn to N, describe arcs, cutting any straight line, as N W. From N draw N n at right angles to N W, which make equal to the straight hight of the article, and from the points in N W draw lines to n. With n as center, and the distances from N to points in N W as radii, strike arcs as shown. From any point, as i, on arc 1, draw a line to n. Set the dividers to the space used in stepping off I J of plan, and, commencing at i, step from arc to arc. as indicated by the small figures, reaching the last in the point 7 or j. Draw j n, thus completing the pattern for part of article indicated in plan by I N J. From N on N W set off the distances Q J and I P, as shown by the points q' and f. Then n q' and n t' will represent respectively the altitudes of the flat triangular pieces forming the sides and the ends of the article. With N Q of plan as radius, and n of pattern as center, strike a small are (q), which intersect with one struck from j of pattern as center, and n q' of diagram as radius, thus establishing the point q of pattern. Draw n q and qj.
With P N of plan as radius, and n of pattern as center, strike a small arc, which intersect with one struck from i of pattern as center, and n t' of the diagram as radius, thus establishing point p of pattern. Draw i p and p n, as shown, thus completing the quarter pattern.
Fig. 569. - Plan and Elevations of an Article with Rectangular Base and Round Top.
Fig. 570. - One-Quarter Plan and Pattern of Article Shown in Fig. 569.
Fig. 571. - The Entire Pattern of Article shown in Fig. 569 in One Piece.
In Fig. 571 i p q j is a duplicate of the pattern indicated by the same letters in Fig. 570. Below this the pattern is duplicated once, and above twice, each alternate pattern being reversed, thus completing the entire pattern in one piece.