US 3196061 A
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Description (OCR text may contain errors)
- w. s. PAULSON ETAL 3,196,061
July 20, 1965 METHOD OF MAKING AN ORNAMENTAL HYPERBOLOID STRUCTURE Filed March 26, 1962 INVENTORS. Wallace 8. Paulson David G. Herbener BY ATTORNEY United States Patent 3,196,061 METHOD 0F MAKING AN ORNAMEN'IAL HYPERBOLOID STRUCTURE Wallace S. Paulson, 5331 E. Asbury Ave., and David G. Herhener, 2994 S. Ingalls Way, both of Denver, Colo. Filed Mar. 26, 1962, Ser. No. 182,44? 2 Claims. (Ql. 156-63) This invention relates to forming articles of manufacture such as pedestals, lamp bases, planters and other ornamental circular columns and bases with axially curvated surfaces.
The principal object of the invention is to provide a method and means whereby a variety of hollow, closed articles of circular or other curvated cross section and of any desired diameter and with any desired degree of axial curvature to their surrounding walls can be quickly and easily formed from a plurality of similar, perfectly straight, elongated elements.
Other objects and advantages reside in the detatil construction of the invention, which is designed for simplicity, economy and efiiciency. These will become more ap parent from the following description.
In the following detailed description of the invention, reference is had to the accompanying drawing which forms a part hereof. Like numerals refer to like parts in all views of the drawing and throughout the description.
In the drawing:
FIG. 1 is an end view of a plank of material, such as Wood, showing how the elongated straight elements of this invention can be formed by making parallel rip cuts, alternating in direction, throughout the length and width of the plank;
FIG. 2 is a perspective view of a typical one of the straight elongated elements;
FIG. 3 is an end view of an assembled loose bundle of the elements in position to be formed into an article of manufacture as will be later described;
FIG. 4 is a top plan view of an article formed by expanding extremities of the loose bundle of FIG. 3;
FIG. 5 is a side elevational view of the article of FIG.
FIG. 6 is a graphic diagram of a basic axial section of an article formed by this invention; and
FIG. 7 is a similar graphic representation of the basic cross sectional contour of each of the straight elements.
The invention comprises forming a plurality of elongated straight elements 10 preferably having inclined radial, side faces 11 leading from a base edge 12 to an apex edge 13 to produce a wedge-shaped cross section, assembling these elements in unattached, slidably contacting relation in a bundle thence rotating portions of the bundle relative to other portions thereof so that the elements will slide on each other to form a closed wall hav ing an axial curvature of any desired degree, depending upon the degree of rotation, without change of any kind in the shape of the straight elements, thence permanently cementing the elements together to form a desired article. The straight elements may be formed in any suitable manner from any suitable material, for instance, they may be formed by rip sawing a wooden plank, such as illustrated at 14 in FIG. 1, or if formed of plastic or metal, they may be cast, molded or extruded with a triangular, wedge-shaped or segment-shaped cross section.
For forming a substantially circular article with longi tudinally curved sides, a plurality of the straight elements are assembled in a circular bundle with the adjacent side faces 11 of contiguous elements in slidable contact as shown in FIG. 3 to provide a straight sided hollow cylinder. The two extremities of the bundle are then twisted or rotated in opposite directions relative to each other to cause the straight elements 10 to incline and slide upon each other out of parallel relation with the axis of the bundle so as to increase the terminal diameters of the bundle relative to the medial diameter to produce a hollow, axially curvated article as illustrated in FIGS. 4 and 5 with a completely closed surrounding wall.
If the resulting article is to be permanent, the radial side faces 11 of the straight members 10 may be coated with a suitable adhesive which will set to produce a rigid, ornamental, vase-like article. If desired, the projecting angularly inclined ends of the straight pieces can be trimmed to produce a finished article. The external surface may be turned or sanded to remove the projecting corners of the base edges 12 to produce a smooth continuous external surface if such a surface is preferred.
The simplest shape produced by this method is a hyperboloid of revolution as diagrammatically illustrated in FIGS. 6 and 7. FIG. 7 diagrammatically illustrates the cross section of the straight elements 10 as a triangle having an altitude a, a base edge width b and an included angle c. FIG. 6 graphically illustrates a typical longitudinal, axial section through a desired article to be produced by this invention having a length L and two internal conical cavities 15 and 16 with coincident apexes, each having a wall angle of d. The outer corners of the base edges 12 of the elements lie in a hyperboloid of revolution as indicated at e.
Many variations of this shape may be obtained by different combinations of a, b, d L, and 0 and variations in the number of straight elements computed from the following equation in which the number of equal-angled elements is represented by n:
The Total Angle, n arctan (tan c/cos d)=360 must have an included angle such that:
Tan C=tan (360/n) cos d Thus, by proper choice and arrangement of elements, virtually unlimited shapes of warped or curvated surfaces can be fabricated, including both open and'closed sections of circular and non-circular cross section having either or both concave and convex external curvature with completely closed walls.
Article cross-sections that are other than circular may be obtained by either differentially shifting the elements so that the amount of overlap will vary at selected portions of the wall, or by using an assembly of elements of varying included angle (0). Articles of closed medial cross section may be obtained by bringing the apex edges to a sharp edge having no width.
While a specific form of the invention has been described and illustrated herein, it is to be understood that the same may be varied within the scope of the appended claims, without departing from the spirit of the invention.
Having thus described the invention what is claimed and desired to be secured by Letters Patent is:
1. The method of forming an ornamental article comprising providing a plurality of similar elongated straight elements having radially extending longitudinal side faces providing a wedge-shaped cross section, assembling said elements in a circular bundle with the adjacent side faces of contiguous elements disposed in slidable contact to provide an elongated straight sided hollow cylinder, twisting the ends of saidcylinder in opposite directions while maintaining the adjacent side faces of contiguous ele ments in contact thereby disposing said elements out of parallel relation with respect to each other and at an angle to the axis of said cylinder, moving the upper and lower ends of said elements radially outwardly from said axis to provide an axially concave annular outer wall thence adhering said elongated elements together.
2. The method of forming an ornamental article comprising providing a plurality of similar elongated straight elements having radiallyextending longitudinal side faces providing a Wedge-shaped cross section, assembling said elements in a circular bundle with the adjacent side faces of contiguous elements disposed in slidable contact to provide an elongated straight sided hollow cylinder, twisting the ends of said cylinder relative to each other While maintaining the adjacent side faces of contiguous elements in Contact thereby disposing said elements out of parallel relation with respect to each other and at an angle to the axis of said cylinder, moving an end of said 4 symmetrical non-cylindrical annular outer Wall thence adhering said elongated elements together.
References Cited by the Examiner UNITED STATES PATENTS Kojima 41-10 XR ALEXANDER WYMAN, Primary Examiner? elements radially outwardly from said axis to provide a 15 JACOB STEINBERG, Examiner-