This research deals with generation of double curvature forms with a single module: an equilateral triangle.
Keywords: dome, geodesic, engineering, invention, discovery, find out, geometry, cupola, coupole, network, strut, connector, node, hub, building, space, structure, architecture, triangle, equilateral, identical, double curvature, doubly curved surface form, Lobel, form, business, venture capital

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Mass Production

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The present invention relates to construction systems and, more particularly structural systems utilising a limited number of prefabricated components to achieve diverse structural combinations.

The industrial production principle of standardization is really a principle of economy, economy of means as well as economy of resource utilization. Although there are innumerable examples of the misuse of technology, there is ample enough evidence to show that well designed mass production techniques can produce more whith less ressources and in less time that any other strategy. The task clearly becomes one of reconciling the principles of industrial production technique, i.e. standardization with the human and ecological realities of change and diversity.

In order to take best advantage of mass production techniques what is needed are systems which use standardized components, yet a set of such components is needed which can be combined in different ways to yield a great variety of alternative structures. What in fact is required are systems composed of minimum sets of component type which are designed in such a way that they may be combined and recombined into an endless diversity of form.

Modular structures can be defined in terms of volumes, surfaces, or linear frameworks. The latter is the more fundamental in a geometric sense, as surfaces can be defined by linear frames, and volumes can be defined by surfaces (and frames). Any framework must consist of nodes (or vertices) and branches (or edges). A framework is simply the interconnection of points in space with linear branches. In a physical structural system the points or nodes become connectors, and the branches become linear structural components or struts.

In addition to a consideration of the purely spatial properties of modular systems (be they frames, surfaces, or volumes) it is also necessary to study carefully the physical consequences of alternative spatial arranfements. In so far as framework structures are concerned, triangulated configurations give rise to the most efficient systems from the point of view of strength per unit of invested resources, i.e. strength per weight. This has been know to aircraft frame designers for many years. It is a point that has been popularized by R. Buckminster Fuller with his geodesic domes.

It can easily be shown that the triangle is the only inherently stable linear framework. All other polygons with more than three sides are unstable. If a triangular frame is constructed in which all of its joints are hinges, it remains just as rigid as if its joints were fixed. If a square or any other polygon is constructed with hingeable joints, it will immediately collapse. Complex structures that are fully triangulated can be constructed with multi-directional hinges at each joint, yet they will remain completely rigid.

There is a two-fold economic advantages in inherently stable triangulated structures: first, their tendency to disperse concentrated and distributed loads over a very large part of the structure and, second, the fact that loads are distributed axially through the linear members. Both of these are ideal conditions for efficient use of materials.

When linear members are loaded axially along their lengths, they experience no bending, only pure compression or pure tension. With complex triangulated frameworks, the direction of loads become far less important than in the usual rectangular based structural design.

Prior art techniques have relied primarily upon a vertical and horizontal structural member to create buildings. Where necessary, framing member which include diagonal braces are added to provide lateral rigidity to the inherently non-rigid orthogonal frameworks. Triangulated structures are therefore the exception and there, general use has been limited.

Triangulated systems have not been used extensively in architectural structures, possibly because they are largely incompatible with architectural profession's spatial sensibilities which appear to be dominated by right angles. Looking at space from a more fundamental and comprehensive point of view, a modular spatial approach can be found which can yield inherently stable, highly efficient, low redundancy structures based upon fully triangulated configurations.

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One of the disadvantages of triangulated systems is the relatively complex nodes that are necessary for joining the many linear members that can frequently meet at a common point.