STRUCTURAL SYSTEM OF TORSION/TOROIDAL ELEMENTS AND METHODS OF CONSTRUCTION THEREWITH

Abstract: The present invention is a structural system of torsion/toroidal elements (184, figure 84) that can be connected to form structures with greater structural strength and efficiency, and which have the capacity to bear compression, tension and flexion loading by conversion of such loading to torsion loading of the connected torsion/toroidal elements. The present invention also includes method of construction using torsion/toroidal elements.

Description: STRUCTURAL SYSTEM OF TORSION/TOROIDAL ELEMENTS AND METHODS OF CONSTRUCTION THEREWITH Technical Field The patent classification system does not contain a classification for structural systems as such, the most appropπate description of the present invention, but does address specific types of structures, such as "static structures" (U S Class 52), "bridges" (U S Class 14), "railway rolling stock" (U S Class/Subclass 105/396+), "ships" (U S Class/Subclass 1 14/65+), "aeronautics" (U S Class/Subclass 244/1 17+), "land vehicles bodies and tops" (U S Class 296) etc With respect to torsion devices, no structural classification could be found, the classifications being restπcted to springs (U S Class 267), etc Also, the present invention has elements that may be considered to be covered generally by U S Class/Subclass 152/1-13, spπng wheels and resilient tires and wheels, and U S Class/Subclass 152/516-520, "run-flat" devices Background Art A significant advance in basic structural systems for stationary structures has not occurred since the advent of prestressed and reinforced concrete, structural steel, and the use of cable as a tensional element There have been some innovative engineering and architectural advances, such as vaπous types of folding structures, tube and ball and other space trusses, and in the field of vehicular structure, such as formed sheet πgidification However, none of these advances has escaped the use of conventional structural elements in compression, tension and flexion mode Although there have been more recent developments in the field of vehicular structure, such as formed sheet πgidification, the fundamental methods have not changed significantly from the πgid rib, stπnger, and truss design The present invention is a significant advance in structural systems, both stationary and moveable, with respect to weight, strength, flexibility and magnitude There does not appear to be any pπor art that this invention builds upon except generally in the field of structural engineeπng, none of which directly addresses structural combinations of torsion elements or toroidal elements There are some superficial graphic similaπties involving shapes and forms to be found in certain patents that claim inventions involving dome or sphere structures which utilize πng or circular elements One is the Ring Structure disclosed by United States Patent No 4,128,104 which is "a structural framework composed of πng members intersecting one another in a particular manner" That disclosure does not specify any utilization of torsion loading of the πng members and requires interlinking ("intersecting") of the ring members The other is the Modular Dome Structure, United States Patent No 3,959,937, which is compπsed of "πng-shaped" elements of equal size which form a dome when connected in a particular manner That disclosure involves "improved building construction for domes or other spheπcal frames", does not teach a universal structural system, teaches against the use of "thin rings of simple toroidal shape or other simple form" because of perceived problematic strength, is limited to "elements of substantially the same size", and does not specify any utilization of torsional strength of mateπals or loading Disclosure of Invention The present invention is a structural system that, in one embodiment, employs elements that are "toroidal" in shape, "toroidal elements", which are connected to form structures, in another embodiment, employs elements which function with torsion as the principal load bearing mode, "torsion elements", which are connected to form structures, and in a preferred embodiment, employs "toroidal torsion elements", structural elements that are "toroidal" in shape and function with torsion as the principal load beaπng mode, which are connected to form structures As used in this disclosure and the appended claims the term "torsion element" means a structural element that functions with torsion as its pπncipal load beaπng mode As used in this disclosure and the appended claims the term "toroidal" means of or pertaining to a "toroid" The term "toroid" is not intended to limit the present invention to employment of elements that are in the shape of a torus, which is mathematically defined as a surface, and the solid of rotation thereby bounded, obtained by rotating a circle which defines the cross section of the rube of the torus about an axis in the plane of the circular cross section As used m this description and the appended claims the term "toroid" means any form with the general features of a torus, 1 e a tube, cylinder or pπsm closed on itself, without regard to any regulaπty thereof, and further means any tubular, cyhndπcal orpπsmatic form which is closed on itself in the general configuration of a torus, thus completing a mechanical circuit forming the "tube" of a "toroid", regardless of the shape of the cross section thereof, which may even vary within a given "toroid" A toroid may be formed by the connection of cyhndπcal or pπsmatic sections, straight or curved, or by the connection of straight and curved sections m any combination or order, and may be of any shape which the closed tube may form elliptical, circular, polygonal, whether regular or irregular, symmetπcal, partially symmetπcal, or even asymmetrical, whether convex or concave outward, partially or completely Moreover, as used in this descπption and the appended claims, the term "toroid" applies to and includes (a) the continuous surfaces of toroids, tube walls of finite thickness, the exterior of which are bounded by the toroidal surface, and the solids that are bounded by the toroidal surface, (b) any framework of elements which if sheathed would have the shape of a toroid, (c) any framework of elements which lays in the locus of a toroidal surface, (d) a bundle or coil of fibers, wires, threads, cables, or hollow tubing that are, bound, wound, woven, twisted, glued, welded, or otherwise bonded together in such a manner as to form in their plurality or individuality a toroidal shape The principal feature of a toroidal structural element is that it has no non-toroidal conventional cross-bracing, diametrical or chordal, within the inteπor peπmeter of its tube that functions by compression, tension or other loading However, a toroidal element may be reinforced within the interior perimeter of its tube by other toroidal elements, as shown in FIGS 78-81 , which may be torsional, conventional or otherwise As used in this disclosure and the appended claims the term "torsion/toroidal element" means a structural element that may be either a torsion element, or a toroidal element, or a toroidal torsion element, the term "torsion/toroidal element" thus encompassing all three alternatives Otherwise, when any one of the foregoing alternative meanings are referred to, that alternative shall be specifically referred to by its proper descπption torsion element, toroidal element, or toroidal torsion element However, reference to a torsion element shall be taken to mean a torsion element which may be toroidal or non-toroidal, and reference to a toroidal element shall mean a toroidal element which may be torsional or non-torsional The structural system is compπsed of a plurality of torsion/toroidal elements connected together so that there is no substantial unwanted movement of the torsion/toroidal elements in relation to one another in the connection Two or more torsion/toroidal elements may be connected in the same connection The connection of the torsion/toroidal elements is the means by which loading is transmitted between and distributed among the torsion/toroidal elements As used in this disclosure and the appended claims the term "connected" means, in addition to its ordinary meaning, being in a "connection" with torsion/toroidal elements, and the term "connection" as used in this disclosure includes, in addition to its ordinary meaning, any combination of components and processes that results in two or more structural elements being connected, and further includes the space actually occupied by such components, the objects resulting from such processes, and the parts of the structural elements connected by contact with such components or objects, but both the terms "connected" and "connection" exclude interlinking ( "intersection") of structural elements as a means for connecting toroidal elements Although the structural system of connected torsion elements may be utilized for constructions without the employment of toroidal elements, and the structural system of connected toroidal elements may be utilized for constructions without the employment of torsion elements, the preferred embodiment and the best mode is in combination with the other, a structural system of connected toroidal torsion elements Thus, although the structural system of torsion elements and the structural system of toroidal elements are each operative separately (without combination with the other), they are joined in the inventive concept of the structural system of toroidal torsion elements by the complementary characteπstics of the toroidal shape with torsion load beaπng The present invention includes a method of construction with the structural system in its vaπous modes, as well as a method of construction of toroidal torsion elements in a process of replication, and the construction of certain advanced structures possible with the system Torsion/toroidal elements use the strength of materials more effectively and have the capacity to redistπbute the loads distπbuted to them by the connections of the structural system of which they are a part The structural system effectively distπbutes most compression, tension, flexion and torsion loading among the connected torsion/toroidal elements of constructions Thus the construction is distinguished from conventional constructions employing elements which function only in compression, tension or flexion, such as beams, struts, joists, decks, trusses, etc However, when elements which function in compression, tension or flexion are constructed using the present invention, the same structural benefit of load distπbution applies The preferred embodiment of the present invention employs toroidal elements that are constructed with the use of torsion elements which are toroidal in shape Torsion elements use the torsional strength of mateπals and have the capacity to bear the torsion loads distributed to them by the connections of the structural system of which they are a part The preferred embodiment using toroidal torsion elements converts most compression, tension and flexion loading of constructions using the system to torsional loading of the torsion elements of which the constructions are compπsed The use of toroidal torsion elements also contπbutes to construction of toroids which are self-supporting The present invention contemplates that torsion/toroidal elements may be constructed of yet other torsion/toroidal elements, so that a given torsion/toroidal element so constructed functions to bear loads by the beaπng of structural loads by its constituent substructures Such substructures may be structural elements, torsion/toroidal, conventional or otherwise, which are part of a combination of structural elements of a scale similar to the given toroidal element, or structural elements of a scale significantly smaller than the given torsion/toroidal element and fundamentally underlying the beaπng capacity of the given torsion/toroidal element In the latter case the structure of a given torsion/toroidal element may be the replication of small substructures of torsion/toroidal elements, which in turn may be replications of still smaller substructures of torsion/toroidal elements This process of structural replication can be continued to microscopic, and even molecular, levels of smallness The system also includes the construction of conventional elements using torsion/toroidal elements which may be used in combination with other torsion/toroidal structures in constructions Moreover, it is one of the features of the present system that conventional elements, such as beams, joists, decks, trusses, etc , constructed using torsion/toroidal elements may be engineered with arching camber and prestressing Although such constrcutions may bear resemblance to conventional trusses, the structural integπty and strength of torsion elements is ultimately dependent on torsion/toroidal elements which may be beanng torsion loads, and is not fundamentally (in the sense of oπginally underlying) or necessarily dependent on elements such as linear chords and struts bearing loads in compression, tension or flexion Torsion/toroidal elements can be made of virtually any mateπal suitable for the loads to which the structure may be subjected and for the environment in which the structure may be utilized It is the fundamental principle of the structural system which is the present invention that torsion elements bear as torsional load the greatest part of the load placed on the structures of which they are a part, excepting localized forces existing in the connection of the torsion elements, and evenly distπbute such loading among the connected torsion elements of which the structures are ultimately and fundamentally constructed The present invention contemplates that structures constructed of connected torsion/toroidal elements may be incorporated in yet other structures together with conventional structural elements in order to bear compression, tension and flexion loads with such torsion/toroidal structures Torsion elements may have virtually any shape that allows them to be connected and thereby function by torsional loading However, the preferred embodiment of the present invention employs torsion elements which are toroidal in shape Such toroidal torsion elements may be used to create a vaπety of new structural forms for both stationary and moveable structures The toroidal shape facilitates replication of structured toroidal torsion elements to produce larger and larger toroidal torsion elements which may be suitable for the dimension of the ultimate structural application A large vaπety of structures made feasible by oπgination of the replication process with torsion/toroidal elements on the order of nanostructures or larger may themselves be considered as materials which can be utilized in conventional structures, such as decking, plates, skins, and sheeting of arbitrary curvature Torsion/toroidal elements may be used to create new structural forms for both stationary and moveable structures The toroidal shape allows for replication of toroidal elements to produce larger and larger toroidal elements which may be suitable to the dimensions of the structural application A large vaπety of structures made feasible by oπgination of the replication process with toroidal elements on the order of nanostructures or larger may themselves be considered as mateπals which can be utilized in conventional structures such as decking, plates, skins, and sheeting of arbitrary curvature Erection of structural frames using the present invention requires only connection of the torsion/toroidal elements, and may use connectors which are prepositioned and even integrated in the design of the torsion/toroidal elements Torsion/toroidal elements may be connected by any means that does not permit unwanted movement in the connection Such means may be any type of joining, such as welding, gluing, fusing, or with the use of fasteners, such as pins, screws and clamps However, the preferred means for connection is by use of a "coupling" The term "coupling" is used in this disclosure to mean a device which connects two or more torsion elements by holding them in a desired position relative to one another, so that when the desired positions of the torsion/toroidal elements are achieved, the torsion/toroidal elements will not be able to unwantedly move relative to each other within the coupling The coupling may itself be constructed of torsion/toroidal elements, or may be solid or have some other structure The term "coupling" also includes a device which connects a torsion/toroidal element to a conventional structural element by holding both the torsion/toroidal element and the conventional structural element in the desired position, so that the structural elements will not be able to unwantedly move relative to each other within the coupling Although, the function of couplings is to hold torsion/toroidal elements in position in relation to each other, there may be motion of the torsion/toroidal elements outside the connection associated with the structural loading of the elements, including rotation of the elements with respect to each other about the axis defined by the grip within the coupling, and sliding of the elements through the grip of the coupling Such motion is expected and appropπate for the distπbution of stress among the elements of a given torsion/toroidal structure The function of couplings in holding structural elements in position may be combined with pπor positional adjustment and actuation of such adjustment In this respect the position of torsion/toroidal elements connected by a coupling with respect to one another may be changed or adjusted and then held in the desired position Accordingly, the coupling must be designed to have the capability for and even to perform such adjustment, and may also be designed to have such adjustment actuated by some motive power Such actuation may implement dynamic distπbution of loading among the structural elements affected or implement dynamic shape shifting, or both This can be achieved by making one or more connections of the structure adjustable, with or without the use of actuation Moreover, such powered actuation of adjustable coupled connections may be computer controlled in order to precisely determine the shape changes and structural effects desired The function of such a coupling, therefore, is to adjust the coupled connections, with or without the use of such controlled actuation, so that a torsion/toroidal element may be moved within a connection in relation to other structural elements connected therein, and then firmly held by the connection in the position resulting from such movement so that the torsion/toroidal element will not have substantial movement within the connection in relation to any other structural element in the connection unless deliberately moved again by the coupling To present the details of the system, the function of its elements, and the method by which structures are constructed using the system, reference is made to the drawings FIGS 1 -4 show an embodiment which demonstrates the fundamental pπnciples of the torsional aspect of the structural system In FIGS 1-4 two torsion elements 3, 4 are connected by two couplings 1, 6 to form a torsional structural module The torsion elements 3 and 4 are shown as open rectangles with a circular cross section to demonstrate the pπnciple, but any cross sectional shape and any element shape may be used with couplings having compatible openings The couplings shown 1, 6 have cylindrical openings, coupling 6 having bearings 7 which allow for free rotational movement of the torsion elements within the coupling, and coupling 1 having spline gπps 2 to engage the spline ends 5 of the torsion elements 3, 4. The purpose of the spline ends 5 being engaged by corresponding spline gπps 2 is to hold the torsion element firmly in relation to the coupling 1 so as to prevent movement of the torsion element within the coupling The purpose of the couplings 6 with beaπngs is to constrain the arms of the torsion elements 3 and 4 to be in alignment under the action of the forces Thus, when the torsion element 3 is subjected to a force which attempts to rotate the arm of torsion element 3 about its axis in relation to the coupling 1 within which 1 it is engaged, the force will result in a torsion load on the arm where the position of coupling 1 is fixed Where the position of coupling 1 is not fixed, such an attempt to change the oπentation of the torsion element 3 will also result in a rotation of the coupling 1 with torsion element 3 in relation to the torsion arm of the other torsion element 4 which is also engaged within coupling 1 This attempt to rotate the coupling 1, the spline gπp 2 of which is engaged to the spline 5 of torsion element 4, will 5 result in a torsion load on the arm of the other torsion element 4 where the position of torsion element 4 is fixed Thus any change in the position of one torsion element 3 connected to another 4 by an engaged coupling 1 will result in transmission of the torsion load on one torsion element 3 to the other 4 The role of coupling 6 is to assist in maintaining the alignment of the arms of the torsion elements 3 and 4 Another embodiment which demonstrates the principle is shown in FIGS 5-8 In this vaπation the orientation of the 10 torsion elements is opposing, but with the transmission of torque loading accomplished with couplings 21, 26 similar to those in FIGS 1 -4 through the addition of an intermediate torsion element 28, in this case a cylindrical bar Again the purpose of the splines 25 is to engage the spline grips 22 of the couplings 21 , thus fixing their rotation with that of the torsion elements 23, 24, and the purpose of the couplings 26 with bearings 27 is to constrain the movement of the arms of the torsion elements 23, 24 and the intermediate torsion element 28 to rotation in alignment with each other In this vaπation the intermediate torsion element 15 28 is acted upon with opposing torque by connection at its opposite ends with couplings 21 that transmit the load on the torsion elements 23 and 24 The transmission of load to the intermediate torsion element 28 occurs in the same manner as the transmission of load between the torsion elements 3 and 4 of the module shown in FIGS 1 -4 Therefore, the load transmitted to the intermediate torsion element 28 by one torsion element 23 is opposite to the torsional load transmitted from the other torsion element 24 In this way the intermediate element 28 provides for additional capacity for beaπng of torsional loading by the structural module 0 Although a means for connection between torsion elements 23 and 24 via a single intermediate torsion element 28 is shown in FIGS 5-8, the connection between torsion elements 23 and 24 as shown in FIGS 5-8 may be accomplished using more than one intermediate torsion element and the appropriate combination and placement of couplings In both of the foregoing vaπations torsional load is distπbuted equally among the connected torsion elements by their action upon each other as understood with Newton's third law, which may be stated in part as "To every action there is always 5 opposed an equal reaction" The spline grip couplings and the corresponding spline ends of torsion elements shown m FIGS 1-4 and FIGS 5-8 are not the only means contemplated for achieving fixed connections between torsion elements and couplings Indeed all means for fixing a coupling to a torsion element, such as welding, gluing, fusing, pinning, screwing, clamping, and the mating of the coupling with a torsion element of any non-circular cross section, are contemplated as appropπate in order for a coupling connecting torsion 0 elements to transmit torsional loading The modules shown in FIGS 1 -4 and 5-8 may themselves be similarly connected in linear arrays and different types of modules shown may be connected to form arrays which may have any shape, and may be closed, circular, or assymetπcal and irregular Closed arrays of connected torsion modules have no terminus for the transmission of loading, as do linear arrays Thus, 5 any torsional load placed on a torsion element in a closed array will be transmitted to and distπbuted among all of the torsion elements in the array As previously indicated the torsion elements may be of virtually any shape so long as they may be connected in a way similar to that as shown in FIGS 1-4 and 5-8, thus providing for the beaπng and transmission of torsional loading An example of another torsion element shape is shown in FIGS 9 and 10, connected in the various ways shown in FIGS 5-8 0 Torsion elements may be angularly connected to produce angular torsion modules and structures and form linear arrays thereof as shown in the example of FIG 13 The same characteristics of transmission of torsional loading exist in this type of configuration as in the structures shown and discussed earlier Angular connections are possible for virtually any type of torsion element as shown in the examples of FIGS 1 1 and 12 Moreover, any type of connection may be used for angular connection of torsion elements Angularly connected torsion elements may also be connected in closed arrays as shown in FIG 14 The angular connection between elements allows for the inclusion of more torsion elements in the array within the same length, thereby providing for a greater capacity of the array to absorb torsional stress Although only circular arrays have been shown, any closed array is possible and will share the same characteπstics of distribution of torsional loads as circular arrays The symmetry of an array and the manner in which it is loaded u ill determine the evenness of the distπbution of torsional stress, whether the array is open or closed Also as can be seen from FIG 14, a closed symmetrical array of torsion elements forms a toroid, the shape of the preferred embodiments of the invention Structural modules of torsion elements, and arrays thereof, connected by one coupling are also possible, as shown in FIGS 15-18 where the torsion elements are toroidal Smoothly curved torsion elements absorb torsion stress vaπably along the length of the toroidal tube Torque applied to any point on such a torsion element along its tube length which tends to twist the body of the torsion element is transmitted along the body of the torsion element as determined by the structure of the torsion element, the capacity of the mateπal used to absorb torsional stress, and the curvature of the torsion element Nevertheless, the load on one curved torsion element fixedly connected with one coupling to another curved torsion element as shown in FIGS 15- 18 will be transmitted to the other in the same manner as for the connected torsion elements shown in FIGS 1 -4 As with all other torsional elements, toroidal torsional elements can be connected in closed arrays as shown in FIG 19, which may form the framework of larger toroidal elements having torsional strength characteπstics Indeed, it is contemplated by this invention that the self-similarity of toroidal torsion elements constructed from smaller toroidal torsion elements can be extended to precisely control all of the structural characteristics of such toroidal torsion elements Through FIG 19 all of the connections between torsion/toroidal elements have been shown in the figures as "external", ι e achieved with an "external" coupling applied to the exteπor surfaces of torsion/toroidal elements Such connections shall be continued to be referred to as ' external", as opposed to "internal" connections, which include all means for connecting torsion/toroidal elements without the use of a coupling or other intermediate device Torsion/toroidal elements in an internally connected combination of torsion elements is shown in the vaπous views in FIGS 20-23 For the purpose of the figures of this disclosure, it shall be understood that all of the closely proximate torsion/toroidal elements shown are connected in the region of their closest proximity by internal connection, unless otherwise indicated such as by connection with couplings Furthermore, for the purpose of the rest of this disclosure, the lack of the appearance of an external coupling at the point of closest proximity of two torsion/toroidal elements shall not be taken to mean that such elements are not connectable by couplings, unless otherwise indicated All connections thus shown in the figures may be internal or external as required by the application, even though not indicated as such in a particular figure This convention is used in the examples of closed arrays shown in FIGS 24 and 25, where the structural modules shown in FIGS 20-23, form the framework of toroidal torsion elements By the convention herein established the circular array shown in FIGS 24 and 25 is compπsed of toroidal torsion elements that are internally connected However, observation of an internal connection, shown m the vaπous views of FIGS.26-33 between two toroids formed as shown in FIGS 24 and 25, demonstrates that internal connections between toroidal elements may be achieved by the use of external connections between their constituent toroidal elements This internal connection, rather than being accomplished by coupling of the constituent toroidal elements of the toroids, could have been accomplished by internal connections between the torsion elements of which the constituent toroidal elements are constructed Such internal connection may also be mediated by additional elements, torsional or otherwise Furthermore, this process may be continually replicated in a self-similar manner on a smaller and smaller scale, down to a fundamental torsion/toroidal element, which may be a construction itself, but not necessarily by formation from a circular array Arrays of angularly connected torsion/toroidal elements that themselves form toroids may be elliptical, as shown in FIGS 35 and 36, or of any other shape, and have various directional characteπstics, such as where lateral flexion of the resulting torsion/toroidal element is converted to torsional loading of its constituent toroidal torsion elements Such varying constructions of torsion/toroidal elements may be combined as needed to meet extπnsic structural requirements by tubularly concentπc connection between such torsion/torsion elements as shown in FIG 34 Constructions from linear arrays of connected torsion/toroidal elements may also be used to form structural members such as rods, tubes, poles or posts, examples of which are shown in FIGS 42 and 43 These constructions may also have directional characteristics similar to that of the circular arrays discussed above, and may be included in compound tubularly concentric constructions as shown in FIG 44 Fundamental torsion/toroidal elements may be fabricated from what can be considered solid mateπal, such as metal, polymers, foams, wood, or tubes of such material Such fundamental torsion/toroidal elements may even be molded as torsion elements connected in modules, partial or whole, in the form of a framework of a torsion/toroidal element Fabrication of fundamental torsion/toroidal elements may proceed from any standard manufactuπng method, such as winding, extrusion, injection molding, layeπng of resins and fabπcs, and fiber compositing Torsion/toroidal elements may also be constructed from other torsion/toroidal elements without the use of connected arrays, such as the interlinkage shown in FIGS 38-41, formed by an apparent braid of six toroids about a central axial toroid, all of which are identical in dimension The pπncipal characteristic of this type of torsion/toroidal element is that the apparent braid of toroids rotates freely about its circular axis impeded only by the internal friction of the toroids in the braid and the fπctional forces between them It is possible to construct a torsion/toroidal element with a tube defined by a closed spiral as shown in FIG 37 The pπncipal characteristic of this type of toroidal element is that the spiral tube rotates freely about its axis, which is the curved line within and at the center of the tube, impeded only by internal friction Such a toroidal tubular spiral can transmit torque about the axis of the tube to any point around the tube, and thereby distπbute torsion stress throughout the tubular spiral Such a toroidal tubular spiral can be stabilized by torsion/toroidal elements connected to the peπphery of the tube as shown in FIG 37, so that the rotation of the spiral about its tubular axis is regulated by the peπpheral torsion/toroidal elements The spiral may itself be a array of connected torsion/toroidal elements Virtually any shape of torsion toroidal element is possible, as shown in FIG 45, and may be constructed by either appropriately shaped arrays of torsion/toroidal elements, or fabπcated as fundamental torsion/toroidal elements The combination and orientations in which structural modules may be constructed of torsion/toroidal elements with the use of couplings is exemplified by the categoπes shown in FIGS 46-49 Examples of couplings that can be used to achieve such combinations and orientations are shown in FIGS 50-52 for two-element connections, as shown in FIGS 1-4 and 5-8, and FIGS 53-56 for the types of connections shown in FIGS 46-49 The spline gπp couplings and the corresponding spline collars of torsion toroidal elements are among several other means contemplated for achieving fixed connections between torsion/toroidal elements and connecting couplings to transmit torsional loading Examples of such other means are welding, gluing, fusing, the use of fasteners, such as pins, screws and clamps, and the mating of the coupling with a torsion/toroidal element of non-circular cross section Couplings may also be designed with vaπous mechanical devices for integrated secuπng against movement of the torsion/toroidal element held Some examples of such a coupling is shown in FIGS 50-52, a split block coupling in which each of the parts of the block, 61 and 63 are fitted with spline gπps 62 The manner in which the coupling effects the connection is to close the block sections 61, 63 around the spline collars of the torsion/toroidal elements to be connected, and bind the block with the compression band 65 tightened into the band groove 64 with a tightening device 66, such as a ratcheted roller on which the compression band is wound The coupling shown in FIGS 53-56 is an open-end coupling in which each of the end caps 83 and 87 and the mam body of the coupling 81 are fitted with spline gπps 82, also demonstrating the type of connection shown in FIG 46 The manner m which the coupling effects the connection is to close end caps 83 and 87 around the spline collars of the torsion elements to be connected, and bind the caps to the main body block with the compression bands 85, which are locked to the mam body by the lock pins 88 and tightened into the band grooves 84 with the tightening devices 86 Torsion/toroidal elements shown in FIGS 57 and 58 as 102, 104 with spline collars 101, 103 are connectable by the couplings which have spline gπps The spline collars may be integral to the torsion/toroidal element, or may be attached by a means for bonding the spline collar to the torsion/toroidal elements or their components, by means for a mechanical linkage within the spline collar, or by or attachment or fastening to the spline collar If a structural element does not have spline collars attached, other forms of connection are possible, such as with a coupling with form gπps, or by internal connection with torsion/toroidal elements constituting such structural elements A split-block coupling with form gπps that uses structural foam that cures to a permanent shape after being compressed about the torsion/toroidal element, or a resilient elastic cushion that gπps the torsion/toroidal element, is similar to that shown in FIGS 50-52 where the form gπps would occupy the location of the spline gπps The block sections of the coupling are then locked in place by either compression bands, as used on the split-block coupling shown in FIGS 50-52, or other means for fastening the block together, such as screws or bolts The formation of structures using the system may proceed from constructions which may be referred to as "structural modules" One basic form of structural module is a connected tπangular array of torsion/toroidal elements shown in FIGS 59 and 60 One type of connected linear array of the triangular structural module is shown in FIGS 61 -63 which forms a rod, beam, or post structure Connected arrays of such modules can form plate or deck structures Another basic structural module is the connected cubic array of torsion/toroidal elements which is shown in FIGS 64 and 65, with a connected linear array shown in FIGS 66 and 67 forming rod, beam or post structures Connected arrays of these structures can form plate, deck and j oist structures as shown in FIG 68 A wide vaπety of such structural modules is possible FIG 69 is an example of the more complex structures, such as arches or πbbing, formed when the structural modules shown are connected in arrays The closed circular array m FIG 70 may also be another form of torsion/toroidal element Structures may also be formed from polygonal torsion/toroidal elements The preferred use of such forms is as a body for a complex toroidal torsion element having internal shafts for the absorption of torsion stress, as shown m FIGS 71-73 in one vaπation of which torsion stress is absorbed by multiple internal shafts 112 The shafts 1 12 are the point region of connection with other structural elements where they are not enclosed by the polygonal toroidal body 111 of the toroidal torsion element The shafts 112 rotate on beaπngs 1 14 which are positioned by beaπng mounts 1 13 which are fixedly attached to the body 11 1 A torque applied to turn the shaft 112 at its point of connection will induce a stress in the shaft 112 if the rotation of the shaft is restπcted in some way In the polygonal toroidal torsion element shown the shaft 112 to which the torque applied is connected at both ends to other shafts 1 12 by means of a universal joint 1 15 which transmits the torque to the other shafts 112 If the rotational motion of any of the shafts 112 are restπcted, a torque on the shaft 1 12 will induce a torsional stress in the shaft 112, and the loading will be transmitted to adjacent shafts 112 by means of the universal joint 1 15 which connects them Restπction of motion of a shaft 1 12 can be provided for by a rotation block 1 16, which is a means of fixing the end of a shaft 112 to the body 1 1 1 or of otherwise resisting rotation so that the end of the shaft 112 will not rotate freely Such a rotation block 1 16 may be applied to the ends of a shaft 1 12 to which the torque may be applied where it is exposed for connection to other structural elements If there are no rotational blocks the shafts will be free to rotate If such free shafts are further connected by universal joints around the sides of the element, the torque will transmitted from the region of application to the other region of connection Thus rotation induced at one side of the element will be transmitted to the other side of the element without substantial constraint within the element However, if the movement of the shafts on one side of the element are restπcted, as by connection to another torsion structural element, a torsional load will result and transmitted equally along the connected shafts and torsion stress will be induced therein As with other torsion/toroidal elements, polygonal torsion/toroidal elements may be connected in an array to form a structural module as shown in FIGS 74-77 The couplings used may be of the split block type shown in FIGS 50-52 Also as with other torsion toroidal elements a wide vaπation in form and combination is possible with polygonal torsion/toroidal elements Polygonal torsion/toroidal elements may range from the pentagonal to the nonogonal, with the number of sides limited only by the application Polygonal torsion/toroidal elements may be combined with other torsion/toroidal elements to form complex torsion/toroidal elements with structural features that can be tailored to any structural application In addition to the connections between torsion/toroidal elements in which the torsion/toroidal elements remain outside of the peripheral tube of the other, previously demonstrated in FIG 34, connections between torsion/toroidal elements where one element is within the space surrounded by the tube of another are a useful structural alternative to combination by constructing torsion/toroidal elements with coaxial tubes Such a variation is shown in FIGS 78 and 79 where the torsion/toroidal elements are coaxial, and in FIGS 80 and 81 where the axes of the torsion/toroidal elements are angulated with each other Certain basic structural forms that are difficult to achieve without significant structural disadvantage using conventional structural systems, are natural using the present invention with no structural disadvantages Among these are spheπcal frameworks, as shown in FIG 84, and framework towers, as shown in FIG 86 Other examples of structures for which torsion/toroidal elements are similarly suitable are shown in FIGS 82, 84, 85, 83, 87 and 88 All of the structural forms demonstrated are also useful in combination with each other, for reinforcement, aesthetics, as well as in the design of complex structures Fundamental to some of these structural forms is a structure in which the hoπzontally compressive support of its torsion toroidal elements by each other results from the application of vertically downward loading on such torsion/toroidal elements The structure, which may be described as a "horizontal arch", is formed by a plurality of torsion/toroidal elements which are connected side-to-side on or in an arc of a curve in the hoπzontal plane, with adjacent members leaning together toward the center of curvature of the arc, as shown in FIG 99 The positions of the bottom of such torsion/toroidal elements are fixed at their base along the horizontal arc which describes the overall shape of the hoπzonal arch Said positions are determined by the placement of each torsion toroidal element so that the sides thereof are in contact, directly, or indirectly within a connection, above and within the peπmeter of said arc of the hoπzontal arch The torsion/toroidal members of the hoπzontal arch are thus forced together horizontally under the application of vertically downward loading near the top of each of the compression members The hoπzontal arch may be employed as a part of successively vertically layered constructions as exemplified in FIGS 100 and 101 , in which each layer subjects the next layer below to vertically downward loading, such as in towers and multi-story buildings The vertical loading of the "horizontal arch" layers forces the torsion/toroidal elements in each layer together hoπzontally, and adds to the hoπzontal cohesiveness of the structure, thus increasing its vertical load beaπng strength With regard to spherical frameworks, an example of which is shown in FIG 84, another useful structural form is possible with the replication of a section as shown in FIG 85, and then connecting it in an appropπate scale to a torsion/toroidal element forming the spheπcal surface shown in FIG 84 The replication of the spheπcal section shown in FIG. 85 is applied once 141 and then again in smaller scale 142 to the first This application of the spheπcal section shown in FIG. 85 can be made in replication to all of the torsion/toroidal elements that form the sphere, and yet again and again to all of the torsion/toroidal elements that form successive replications, until a practical limit is reached beyond which the process has no structural efficacy Such a replicated spheπcal framework can be utilized as an implosion resistant pressure vessel, in which pressures mteπor to the vessel may be maintained at a lower level than the pressure outside the vessel The use of torsion/toroidal elements may also be applied to create structures which are dynamic, with the constituent elements capable of movement by design, not only by deflection as a result of loading, but also by the active management of structural stresses Torsion/toroidal elements may also be varied in shape dynamically so as to achieve alteration of the shape, size and volume of the structure of which they are constituent Generally, structures such as buildings, bπdges, even automobiles, seacraft, airframes and spaceframes are considered to be static structures in accordance with their manner of performance That is, the expectation of performance for such structures is that they respond to the loads to which they are subjected by adequate management of the stress on the mateπals used and the means by which the mateπals are connected to compπse the structure There are some structures that are built with moving parts, such as a roof that opens by sliding or some other aperture that is created by actuation, manual or otherwise, as in the housing of an astronomical observatory The present invention contemplates its application to create a dynamic structure, a structure in which the stress of the mateπals and their connections are managed by automated actuation of the coupling of torsion/toroidal elements and the shifting of the size and shape of structures by actuation of couplings An example of an actuated coupling which can perform a fundamental shifting of shape is shown in FIGS 89-91, in which a motor 135 rotates a beaπng 133 supported spline gπp 132 by the rotational power it delivers to the dπve 136 through the use of a transmission 134 When the motor 135 is powered, the spline grips 132 are dπven, in a controlled manner to rotate and thus rotate a torsion element held in a grip in relation to the body 131 of the coupling, as well as any other torsion/toroidal element held in the other spline gπp 132 The manner which the change in shape of a 20 element array can be effected using such actuated couplings is demonstrated in FIGS 92 and 93 Couplings such as those descπbed above and shown in FIGS 89-91 (but not shown in FIGS 92 and 93) would connect the torsion/toroidal elements, in the region of closest proximity of the elements, and would cause the angulation of the elements to change with sufficient precision so as to achieve the exact shape and size of the resulting structure required Such a change of shape or size could be directed to take place in an organized way for all of the torsion/toroidal elements of the structure, including replicated substructures, which would result in a change of shape or size of the entire structure An example of such an operation is shown in the schematic seπes of FIGS 94-98, where the frame of the surface of the prolate spheroid (FIG 94) is transformed in stages (FIGS 95-97) to the frame of the surface of a sphere (FIG 98) by the changing of the shape of the constituent connected eliptical torsion/toroidal elements compπsing the frame of the surface of the prolate sphere to more circular torsion/toroidal elements This transformation results in a reduction of the volume bounded by the framework Other transformations are possible, such as where the frame of surface of the sphere is transformed to the frame of the surface of an oblate spheroid, by the changing of the shape of the constituent connected torsion/toroidal elements compπsing the frame of the surface of the sphere to more elliptical torsion/toroidal elements This transformation would result in an increase in the volume bounded by the framework A similar but isovolumetπc pair of transformations is also possible, as is the reversal of the transformations descπbed This aspect of the present invention thus demonstrated for spheroids is a general property of the structural system This can be demonstrated further, schematically, with the transformation of a plane array of connected torsion/toroidal elements to a connected array of torsion/toroidal elements in the surface of a paraboloid, which can be accomplished by a calculated and controlled changing of the shape of the constituent connected torsion toroidal elements compnsing the framework of the plane to more elliptical torsion toroidal elements, vaπably to form the framework of the paraboloid Such shape shifting may be used to alter the shape or size of any array of elements not only those that provide the framework of surfaces, but also the framework of solids The present invention may also be embodied in wheel and tire structures as a torsion/toroidal wheel body, which has a toroidal shape without a central hub, and is the component that rotates in direct contact with the underlying surface or other wheels or rollers against and on which it may be operated or dπven, as shown in FIG 102, and as a tire structure that includes a circular array of a plurality of toroidal torsion support elements connected to form a toroidal shape, as shown m FIGS 103 and 104 The structure of the toroidal wheel body is the framework of toroidal torsion elements, as shown in FIGS 19, 87 and 88, is self-supporting, and may be constructed to be flexible in order to conform to lrregulaπties of surfaces In advanced forms of this embodiment of the invention the toroidal wheel body need not be circular, and its shape may be continuously controlled by internal actuators, such as those shown in FIGS 89-91, to conform to the surface and to the dπve mechanism The toroidal wheel body framework may be used directly as a toroidal wheel body, or sheathed in a casing, as shown in FIG 102 Without a casing, the framework toroidal wheel body can operate on mud, sand, snow, or other loose mateπal constituting the underlying surface The tire structure may be used as an insert in a tire, as shown in FIG 105, incorporated directly in the structure of the tire body or carcass, as shown in FIG 103, or connected to a central band, as shown in FIG 103, or hub structure for receiving an axle to form a complete wheel structure An object of this embodiment of the invention is to provide a non-pneumatic support for a wheel, as part of a non-pneumatic tire or as part of the wheel itself, which can be assisted with other pneumatic, fluidic, or mechanical means with inclusions of those means within the tube of the toroidal structure of the invention Although the present invention provides a non-pneumatic tire support structure, it may also be used in conjunction with pneumatic, fluid filled, or other cushion elements The open inteπor of the toroidal tube of the tire support structure also permits the inclusion of other types of toroidal structures within the toroidal tube, as shown in FIG 34, and to allow for other applications of the wheel and tire structure The method of constructing any given toroidal element framework from other toroidal elements, such as the toroids shown in FIGS 19, 24 and 25, is commenced with the determination of the component curvatures of the required toroidal shape followed by the planning of the toroidal framework For example, a circular toroidal shape in one plane will have only one radius of curvature, the radius of the circular toroidal shape A more complex toroidal shape, such as the eliptical toroid shown in FIGS 35 and 36, will have more than one radius of curvature, the number depending on the number of elements to be used in the construction and the closeness of the approximation to the curvatures of the ellipse required For such complex curved toroids the number of constituent elements and the radii of curvature will be interrelated FIG 106 is a schematic plan for construction of a toroidal framework with smaller toroidal elements 151 showing the dimensional quantities involved For the construction of a given circular toroidal framework with a tube of approximately circular cross section, where the torus radius is RT, the toroidal tube radius is Tr, the number of elements is n, the angle of arc occupied by one element is Phi = 360/n, and the radius of a toroidal element is r, the relations among the angles and lengths labeled in FIG 106 are as follows RO = RT + Tr, RI = RT - Tr, Ro = RO - r, Ri = RJ + r, Sm(Theta) = r/Ri, Sm(Psι) = r/Ro, Li = r/Tan(Theta), Lo = rtTan(Psι), x = Ro*Sm(Phι - Psi), (* indicating multiplication between adjacent quantities), Ld = Ro * Cos(Phι - Psi) - Li, Tan(Alpha) = (x - r)/Ld, Ej(dιa) = (x - r)/Sιn(Alpha) These relations may be solved for Li, Ej(dιa) and Alpha, for a given RT, Tr, n and r, and together will be sufficient for the plan of the circular toroidal framework This set of relations may be solved numeπcally by standard mathematical methods, and shall hereafter be referred to as the toroidal element framework planning algoπthm The construction of a toroidal framework involving multiple radii of curvature, even in more than one plane, may be similarly planned by solving the relations for each circular framework with which each segment of the toroidal framework is approximated The construction of the toroidal element framework may then be earned out by prepaπng a jig/mold for positioning the elements that constitute the toroidal framework from the specifications provided by the use of the toroidal element framework planning algoπthm, positioning the constituent toroidal elements in the jig/mold, and connecting the constituent toroidal elements so positioned For example, a simplejig/mold for a tonodal framework in one plane may be prepared by inserting a seπes of pins 152 in a flat surface on which a plan as shown m FIG 106 has been laid, the position of the pins outlining the positions of the constituent elements 151 The constituent elements may then be placed between the pins in the positions so outlined and then connected The positions of the constituent elements may also be outlined by tπangular or rectangular blocks, or other type of stop or clamp, or other means for positioning which hold or define the angles between the constituent elements in accordance with the plan for construction of the toroidal framework. Such other means of positioning also include depressions formed in the plan surface which could accomodate the constituent elements The means for positioning may also be adjustable to conform to plans for construction of vaπously dimensioned toroidal frameworks with varying constituent elements The connections may then be applied manually or with the use of robotics with the jig/mold containing the toroidal components stationary or m motion, rotational or otherwise A jig/mold is also possible for non-flat surfaces using the same pπnciples of construction therefor as descnbed above, except that curvature in the additional dimension would have to be taken into account m setting the pins at the proper angles to the planes of tangency to the non-flat surface to properly position the toroidal elements to be connected The progression of construction of a dome with toroidal elements is demonstrated for a dome with interleaved layers of toroidal elements in FIGS 99- 101 The method of constructing such a dome commences with the determination of the shape of the base of the dome The base may be circular or that of a more complex curve which may be approximated by segments of components with vaπous curvatures FIGS 107 and 108 are schematic diagrams for construction of a dome framework with toroidal elements 163 showing the dimensional quantities involved The vertical planes 161 and 162 are in the diagram only for the purpose of demonstrating the relationship among the dimensions of the dome framework and the toroidal elements of which it is constructed 163. For the construction of a given spheπcal dome framework where the number of base toroidal elements is n, the sphere radius is S, the hoπzontal element angle is f = 360/n, the declination of the base is t, the vertical element angle is e, and the element join angle is p, the relations among the angles and lengths labeled in FIGS 107 and 108 is as follows: for the element radius, R • = S*Sm(e/2), for the upper base radius, Ur = Cos(t + e), for the upper base height, Uh = S*Sιn (t + e), for the lower base radius, Lr = S*Cos(t), for the lower base height, Lh = S*Sm(t ), and the relation between e and p is given by the following simultaneous equations This set of relations may be solved numerically by standard mathematical methods, and shall hereafter be referred to as the toroidal dome framework planning algoπthm The toroidal dome framework algoπthm may be modified to assist in the planning of 10 toroidal dome frameworks of interleaved and stacked layers for spheroid structures of virtually any base shape or elevation The construction of the dome framework may then be carried out by connecting the toroidal elements of the sizes prescribed by the use of the toroidal dome framework planning algoπthm at the locations on said toroidal elements indicated by the use of the toroidal dome framework planning algoπthm, positioning the constituent toroidal elements according thereto, which may be facilitated by the use of a jig/mold from the specifications provided by the use of the toroidal dome framework planning ' *• > algoπthm, and connecting the constituent toroidal elements so positioned The connections may then be applied manually or with the use of robotics Such domes may also be joined in opposition at their bases to form complete or partial spheroid constructions In the case of construction of towers, such as those shown in FIGS 87 and 88, the method of construction would proceed similarly While the invention has been disclosed in connection with a preferred embodiment, it will be understood that there is 20 no intention to limit the invention to the particular embodiment shown, but it is intended to cover the vaπous alternative and equivalent constructions included within the spiπt and scope of the appended claims Bnef Descπption of the Drawings FIG 1 is a plan view of two open rectangle torsion elements connected in the same oπentation by two couplings 25 FIG 2 is an exploded view of the connection of the open rectangle torsion elements shown in FIG 1 FIG 3 is a perspective view of the torsion elements in FIG 1 FIG 4 is an exploded view of the connection of the open rectangle torsion elements shown in FIG 3 FIG 5 is a plan view of two open rectangle torsion elements connected in opposite oπentation via an intermediate torsion element by four couplings 30 FIG 6 is an exploded view of the connection of the open rectangle torsion elements shown in FIG 5 FIG 7 is a perspective view of the torsion elements in FIG 5 FIG 8 is an exploded view of the connection of the open rectangle torsion elements shown in FIG 7 FIG 9 is a plan view of two 'M'-shaped torsion elements connected in opposite oπentation via an intermediate torsion element by four couplings " FIG 10 is a perspective view of the torsion elements in FIG 9 FIG 11 is a perspective view of two 'U'-shaped open rectangle torsion elements connected at an angle m opposite oπentation by two couplings FIG 12 is a perspective view of two 'U'-shaped open rectangle torsion elements connected at an angle in opposite oπentation by four couplings via an intermediate torsion element 40 FIG 13 is a perspective view of 6 connected pairs of open rectangle torsion elements connected in a linear array, each pair being connected to one another at an angle by two couplings FIG 14 is a perspective view of 32 pairs of 'U'-shaped torsion elements connected at an angle in opposite oπentation by four couplings via an intermediate torsion element connected in a circular array forming a toroid FIG 15 is a perspective view of two toroidal torsion elements connected at an angle by one coupling 5 FIG. 16 is a side view of the toroidal torsion elements in FIG. 15. FIG. 17 is a plan view of the toroidal torsion elements shown in FIG. 15. FIG. 18 is a bottom view of the toroidal torsion elements shown in FIG. 15. FIG. 19 is a perspective view of 32 pairs of toroidal torsional elements shown in FIGS. 15-18 connected in a circular array forming a toroid. FIG. 20 is a perspective view of two toroidal torsion elements connected at an angle without an external coupling. FIG. 21 is a side view of the toroidal torsion elements in FIG. 20. FIG. 22 is a plan view of the toroidal torsion elements in FIG. 20. FIG. 23 is a bottom view of the toroidal torsion elements in FIG. 20. FIG.24 is a plan view of 64 pairs of angularly connected toroidal torsional elements connected in a circular array forming a toroid. FIG. 25 is a perspective view of the toroid shown in FIG. 24. FIG. 26 a side view of two toroids such as the one shown in FIG. 24 connected internally by couplings connecting a plurality of the toroidal elements of one with proximate toroidal elements of the other. FIG. 27 is a fragmentary view of the region of internal connection between the toroids in FIG. 26. FIG. 28 is another side view of the two toroids shown in FIG. 26. FIG. 29 is a fragmentary view of the region of internal connection between the toroids in FIGS. 20-23. FIG. 30 is a view of the two toroids in the direction of the arrow in FIG. 28. FIG. 31 is a fragmentary view of the region of internal connection between the toroids in FIG. 30. FIG. 32 is a perspective view of the two toroids in the direction of the arrow in FIG. 30. FIG. 33 is a fragmentary view of the region of internal connection between the toroids shown in FIG. 32. FIG. 34 is a perspective view of a toroid formed by two tubularly concentric toroids, the outer and the inner both being 32 pairs of toroidal torsional elements shown in FIGS. 20-23 connected in a circular array forming a toroid, but with different angular orientation of the pairs of toroidal elements. FIG. 35 is a plan view of 20 pairs of toroidal torsional elements as shown in FIGS. 20-23 connected in a eliptical array forming a toroid. FIG. 36 is a perspective view of the toroid formed by the eliptical array shown in FIG. 35. FIG. 37 is a perspective view of a toroidal element with a circular spiral tube, the tube of which is bordered by other coaxial toroidal elements of lesser tubular diameter which are bonded, bound or otherwise connected to the central toroidal element. FIG. 38 is a plan view of a toroidal element consisting of seven interlinked toroidal elements, the tubes of which may be bonded, bound or otherwise connected to one another. FIG. 39 is a cross section of the toroidal element in FIG. 38. FIG. 40 is a perspective view of the toroidal element in FIG. 38. FIG. 41 is a side view of the toroidal element in FIG. 38. FIG. 42 is a perspective view of a plurality of pairs of toroidal elements as shown in FIGS. 20-23 connected in a linear array to form a straight cylindrical rod, post or tube. FIG.43 is a perspective view of a plurality of pairs of toroidal elements connected in a linear array to form a straight cylindrical rod, post or tube, with a different angular orientation from those comprising the structure shown in FIG. 42. FIG. 44 is a perspective view of the linear array shown in FIG. 42 which is connected to and coaxially encloses the linear array shown FIG. 43. FIG. 45 is a perspective view of a toroidal element with two opposite semi-eliptical sides and two opposite straight sides. FIGS. 46-49 show various connections between toroidal elements (even numbered showing the plan view and odd numbered showing a perspective view). FIGS. 50, 51, and 52 are perspective views of a coupling with splined grips showing for connecting two elements showing, respectively, the coupling open, the compression band, and the coupling closed with the compression band applied. FIGS 53, 54, 55, and 56 are perspective views of a coupling with splined gπps for connecting two axially askew toroidal elements showing, respectively, the coupling open, the compression bands, the coupling closed with compression bands applied, and the coupling w ith an arbitary angle between the gπp axes (also with compression bands applied) FIGS 57-58 are perspective views of toroidal elements with two spline collars on opposite sides of the element attached to the toroidal elements of which they are compπsed FIG 59 is a side view of a structural module compπsed of three toroidal elements connected to form a tπangle FIG 60 is a perspective view of the structural module shown in FIG 59 FIG 61 is a side view linear array of 8 of the structural modules shown in FIG 59 forming the structure of a post, beam or rod of tπangular cross section FIG 62 is a top view of the linear array shown in FIG 61 FIG 63 is a perspective view of the linear array shown in FIG 61 FIG 64 is a side view of a structural module compπsed of six toroidal elements connected to form a rectangular box FIG 65 is a perspective view of the structural module in FIG 64 FIG 66 is a side view linear array of 8 of the structural modules shown in FIG 64 forming the structure of a post, beam or rod of rectangular cross section FIG 67 is a perspective view of the structure shown in FIG 66 FIG 68 is a perspective view of a double width of a 3 deep array of a linear array of 8 of the structural modules shown in FIG 64 forming the structure of a joist or beam FIG 69 is a perspective view of a tπple width semicircular array of 45 rectangular structural modules of toroidal torsion elements connected in a semicircular array to form an arch FIG 70 is a perspective view of 90 rectangular structural modules of toroidal torsion elements connected in a circular array FIG 71 is a cutaway plan view of a hexagonal toroidal element with 2 sets of 3 rotationally joined internal shafts, one in each opposing half of the hexagon FIG 72 is a cutaway perspective view of the toroidal element m FIG 71 FIG 73 is a cutaway side view of the toroidal element in FIG 71 FIG 74 is a side view of two hexagonal toroidal elements shown m FIG 71 angularly connected by one coupling FIG 75 is a plan view of the two toroidal elements in FIG 74 FIG 76 is a bottom view of the two toroidal elements in FIG 74 FIG 77 is a perspective view of the toroidal elements in FIG 74 FIG 78 is a perspective view of a toroidal element as shown in FIG 24 connected to a similar concentπc toroidal element within it, the radii of the toroidal elements compπsing the inner and outer toroidal elements being equal FIG 79 is a perspective view of a toroidal element formed by 32 pairs of toroidal torsional elements shown m FIG 21 connected in a circular array connected to a concentπc inner toroidal element formed by 32 pairs of the angularly connected toroidal torsional elements oriented as shown in FIG 22 connected in a circular array FIGS 80 through 81 show two types of concentric connections of two toroidal elements at different angles (even numbered showing the plan view and odd numbered showing a perspective view) FIG 82 is schematic elevation of a dome structure formed by successive interleaved layers of equal numbers of toroids of upwardly diminishing diameter, each toroid connected at six points to those adjacent capped by a similar dome structure of lesser diameter to form a compound dome structure FIG 83 is a schematic elevation of a spheπcal structure formed by two dome structures formed by successive layers of equal numbers of toroidal elements of upwardly diminishing diameter, each toroidal element connected at four points to those adjacent, connected in opposite polar oπentation FIG 84 is a side view of a spheπcal dodecahedral structure compπsed of twenty connected toroidal elements with the gaps bπdged by toroidal elements of lesser diameter, with a group of elements as shown in FIG 85 scaled to connect to the topmost toroidal element of the structure, with a similar connection of a similar group similarly scaled to connect to the topmost toroidal element of the first group FIG 85 is a group of 6 connected toroidal elements which compπse the frontmost section of the spheπcal/dodecahedral structure in FIG 84 FIG 86 is a perspective view of a tower structure formed by a vertical array of connected pπsmatic structural modules of upwardly diminishing dimension FIG 87 is a schematic elevation of a conical tower structure formed by successive layers of equal numbers of toroids of upwardly diminishing diameter, each toroid connected at four points to those adjacent FIG 88 is a schematic elevation of a conical tower structure formed by successive interleaved layers of equal numbers of toroids of upwardly diminishing diameter, each toroid connected at six points to those adjacent FIGS 89, 90, and 91 are perspective views of an actuated two element coupling with spline gπps, the latter two being cutaway views showing the motors, transmissions and drives for each of the spline gπps within the body of the coupling FIGS 92 and 93 show a series of plan views of a toroidal element shifting shape from that of a circular array of 40 toroidal elements forming a circular toroid to that of an eliptical array forming an eliptical toroid FIGS 94 through 98 show a series of schematic elevations of the shifting of shape of a prolate spheπcal structure to an oblate spherical structure in phases through intermediate structures of lesser volume FIG 99 is a perspective view of a circular hoπzontal arch of 20 toroidal members FIG 100 is a perspective view of a structure formed from two interleaved layers of circular horizontal arches, as shown m FIG 99 FIG 101 is a perspective view of a structure formed from three interleaved layers of circular hoπzontal arches, as shown in FIG 99 FIG 102 is a perspective cutaway view of a toroidal wheel body framework sheathed in a casing FIG 103 is a cutaway of a perspective view of a wheel and tire structure (the lowest five elements of which are shown in detail with the rest of the elements being shown diagrammatically) embedded in a matπx FIG 104 is perspective view of a wheel and tire structure (the lowest five elements of which are shown in detail with the rest of the elements being shown diagrammatically) supported by a common band FIG 105 is a perspective view of a tire with the wheel and tire structure shown in FIG 104 installed FIG 106 is a mathematical diagram to demonstrate the relationships among the angles and lengths of a plan for construction of a toroidal element framework with smaller toroidal elements showing the dimensional quantities involved FIG 107 is a perspective view of a schematic mathematical diagram of a dome showing the dimensional quantities to demonstrate the relationships among the angles and lengths of a plan for construction of a toroidal dome framework FIG 108 is an elevation of a schematic mathematical diagram of a dome showing the dimensional quantities to demonstrate the relationships among the angles and lengths of a plan for construction of a toroidal dome framework Best Mode for Carrying Out Invention The best mode is the preferred embodiment of the present invention and employs toroidal elements that are constructed with the use of torsion elements which are toroidal in shape The preferred embodiment using toroidal torsion elements converts most compression, tension and flexion loading of constructions using the system to torsional loading of the torsion elements of which the constructions are compπsed The use of toroidal torsion elements makes possible the construction of toroids which are self-supporting Industπal Applicability The use of the invention includes every conceivable structure bπdges, towers, furniture, aircraft, land and sea vehicles, appliances, instruments, buildings, domes, airships, space structures and vehicles, and planetary and space habitats The magnitude I of such structures contemplated and made structurally and economically feasible by the system range from the minute to the gigantic. The structures that are possible with the use of the present invention are not limited to any particular design, and may even be freeform. Some of the structural forms can be applied to construct buildings for unstable foundation conditions and which can survive foundation movement and failure. The principal objects of the present invention are: 1. To provide a universal structural system for all types of immobile and mobile structures comprised of connected torsion/toroidal elements and having a high degree of structural integrity, strength, efficiency, and flexibility. 2. To provide a structural system in which structural loading in the form of compression, tension and flexion is converted to 10 torsional loading of the torsion elements of which it is constructed so that such torsion elements bear the greatest part of the structural loading. 3. To provide a structural system in which a structure constructed of torsion/toroidal elements is uniformly loaded so that the material of which such torsion elements are composed is uniformly stressed, thereby achieving a high strength-to-weight ratio. 4. To provide a structural system in which loads are well distributed over all of the torsion/toroidal elements. 5 5. To provide a structural system which is integrated and attractive in appearance, allowing for aesthetic design with self- supporting toroidal torsion elements in which curved structures are architecturally natural. 6. To provide a structural system with dynamic shape shifting and dynamic redistribution of loading by adjustable and/or actuated structural connections while maintaining structural strength and integrity. 7. To provide a structural system which is economical, adaptable to automated design, automated fabrication, and efficient 0 structurally and in ultimate assembly, in its smallest elements and its largest structural forms. 8. To provide a structural system in which all structural characteristics of all elements can be precisely predicted, designed, and known. 9. To provide a structural system in which conventional structural elements such as beams, joists, decks, trusses, etc. can be constructed of torsion/toroidal elements and incorporated in conventional structures as conventional structural elements. 5 10. To provide a structural system in which various torsion/toroidal elements may be standardized and databased with all dimensional, material and loading characteristics so as to provide for automated selection of components for structural design therewith. 11. To provide a structural system that is compatible with conventional structural systems. 0 5 0 5

Claims: CLAIMS What I claim as my invention is Claim 1 A structural system compπsing (a) a plurality of torsion/toroidal elements, and (b) means for connecting the torsion/toroidal elements Claim 2 The structural system of claim 1 in which the torsion/toroidal elements are held firmly in position with respect to each other in a connection Claim 3 A structural system compπsing a plurality of torsion/toroidal elements which are connected to form a structure Claim 4 The structural system of claim 3 in which the torsion/toroidal elements are held firmly in position with respect to each other in one or more connections Claim 5 A structural system compπsing a plurality of torsion/toroidal elements which are connected so that the torsion/toroidal elements are held firmly m position in one or more of the connections Claim 6 A structural system compπsing (a) a plurality of torsion elements, and (b) means for connecting the torsion elements Claim 7 The structural system of claim 1 in which the torsion elements are held firmly in position with respect to each other in a connection Claim 8 A structural system compπsing a plurality of torsion elements which are connected to form a structure Claim 9 The structural system of claim 8 in which the torsion elements are held firmly in position with respect to each other in one or more connections Claim 10 A structural system compπsing a plurality of torsion elements which are connected so that the torsion elements are held firmly in position in one or more of the connections Claim 11 A structural system compπsing (a) a plurality of toroidal elements, and (b) means for connecting the toroidal elements Claim 12 The structural system of claim 1 in which the toroidal elements are held firmly in position with respect to each other in a connection Claim 13 A structural system compπsing a plurality of toroidal elements which are connected to form a structure Claim 14 The structural system of claim 13 in which the toroidal elements are held firmly in position with respect to each other in one or more connections Claim 15 A structural system compπsing a plurality of toroidal elements which are connected so that the toroidal elements are held firmly in position m one or more of the connections Claim 16 A structural system for non-domical and non-spheπcal structures compπsing (a) a plurality of toroidal elements, and (b) means for connecting the toroidal elements Claim 17 The structural system of claim 16 in which the toroidal elements are held firmly in position with respect to each other in a connection Claim 18 A structural system for non-domical and non-spheπcal structures compπsing a plurality of toroidal elements which are connected to form a structure Claim 19 The structural system of claim 18 in which the toroidal elements are held firmly in position with respect to each other in one or more connections Claim 20 A structural system for non-domical and non-spheπcal structures compπsing a plurality of toroidal elements which are connected so that the toroidal elements are held firmly in position in one or more of the connections Claim 21. A structural system of toroidal elements for domical and spherical structures comprising: (a) a plurality of toroidal elements; (b) said elements disposed on the surface of an imaginary dome,; (c) most of said elements being connected to four other of said elements; and (d) said elements being arranged in row-like layers, with the first such layer being the frame of the structure at the base of the structure, and each successive layer being attached in the direction of the pole of the structure to form the frame of a domical or spherical structure. Claim 22. A structural system of toroidal elements for domical and spherical structures comprising: (a) a plurality of toroidal elements; (b) said elements disposed on the surface of an imaginary dome; and (c) said elements being connected to other of said elements in an arrangement of row-like layers, with the first such layer being the frame of the structure at the base of the structure, and each successive layer being attached in the direction of the pole of the structure to form the frame of a domical or spherical structure. Claim 23. A structural system of toroidal elements for domical and spherical structures comprising: (a) a plurality of toroidal elements; and (b) means for connecting the toroidal elements; (c) said elements including successive layers of a plurality of elements; and (d) said layers being successive from the base to the pole of the structure, each of said layers being arranged on a closed curve so that each said layers forms a horizontal arch throughout its extent which is convex outward from the area enclosed by the closed curve for each layer, the lowest of said layers being at the base of the structure, and each succesive layer being arranged on a closed curve which includes the points of connection of the bottom of each element of that layer with the elements of the previous successive layer to form the frame of a domical or spherical structure. Claim 24. A structural system of toroidal elements for domical and spherical structures comprising: (a) a plurality of toroidal elements; and (b) means for connecting the toroidal elements; (c) said elements including successive layers of a plurality of elements, said layers being successive from the base to the pole of the structure, each of said layers being arranged so that a a first plurality of toroidal elements are connected side-to-side in an arc of a curve in the plane of the base of the structure with adjacent toroidal elements leaning together toward the center of curvature of the arc; wherein the positions of said toroidal elements are fixed at their base along the horizontal arc so that a row-like layer of toroidal elements are disposed on the surface of an imaginary hemisphere which coincides with the structure; said positions being determined by the placement of each of said toroidal elements so that they are laterally connected above and within the perimeter of said arc of the curve to form the frame of a domical or spherical structure Claim 25. The structural system as in any one of claims 21-24 inclusive in which the size of the toroidal elements varies. Claim 26. The structural system as in any one of claims 21 -24 inclusive in which the size of each toroidal element in each of said layers is substantially the same within each layer. Claim 27. The structural system as in any one of claims 21 -24 inclusive in which the size of the toroidal elements which comprise each of said layers are smaller than the toroidal elements in the next successive layer. Claim 28. The structural system as in any one of claims 21 -24 inclusive in which most toroidal elements above the base layer and below the layer nearest the pole are connected to four other toroidal elements to form the frame of a domical, hemispherical or spherical structure. Claim 29. The structural system as in any one of claims 21 -24 inclusive in which most toroidal elements above the base layer and below the layer nearest the pole are connected to six other toroidal elements to form the frame of a domical, hemispherical or spherical structure. Claim 30. The structural system as in any one of claims 1-24 inclusive in which none of the connections result from interlinking or intersection of elements Claim 31 The structural system as in any one of claims 1-24 inclusive in which one or more connections are adjustable so that the position of one or more of said elements in a connection may be changed in the connection Claim 32 The structural system as in any one of claims 1-24 inclusive in which connections are such that such an element in a connection will not have substantial movement in the connection Claim 33 The structural system as in any one of claims 1 -24 inclusive in which connections are such that such an element having been positioned in a connection will not have substantial movement in the connection Claim 34 The structural system as in any one of claims 1 -24 inclusive in which connections are such that such an element having been positioned in a connection by adjustment of the connection will not have substantial movement m the connection Claim 35 The structural system as in any one of claims 1 -24 inclusive in which connections are such that any motion of such an element in a connection will be regulated by the connection Claim 36 The structural system as in any one of claims 1-24 inclusive in which connections are such that such an element may be moved in a connection and that such movement will be regulated by the connection Claim 37 The structural system as in any one of claims 1-24 inclusive in which connections are such that such an element may be moved in a connection and that such movement will be regulated by the connection so that said element will not thereafter otherwise have substantial movement in the connection Claim 38 The structural system as in any one of claims 1-24 inclusive in which connections are such that after such an element is moved in a connection such movement will be regulated by the connection so that said element will not thereafter otherwise have substantial movement in the connection Claim 39 The structural system as in any one of claims 1-24 inclusive in which connections are such that after such an element is moved by a connection m the connection such movement will be regulated by the connection so that said element will not thereafter otherwise have substantial movement in the connection unless moved by the connection Claim 40 The structural system as in any one of claims 1-24 inclusive in which connections are such that such an element may be moved by a connection and then held by the connection m the position resulting from such movement so that said element will not have substantial movement the connection unless again moved by the connection Claim 41 The structural system as in any one of claims 1 -24 inclusive in which one or more connections are actuated so that one or more of such elements may be moved by a connection and then held by the connection in the position resulting from such movement so that said element will not have substantial movement in the connection unless again moved by the connection Claim 42 A method of constructing any given toroidal element framework from other toroidal elements which compπses determining the component curvatures of the required toroidal shape, planning the toroidal framework using the toroidal element framework planning algorithm, positioning the constituent toroidal elements as prescπbed by said planning algoπthm, and connecting the constituent toroidal elements so positioned Claim 43 A method of construction of a dome with toroidal elements which compπses determining the shape of the dome and the shape of the base of the dome, planning the toroidal dome framework using the toroidal dome framework planning algoπthm, positioning the constituent toroidal elements as prescπbed by said planning algoπthm, and connecting the toroidal elements so positioned at the locations on said toroidal elements indicated by the use of said planning algoπthm Claim 44 The methods of claims 41 or 42 in which a third step is added following the first two steps, which compnses prepaπng a jig/mold for positioning the toroidal elements from the specifications provided by the use of said planning algoπthm Claim 45 The methods of claims 41 or 42 in which a third step is added following the first two steps, which compπses prepaπng the toroidal elements of the sizes prescπbed by the use of said planning algoπthm Claim 46 A toroidal element framework planning algoπthm, which compπses the diagram shown in FIG 106 showing the geometπc relations among the angles and lengths, and the following relations to be solved by standard mathematical procedures for the quantities Li, Ej(dιa) and Alpha, for a given RT, Tr, n and r, wherein the torus radius is RT, the toroidal tube radius is Tr, the number of elements is n, the angle of arc occupied by one element is Phi = 360/n, and the radius of a toroidal element is r RO = RT + Tr; RJ = RT - Tr; Ro = RO - r; Ri = RJ + r; Sin(Theta) = r/Ri; Sin(Psi) = r/Ro; Li = rΛTan(Theta); Lo = r/Tan(Psi); x = Ro * Sin(Phi - Psi), (* indicating multiplication between adjacent quantities); Ld = Ro * Cos(Phi - Psi) - Li; Tan(Alpha) = (x - r)/Ld; Ej(dia) = (x - r)/Sin(Alpha). Claim 47. A toroidal dome framework planning algorithm which comprises: the diagrams shown in FIGS. 107 and 108 showing the geometric relations among the angles and lengths; and the following relations to be solved by standard mathematical procedures for the quantities e and p, and thus all dependent quantities; wherein the number of base toroidal elements is n, the sphere radius is S, the horizontal element angle is f = 360/n, the declination of the base is t, the vertical element angle is e, and the element join angle is p, the relations among the angles and lengths labeled in FIGS. 107 and 108 is as follows: for the element radius, R = S * Sin(e/2); for the upper base radius, Ur = Cos(t + e); for the upper base height, Uh = S * Sin (t + e); for the lower base radius, Lr = S * Cos(t); for the lower base height, Lh = S * Sin(t); and the relation between e and p is given by the following simultaneous equations: e = 2 • ArcSin[Tan(θ.5 * f) • Tan(45 - 0.5 • p)] 2 » S » Sin(0.5 » e) ÷ p = ArcCos [S • Cos(t + e) • Sm(0.5 • t) + Cos(t) • Tan(θ.5 • /)]J Claim 48. A method for providing structures utilizing torsion/toroidal elements, which comprises: fabricating a plurality of torsion/toroidal elements; and connecting the torsion/toroidal elements so that a structure is formed. Claim 49. A method for providing structures utilizing torsion elements, which comprises: fabricating a plurality of torsion elements; and connecting the torsion elements so that a structure is formed. Claim 50. A method for providing structures utilizing toroidal elements, which comprises: fabricating a plurality of toroidal elements; and connecting the toroidal elements so that a structure is formed. Claim 51. A horizontal arch comprising a plurality of torsion/toroidal elements which are connected side-to-side in an arc of a curve in the horizontal plane with said adjacent torsion/toroidal elements lean together toward the center of curvature of the arc; wherein the positions of said torsion/toroidal elements are fixed at their base along the horizontal arc so that the overall shape of the horizontal arch is described thereby; said positions being determined by the placement of each of said torsion/toroidal elements so that the sides thereof are connected above and within the perimeter of said arc of the horizontal arch. Claim 52. A toroidal wheel body comprising a toroidal framework structure of connected torsion elements. Claim 53. The toroidal wheel body of claim 51 wherein the shape of the toroidal wheel body is continuously controlled by actuation of the connections of the torsion elements. Claim 54. A non-pneumatic wheel and tire structure comprising: (a) a plurality of supporting toroidal torsion elements connected in a circular array to form a toroidal shape in which the axis of each toroidal torsion element is perpendicular to the axis of said circular array forming said toroidal shape; (b) wherein said supporting toroidal torsion elements are resilient in the radial direction of said toroidal shape of the wheel and tire structure, so that loading of the wheel and tire structure loads the supporting toroidal torsion elements by said toroidal torsion support elements radially inward toward the center of the wheel and tire structure. Claim 55. The non-pneumatic wheel and tire structure of Claim 53, wherein the toroidal support elements are connected by being embedded in a matrix of resilient elastomeric material, Claim 56. The non-pneumatic wheel and tire structure of Claim 53, wherein the toroidal support elements are connected by attachment to a band which located is at a position which is immedately radially inward of the position of each toroidal support element in the wheel and tire structure Claim 57 The non-pneumatic wheel and tire structure of Claim 53, wherein the toroidal support elements are connected by mutual connection to a central hub structure for receiving an axle Claim 58 A non-pneumatic wheel and tire structure compπsing (a) a plurality of self-supporting toroidal torsion elements, and (b) a means for connecting said supporting toroidal torsion elements to each other, (c) wherein said toroidal torsion support elements are connected in a circular array to form a toroidal shape in which the axis of each toroidal support element is perpendicular to the axis of said circular array of toroidal torsion elements forming the toroidal shape, and (d) wherein the toroidal support elements are resilient in the radial direction of said toroidal shape of the wheel and tire structure, so that loading of the wheel and tire structure loads said toroidal torsion elements by compressing said toroidal torsion support elements radially inward toward the center of the wheel and tire structure Claim 59 A jig/mold for positioning torsion/toroidal elements for construction of a toroidal element framework compπsing (a) a surface plate, and (b) means for positioning torsion/toroidal elements on the surface plate, so that the torsion/toroidal elements are held in the positions so outlined for in order to be connected to form a toroidal element Claim 60 A jig/mold for positioning torsion/toroidal elements for construction of a toroidal element framework compπsing (a) a surface plate, and (b) stops attached to the surface plate outlining the positions of the torsion/elements on the surface plate, so that the torsion/toroidal elements are held in the positions so outlined for in order to be connected to form a toroidal element Claim 61 Thejig/mold of claim 58 or 59 in which the specifications for positioning of the torsion toroidal elements is provided by the use of the toroidal element framework planning algoπthm

Inventors: PROVITOLA ANTHONY I, PROVITOLA, ANTHONY, I.
Applicants: PROVITOLA ANTHONY I, PROVITOLA, ANTHONY, I.
Application year: 2000
Main classification: E04B1
IPC codes: B60C19, E04B1