Foldable and curvilinearly extensible structure
BACKGROUND 
     1. Field of the Invention 
     This invention relates to a foldable and extensible structure and, more particularly, to a foldable and curvilinearly extensible structure and method, the structure fabricated from a plurality of base modules, each base module being configurated from six rigid members flexibly interconnected end-to-end by swivels in a closed configuration generally approximating a double isosceles triangle in appearance when folded flat and having intersecting rigid members pivotally secured with the location of one pivot at the midpoint of the base of the isosceles triangle as defined by the respective rigid members and the other two pivots offset from the swivels adjacent the base by a distance equal to one-half the base to thereby impart a desired external contour to the curvilinear configuration and to provide the desired folding and unfolding characteristics. 
     2. The Prior Art 
     Extensible structures are well-known in the art and one particularly familiar form of an extensible arm structure is the common &#34;scissors&#34; extension arm. The scissors extension arm involves at least a first pair of pivotally joined rigid members. The structure may also include additional pairs of rigid members adjoined to the ends of the first pair in an end-to-end relationship. Lateral movement of the free ends of the rigid members imparts a corresponding movement to the pivotally interconnected pairs of rigid members resulting in a linear contraction and/or extension of the scissors extension arm. While this well-known apparatus is found in numerous applications, it is generally considered to be a two-dimensional configuration and therefore lacks the necessary structural stability for various applications. Additionally, the nature of the construction limits the extension of the scissors extension arm to a generally straight line. 
     The foregoing limitations of a two-dimensional structure have been overcome by the apparatus disclosed in my previous patent, U.S. Pat. No. 4,155,975, issued Sept. 26, 1978. In this patent, the basic element of the foldable and extensible structure is a foldable and extensible base module. The base module is fabricated from six equal-length, rigid members swivelly interconnected end-to-end in a closed figure with intersecting rigid members being pivotally connected adjacent the midpoint of the rigid members. A plurality of the base modules are selectively interconnected at adjacent swivels and may include additional rigid struts to thereby provide an enlarged, foldable and extensible truss-like structure. However, in each of the configurations set forth in this patent, extension is limited to a straight line or plane and is, therefore, incapable of being extended in a curvilinear configuration. 
     Zeigler (U.S. Pat. No. 3,968,808) discloses a collapsible, self-supporting structure made up of a network of rod elements pivotally joined at their ends and forming scissor-like pairs in which rod element crossing points are pivotally joined. 
     Zeigler (U.S. Pat. No. 4,026,313) discloses a collapsible, self-supporting structure in which basic assemblies of crossed rod elements are employed to achieve the desired shape. Further, the crossing points of crossed rod element in the structure may include limited sliding connections to affect the transfer of collapsing force to other crossing points which are pivotally joined. 
     Lotto, et al (U.S. Pat. No. 4,017,932) discloses a temporary, modular, self-erecting bridge which is expandable to form a truss-like structure. 
     While the foregoing list of references have come to the attention of the inventor, no representation is made that all of these references may be &#34;prior art&#34; within the meaning of that term under the provisions of 35 USC 102 or 35 USC 103, although these references are disclosed herein so as to fully comply with the duty of candor and good faith as required in 37 CFR 1.56. 
     In view of the foregoing, it would be an advancement in the art to provide a foldable and extensible structure which is extensible in a generally curvilinear orientation, the curvature of the curvilinear configuration being a function of the length of the rigid members with a corresponding placement of the pivotal points on the structure, and the degree of extension of the structure. It would also be an advancement in the art to provide a novel foldable and curvilinearly extensible structure wherein the rigid members are configurated with a predetermined arcuate curve therein to thereby provide a predetermined toroidal profile to the structure. 
     BRIEF SUMMARY AND OBJECTS OF THE INVENTION 
     The present invention relates to a foldable and curvilinearly extensible structure fabricated from a plurality of basal modular elements with each basal modular element or base module being configurated from six rigid members flexibly joined end-to-end by swivels into a closed structure having a generally double, isosceles triangular profile when folded flat. The intersecting rigid members are pivotally interconnected. 
     The rigid members that form the base of the isosceles triangle are pivotally joined at their midpoint while the pivots for the other two sets of rigid members are each offset from the intervening swivels by a distance that equals one-half the length of the base or, correspondingly, are offset from the swivel by the same distance as the basal pivot. 
     It is, therefore, a primary object of this invention to provide improvements in foldable and curvilinearly extensible structures. 
     Another object of this invention is to provide improvements in the method of providing foldable and curvilinearly extensible structures. 
     Another object of this invention is to provide a foldable and curvilinearly extensible structure wherein a plurality of basal modular elements are selectively interconnected end-to-end for the purpose of providing a curvilinearly extensible structural element. 
     Another object of this invention is to provide a truss-like structure wherein a plurality of basal modular elements are selectively interconnected to provide a structure which is foldable and curvilinearly extensible into a truss structure having a generally cylindrical profile. 
     Another object of this invention is to combine rigid members having predetermined lengths to provide a foldable structure having a predetermined isosceles triangular profile and being curvilinearly extensible. 
     These and other objects and features of the present invention will become more fully apparent from the following description and appended claims taken in conjunction with the accompanying drawing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a perspective view of a basal modular element for a first preferred embodiment of this invention shown in the generally open or extended configuration; 
     FIG. 2 is a perspective view of a plurality of the basal modular elements of FIG. 1 shown interconnected to provide a first preferred embodiment of the foldable and curvilinearly extensible structure of this invention; 
     FIG. 3 is a perspective view of another preferred embodiment of the basal modular element of this invention shown in the partially opened configuration; 
     FIG. 4 is a perspective view of a plurality of basal modular elements of FIG. 1 interconnected to form another preferred embodiment of the foldable and curvilinearly extensible structure of this invention; 
     FIG. 5 is a perspective view of another preferred embodiment of the basal modular element of this invention showing each of the rigid members having a predetermined curved configuration; 
     FIG. 6 is a perspective view of a plurality of modular elements of FIG. 5 interconnected end-to-end to provide another preferred embodiment of the foldable and curvilinearly extensible structure of this invention. 
     FIG. 7 is a perspective view of a pair of modular elements joined side by side; 
     FIG. 8 is a perspective view of a plurality of pairs of modular elements of FIG. 7 interconnected in another preferred embodiment of the foldable and curvilinearly extensible truss structure of this invention to create a vault-like structure having a generally cylindrical profile; 
     FIG. 9 is a schematic, side elevation of the truss structure of FIG. 8 to more clearly illustrate the cylindrical curvature of the curvilinearly extensible structure; and 
     FIG. 10 is a diagramatic representation of the pivot points for the isosceles triangular configuration of the basal modular elements of this invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The invention is best understood by reference to the drawing wherein like parts are designated by like numerals throughout. 
     Referring now to FIG. 1, a first preferred embodiment of the base module of this invention is shown generally at 10 and includes a plurality of rigid members 11-16 flexibly interconnected end-to-end by flexible swivels 17a-17f, respectively. Representative swivel arrangements are shown in my patent, U.S. Pat. No. 4,115,975 issued Sept. 26, 1978. Swivels 17a-17f provide the necessary twisting and hinge-type movement between the interconnected rigid members 11-16 when base module 10 is flexed between the flat and the extended configurations. 
     The respective lengths of adjoining pairs of rigid members 11-16 are selectively predetermined to thereby provide an essentially isosceles triangular profile when base module 10 is folded into a flat configuration. For example, rigid members 11 and 14 are provided with a length that is longer than the equal lengths of rigid members 12, 13, 15 and 16. This configuration presents a profile corresponding to an isosceles triangle with a wide base as represented by rigid members 11 and 14 so that the sides of the triangle represented by rigid members 12 and 15 on one side and rigid members 13 and 16 on the other side are essentially equal in length. 
     Rigid members 11 and 14 are pivotally interconnected by a pivot 18a while rigid members 12 and 15 are pivotally interconnected by a pivot 18b and rigid members 13 and 16 are pivotally interconnected by a pivot 18c. It will be noted that pivot 18a is located at the midpoint of each of rigid members 11 and 14. However, pivots 18b and 18c are offset a predetermined distance from the interceding swivels of the respective rigid members. The relationship between the lengths of the rigid members that form the isosceles triangle and the relationship between the location of the respective pivots can best be understood by reference to the schematic illustration of FIG. 10. 
     With particular reference now to FIG. 10, an isosceles triangle ABC is shown generally at 100 and has a base AC with equal sides represented by leg AB and leg BC. A pivot 102 is located at the midpoint of base AC so that the distance from pivot 102 to corner A is represented by distance x and likewise the distance from pivot 102 to corner C is also represented by the distance x. Importantly, pivot 103 is located distance x from corner A and pivot 104 is also located distance x from corner c. Any significant alteration of the relationship of the respective pivots from the foregoing relationship will interfere with the foldable and also the curvilinear extension characteristics of the structure of this invention. 
     While triangle ABC of FIG. 10 is shown with base AC shorter than coequal legs AB and BC, the foregoing relationship must be followed when base AC is longer than legs AB and BC. The only difference will be in the direction in which the structure will curve when unfolded. 
     Referring again to FIG. 1, the base of the isosceles triangle of base module 10 is represented by rigid members 11 and 14. Accordingly, it is to be clearly understood that pivot 18b is located equidistantly from swivels 17a and 17d as is pivot 18a from swivels 17a and 17d. Likewise, pivot 18c is also located equidistantly from swivels 17c and 17f along with pivot 18a from the same swivels. 
     Since the base represented by rigid members 11 and 14 is longer than the remaining rigid members, the foregoing relationship places pivots 18b and 18c closer to swivels 17b and 17e. The resulting placement of pivots 18b and 18c means that the assembled truss member, as will be discussed more fully hereinafter with respect to FIG. 2, will tend to place swivels 17b and 17e on an inside portion of the resultant curvilinear profile. 
     Attention should also be directed to the inside/outside relationship between the pivotally joined rigid members 11-16. In particular, the relationship alternates for each rigid member in the serial sequence. For example, rigid member 11 is pivotally connected to the outside of rigid member 14 whereas rigid member 12 is pivotally connected to the inside of rigid member 15. Correspondingly, rigid member 13 is pivotally connected to the outside of rigid member 16. The terms &#34;inside&#34; and &#34;outside&#34; have been arbitrarily chosen herein to designate the appropriate position relative to the internal structure of base module 10. 
     Referring now also to FIG. 2, a plurality of base modules 10 (shown herein as base modules 10a-10e) are selectively interconnected in an end-to-end relationship to provide this one preferred embodiment of the foldable and curvilinearly extensible truss element 20 of this invention. In particular, swivels 17b, 17d, and 17f are flexibly interconnected with corresponding swivels of base module 10b in interties 22a-22c, respectively, thereby flexibly interconnecting base module 10a with base module 10b. Corresponding flexible interties are also made between each of base modules 10b-10e thereby providing the foldable and curvilinearly extensible truss-like structure 20. However, it should be pointed out that the foregoing inside/outside relationship between adjacent rigid members is alternated between successive base modules 10a-10e. This successive alternation corrects the tendency for the assembled truss element 20 to form a generally twisting characteristic in the structure. In particular, each of rigid members 11-16 are interconnected end-to-end and are foldable into a generally flat, double, isosceles triangular configuration. The double triangular configuration is composed of two isosceles triangles (when folded flat and viewed in plan view) with the first triangle including rigid members 11, 12 and 13 and the second triangle including rigid members 14, 15 and 16. However, since all of rigid members 11-16 are interconnected end-to-end, the overlying pairs of swivels (swivels 17a and 17d; swivels 17b  and 17e; and swivels 17c and 17f) tend to be offset from each other by approximately the thickness of the respective rigid members. Therefore, in the absence of an alternating base module internal structure, the total structure of truss element 20 would tend to twist by an amount approximating the thickness of the rigid members of each base module to the next base module. 
     The degree of curvature of truss element 20 is a function of the relative lengths of the respective rigid members and the degree of extension of truss element 20. Accordingly, any person practicing the teachings of this invention will be able to use simple, well-known mathematical relationships to selectively predetermine the distance to be covered by truss element 20, the degree of desired curvature, and the degree of extension for the various base modules 10a-10e therein. These mathematical concepts are well-known in the art and are, therefore, not included herein for each of presentation and simplicity. The foregoing calculation will necessarily include a determination of the length of rigid members 11 and 14 for the purpose of providing the desired overall profile characteristics to truss structure 20. For example, increasing the length of rigid members 11 and 14 shifts the location of pivots 18b and 18c in the remaining rigid members and provides a corresponding change in the curvature of truss element 20. Correspondingly, foreshortened rigid members 11 and 14 relative to the remaining rigid members provides a corresponding alteration in the overall appearance of truss element 20. 
     With reference now to FIG. 3, another preferred embodiment of the base module of this invention is shown as base module 30. Base module 30 differs from base module 10 (FIG. 1) primarily in the length of its base as defined by rigid members 32 and 35, as will be set forth more fully hereinafter. 
     Base module 30 is fabricated from a plurality of rigid members 31-36 serially interconnected end-to-end by swivels 37a-37f, respectively. Rigid members 32 and 35 are pivotally interconnected at their respective midpoints by pivot 38b. Pivot 38a pivotally interconnects rigid members 31 and 34 while pivot 38c pivotally interconnects rigid members 33 and 36. It should be particularly noted that pivot 38a is equidistantly located from swivels 37a and 37d along with pivot 38b. Correspondingly, pivot 38c is located equidistantly with pivot 38b from swivels 37b and 37e. This relationship is best seen by reference again to the foregoing discussion regarding the schematic illustration of FIG. 10. 
     The length of rigid members 32 and 35 in relation to the remaining rigid members, rigid members 31, 33, 34 and 36, in conjunction with the predetermined placement of pivots 38a and 38c imparts the desired curvilinear extension characteristics to a truss structure fabricated from a plurality of base modules 30 serially interconnected in an end-to-end relationship as will be set forth more fully hereinafter with respect to the discussion relating to FIG. 4. 
     Referring now more particularly to FIG. 4, a truss element 40 is shown and is fabricated from a plurality of base modules similar to base module 30 (FIG. 3) and shown herein as base modules 30a-30h. In particular, swivels 37b, 37d, and 37f are interconnected with corresponding swivels of adjacent base module 30b to form interties 42a-42c, respectively. Corresponding interties are made between adjacent swivels of base modules 30b-30h to provide the curvilinearly extensible structure of truss element 40. However, as set forth hereinbefore with respect to FIGS. 1 and 2, each of base modules 30a-30h are sequentially alternated with respect to the &#34;inside&#34; and &#34;outside&#34; relationship between the intersecting rigid members. 
     The basal portion of truss structure 40, as represented by rigid members 32 and 35 (see also FIG. 3), forms a curvilinear surface which generally represents a segment of a cylindrical surface whereas the apex of the triangular configuration as represented by swivels 37c and 37f (see also FIG. 3) generally represents an arc which is substantially parallel to the cylindrical planar surface represented by rigid members 32 and 35. Accordingly, in comparison with truss element 20 (FIG. 2), truss element 40 is configurated with an arch-like inner surface corresponding to the cylindrical surface as represented by rigid members 32 and 35. On the other hand, the truss element 20 (FIG. 2) provides an outer cylindrical surface as represented by rigid members 11 and 14 as the outer surface to truss element 20. 
     The circular arch superintended by truss element 40 will, therefore, be a function of the length of rigid members 31, 33, 34 and 36 in relation to rigid members 32 and 35 which determines the location of pivots 38a and 38c in combination with the degree of extension of base modules 30a-30h that make up truss element 40. 
     Referring now more particularly to FIG. 5, another preferred embodiment of the novel base module of this invention is shown generally at 50 and includes a plurality of rigid members 51-56 serially interconnected in an end-to-end relationship by swivels 57a-57f, respectively. While base module 50 is substantially similar to the construction of base module 10 (FIG. 1) is should be particularly noted that each of rigid members 51-56 are formed with a predetermined curvature therein. The curvature of each of rigid members 51-56 is selectively oriented so that when base module 50 is folded into the generally flat or triangular configuration, the arcuate curvatures of corresponding pairs of rigid members 51 and 54; 52 and 55; and 53 and 56, are substantially parallel. In each instance, the curvature is outwardly from the center of the generally triangular configuration of flat folded base module 50. 
     Rigid members 51 and 54 form the &#34;base&#34; to the isosceles triangle represented by base module 50 when folded into a generally flat configuration and are pivotally joined at their respective midpoints. Rigid members 51 and 54 are also longer than the remaining equal length rigid members, rigid members 52, 53, 55, and 56. Thus, rigid members 52 and 55 are pivotally joined at a distance from swivels 57a and 57d equal to the distance that pivot 58a is located from swivels 57a and 57d. Correspondingly, rigid members 53 and 56 are pivotally joined at pivot 58c located at a distance from swivels 57c and 57f equal to the distance that pivot 58a is from swivels 57c and 57f. The respective lengths of rigid members 51 and 54 with respect to the lengths of rigid members 52, 53, 55, and 56 with the corresponding placement of pivots 58b and 58c, imparts the desired curvilinear characteristic to truss element 60 (FIG. 6) similar to that found in base module 10 in its relationship to truss element 20 (FIG. 2) as set forth hereinbefore. 
     With particular reference to FIG. 6, truss element 60 is shown as fabricated from a plurality of base modules 50a-50e similar to base module 50 (FIG. 5). Base module 50a is flexibly interconnected in an end-to-end relationship to base module 50b by flexibly interconnecting swivels 57b, 57d and 57f to corresponding swivels on base module 50b in interties 62a-62c. Corresponding interconnection is made between the successive base modules 50d-50e, respectively. Accordingly, truss element 60 is foldable and curvilinearly extensible in a generally curvilinear profile substantially identical to the extension of truss element 20 (FIG. 2). Additionally, the degree of curvature of truss element 60 in the extension thereof will be a function of the respective length relationships between rigid members 51 and 54 with respect to rigid members 52, 53, 55, and 56. The resultant length of rigid members 51 and 54 will selectively predetermine the location of pivots 58b and 58c. These features combined with the number and degree of extension of base modules 50a-50e will selectively determine the arch superintended by truss element 60. 
     Importantly, however, it should be noted that the arcuate profile of each of rigid members 51-56 also imparts an overall toroidal contour to the internal portion of truss element 60 when truss element 60 is extended into a predetermined degree of extension. The interrelationship between the extension of truss element 60 to obtain the toroidal profile will, therefore, also be a function of the curvature of each of rigid members 51-56. The formation of a generally toroidal surface by truss element 60 would provide a useful structure for supporting an internally placed toroidal surface (not shown) for any suitable purpose. Additionally, the internal relationship between adjacent base modules 50a-50e will be selectively alternated to preclude the previously discussed &#34;twisting&#34; of truss element 60. 
     Referring now to FIG. 7, another basal element of the truss structure of this invention is shown wherein a pair of base modules 70a and 70b are joined in a side-to-side relationship through flexible interties 92a and 92b. In particular, base module 70a is fabricated from a plurality of rigid members 71-76 flexibly interconnected in an end-to-end relationship by swivels 77a-77f, respectively. Rigid members 71 and 74 are pivotally interconnected at their respective midpoints by pivot 78a. Rigid member 72 is pivotally interconnected to rigid member 75 by pivot 78b while rigid member 73 is pivotally interconnected to rigid member 76 by swivel 78c. Swivels 78b and 78c are located so that the respective distance from the adjacent swivel between it and swivel 78a is the same to thereby impart the desired curvilinear characteristics to the truss structure as will be set forth more fully hereinafter and as also set forth hereinbefore with respect to each of the structures of this invention. Base module 70b is fabricated from a plurality of rigid members 81-86 flexibly interconnected in an end-to-end relationship by swivels 87a-87f, respectively. Correspondingly, rigid members 81 and 84 are pivotally interconnected by pivot 88a adjacent their midpoint. Pivot 88b pivotally joins rigid members 82 and 85 while rigid members 83 and 86 are pivotally joined by pivot 88c. The placement of pivot 88b relative to rigid members 82 and 85 is such that the distance from pivot 88b to swivels 87a and 87d is equal to the distance from pivot 88a to these same swivels. Pivot 88c is likewise located on rigid members 83 and 86 equidistantly with pivot 88a from swivels 87c and 87f. 
     Intertie 92a flexibly interconnects swivel 77c of base module 70a with swivel 87a of base module 70b. Correspondingly, intertie 92b flexibly interconnects swivel 77f of base module 70a with swivel 87d of base module 70b. The particular orientation of base module 70a to base module 70b is such that rigid members 71 and 74 of base module 70a in cooperation with rigid members 81 and 84 of base module 70b define a generally planar configuration across the corresponding surface of base modules 70a and 70b. Additional base modules (not shown), comparable to base modules 70a and 70b, can be joined also in a side-to-side relationship therewith to further extend laterally the basal structure 70. For example, additional interties may be made with swivel 77a and 77d of base module 70a in addition to swivels 87c and 87f of base module 70b. 
     Referring now more particularly to FIG. 8, another preferred truss structure embodiment of this invention is shown generally at 80 and is fabricated from a plurality of basal elements such as basal element 70 (FIG. 7) (fabricated from base modules 70a and 70b) flexibly joined in an end-to-end relationship with additional basal elements. For example, base modules 70a and 70b are joined in a side-to-side relationship (see also FIG. 7) and are, in turn, flexibly joined end-to-end with corresponding base modules 70c and 70d, respectively. Additionally, base modules 70c and 70d are flexibly joined end-to-end with base modules 70e and 70f, respectively, while base modules 70g and 70h, respectively, are flexibly joined therewith. Accordingly, the planar configuration defined by rigid members 71 and 74 in conjunction with rigid members 81 and 84 (FIG. 7) becomes a substantially widened cylindrical surface when truss structure 80 is curvilinearly extended. The curvature of the resulting cylindrical surface is a function of the various features set forth hereinbefore. 
     Truss structure 80 is shown as being fabricated from base modules 70a and 70b (FIG. 7) which are similar in construction to base module 10 (FIG. 1) so that truss structure 80 is then generally similar in its basic construction to truss element 20 (FIG. 2). 
     Therefore, it will be seen that the configuration of truss structure 80 is substantially identical to truss element 20 (FIG. 2) with the exception that truss structure 80 consists of two side-by-side truss elements similar to truss element 20 (FIG. 2) joined in a side-to-side relationship. However, a similar configuration for truss structure 80 may also be prepared using the combination of features relative to the structure of base module 30 (FIG. 3) as the basal element for a plurality of truss elements similar to truss element 40 (FIG. 4). Correspondingly, truss structure 80 may also be prepared from a combination of base modules 50 (FIG. 5) connected into a plurality of joined truss elements similar to truss element 60 (FIG. 6). In any of these configurations, the length of the base of the triangular (isosceles) profile relative to the two legs predetermines the placement of the respective pivots in those legs and, thereof, the curvature characteristics of the particular truss element or truss structure. 
     With reference now to FIG. 9, trus structure 80 is indicated schematically as extending in a semicircular arch to provide thereby a semicylindrical vault. This figure is included herein primarily for the purpose of showing the arch-forming characteristics of truss structure 80 of FIG. 8 when viewed in a side elevation. The broken lines schematically illustrate the continuum formed when the overall truss structure is extended with additional basal elements similar to basal element 70 (FIG. 7). 
     The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive and the scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.