Abstract:
A linkage comprised of at least four links is provided. Each of the links has a polygonal profile with each link having at least two hinged axes that do not intersect one another. Each link is connected to at least two other links by the non-intersecting axes such that the linkage can smoothly transform from an extended surface into a compact bundle. The linkage can be constructed into the form of a foldable chair, a foldable table or a foldable wall.

Description:
BACKGROUND OF THE INVENTION 
     This application claims priority of provisional patent application No. 60,697,416, filed Jul. 8, 2005. 
    
    
     There are numerous inventions and discoveries relating to methods for folding sheets of material. Some of these methods relate to forming a three dimensional shape from a two dimensional sheet. Other methods take this a step further in that they provide for a folding and unfolding process that is smooth and continuous. One might term this second type “reversible origami”. 
     A critical inventive component of such methods are various tiling patterns that may be scored into sheets of material. One of the most famous of these patterns is “Miura-Ori” (“ori” being the Japanese term for folding)—named after its inventor Professor Koryo Miura, from Tokyo University. This particular pattern, consisting of a grid of parallelograms, allows for a sheet of material to be compacted down in two dimensions. 
     Also known in the art are various patterns including those disclosed in my own U.S. Pat. Nos. 5,234,727 and 4,981,732. These disclosures relate to novel shapes that may be developed from a sheet of material, which may then be smoothly folded down to compact bundles. 
     Such methods have numerous uses for foldable structures and products, including sails, tents, and novel packaging. 
     In general, these methods require sheets of material whose thickness is very minor when compared to their planar extent. To the degree that the sheet has a thickness of any significance, it is generally required that its material have flexibility and compressibility in order to allow folding to occur. 
     However, this requirement for flexibility results in significant limitations with regards to the provision of foldable forms requiring a high degree of structural rigidity. Applications that require rigidity include any large-scale structures, as well as products such as foldable furniture, boxes, or foldable dividers. 
     Accordingly, it would be desirable to provide foldable forms with a high degree of structural rigidity in which the sheets thereof can have significant thickness. 
     SUMMARY OF THE INVENTION 
     Generally speaking, in accordance with the invention, a method whereby a sheet of material of significant thickness and rigidity may be provided with a network of hinges that allow the assembly to smoothly fold down to a compact bundle, and then instantly open into an extended structurally rigid shape, is provided. 
     A critical innovation of the disclosed method is in the spatial arrangement of the hinges or “fold-lines”. In the earlier inventions referred to above, all hinges lie within the basic plane of the sheet. As the sheet folds in such inventions, the hinges take on a three-dimensional arrangement, whereby neighboring hinges have intersecting axes. 
     In the present invention, provision is made for hinges that lie in different planes, whereby their axes do not intersect and thus are offset relative to each other and to the basic plane of the structure. Such offsets allow for a thick sheet of material to fold down into a cubic bundle. 
     Further disclosed herein are various applications for this folding method, which include folding chairs, tables and self-supporting space dividers. 
     It will therefore be shown that objects and advantages of the invention will be found in the following description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a first link used in the inventive assembly; 
         FIG. 2  is an elevational view of the link of  FIG. 1 ; 
         FIG. 3  is a plan view of the link of  FIG. 1 ; 
         FIG. 4  is a second elevational view of the link of  FIG. 1 ; 
         FIG. 5  is an exploded view of a first embodiment of the inventive link assembly; 
         FIG. 6  is a perspective view of the inventive link assembly of  FIG. 4 ; 
         FIG. 7  is a perspective view of the link assembly of  FIG. 5  in a partially folded condition; 
         FIG. 8  is a perspective view of the link assembly of  FIG. 5  in a further folded condition; 
         FIG. 9  is a perspective view of the link assembly of  FIG. 5  in a fully folded condition; 
         FIG. 10  is a perspective view of a second embodiment of the inventive link assembly; 
         FIG. 11  is a perspective view of a third embodiment of the inventive link assembly; 
         FIG. 12  is a perspective view of the assembly of  FIG. 11  in a partially folded condition; 
         FIG. 13  is a perspective view of the assembly of  FIG. 11  in a further folded condition; 
         FIG. 14  is a perspective view of the assembly of  FIG. 11  in a completely folded condition; 
         FIG. 15  is a perspective view of a fourth embodiment of the inventive link assembly; 
         FIG. 16  is an elevational view of the link assembly of  FIG. 15 ; 
         FIG. 17  is a perspective view of a fifth embodiment of the inventive link assembly; 
         FIG. 18  is a perspective view of the link assembly of  FIG. 17  in a partially folded condition; 
         FIG. 19  is a perspective view of the link assembly of  FIG. 17  in a further folded condition; 
         FIG. 20  is a perspective view of the link assembly of  FIG. 17  in a completely folded condition; 
         FIG. 21  is a perspective view of a second link used in the inventive assembly; 
         FIG. 22  is an elevational view of the link of  FIG. 21 ; 
         FIG. 23  is a plan view of the link of  FIG. 21 ; 
         FIG. 24  is a perspective view of a third link superimposed over the link of  FIG. 21 ; 
         FIG. 25  is a detailed perspective view of the third link of  FIG. 24 ; 
         FIG. 26  is an elevational view of the link of  FIG. 25 ; 
         FIG. 27  is a plan view of the link of  FIG. 25 ; 
         FIG. 28  is a plan view of a sixth embodiment of the inventive link assembly; 
         FIG. 29  is a side elevational view of the link assembly of  FIG. 28 ; 
         FIG. 30  is a perspective view of the link assembly of  FIG. 28  in an unfolded condition; 
         FIG. 31  is a perspective view of the link assembly of  FIG. 28  in a partially folded condition; 
         FIG. 32  is a perspective view of the link assembly of  FIG. 28  in a further folded condition; 
         FIG. 33  is a perspective view of the link assembly of  FIG. 28  in yet a further folded condition; 
         FIG. 34  is a perspective view of the link assembly of  FIG. 28  in a fully folded condition; 
         FIG. 35  is a perspective view of a seventh embodiment of the inventive link assembly in a folded condition; 
         FIG. 36  is a perspective view of the link assembly of  FIG. 35  in a partially folded condition; 
         FIG. 37  is a perspective view of the link assembly of  FIG. 35  in an unfolded condition; 
         FIG. 38  is a perspective view of the link assembly of  FIG. 35  in a second alternative unfolded condition; 
         FIG. 39  is a perspective view of an eight embodiment of the inventive link assembly in a partially folded condition; 
         FIG. 40  is a perspective view of the link assembly of  FIG. 39  in a further folded condition; 
         FIG. 41  is a perspective view of a perspective view of the link assembly of  FIG. 39  in a completely folded condition; 
         FIG. 42  is a perspective view of a ninth embodiment of a link assembly made in accordance with the invention; 
         FIG. 43  is a perspective view of the link assembly of  FIG. 42  in a partially unfolded condition; 
         FIG. 44  is a perspective view of the link assembly of  FIG. 42  in a further unfolded condition; 
         FIG. 45  is a perspective view of the link assembly of  FIG. 42  in a still further unfolded condition; 
         FIG. 46  is a perspective view of the link assembly of  FIG. 42  in a fully unfolded condition; 
         FIG. 47  is a perspective view of a tenth embodiment of the inventive link assembly; 
         FIG. 48  is a perspective view of the embodiment of  FIG. 47  in a first folded condition; 
         FIG. 49  is a perspective view of the embodiment of  FIG. 47  in a second folded condition;  FIG. 50  is a perspective view of the embodiment of  FIG. 47  in a third folded condition; and  FIG. 51  is a perspective view of the embodiment of  FIG. 47  in a fully folded condition. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 1  shows a perspective view of a link  6  that is comprised of two planes  7  and  9 . Plane  7  has an axis  2  lying along one edge. Plane  9  has an axis  4  lying along one edge. Axes  2  and  4  do not intersect. 
       FIG. 2  shows link  6  in elevation view. Axis  2  forms an angle  3  relative to plane  9 . 
       FIG. 3  shows link  6  in plan view. Axis  4  forms an angle  5  relative to plane  7 . 
       FIG. 4  shows a second elevation view of link  6 . 
       FIG. 5  shows an exploded view of assembly  30  which is comprised of four links  6 ,  8 ,  14  and  20 . Link  6  has two non-intersecting axes  2  and  4 . Similarly, links  8 ,  14  and  20  have two non-intersecting axes each, respectively  10  and  12 ,  16  and  18 ,  22  and  24 . 
       FIG. 6  shows a perspective view of assembly  30 . Link  6  has been attached to link  8  by pivotally joining axes  2  and  10 . Likewise, link  8  has been attached to link  20  by pivotally joining axes  12  and  24 . In a similar manner, axes  22  and  16  join links  20  and  14 , while axes  18  and  4  join links  14  and  6 . 
     Axes  2 , 10  lies in a common plane with axes  16 , 22  and therefore these axes intersect each other. Likewise, axes  12 , 24  and  4 , 18  intersect each other. However, axes  2 , 10  and  16 , 22  do not intersect axes  12 , 24  nor do they intersect axes  4 , 18 . 
       FIG. 7  shows assembly  30  in a partially folded position. 
       FIG. 8  shows assembly  30  in a further folded position. The relationships of the respective axes with regards to whether they intersect is unchanged from that which is described in  FIG. 5 . 
       FIG. 9  shows assembly  30  in a fully folded position, wherein the four links  6 , 8 , 14  and  20  form a volumetric stack. The intersecting relationships between the axes remain unchanged. 
       FIG. 10  shows an assembly  60  which is comprised of four links  62 ,  64 ,  66  and  68  which are pivotally joined by axes  72 ,  74 ,  76  and  78  respectively. Links  62 ,  64 ,  66  and  68  are each comprised of two planes and each have two non-intersecting axes. Axes  74  and  78  lie in a common plane; likewise, axes  72  and  76  lie in a common plane. 
       FIG. 11  shows an assembly  80  which is comprised of four links  82 ,  84 ,  86  and  88  which are pivotally joined by axes  92 ,  94 ,  96  and  98  respectively. Links  82 ,  84 ,  86  and  88  are constructed as three dimensional volumes. The geometric relationship between axes  92 ,  94 ,  96  and  98  is identical to that shown between axes  72 ,  74 ,  76  and  78  as shown in  FIG. 10 . 
       FIG. 12  shows assembly  80  in a partially folded position.  FIG. 13  shows assembly  80  in a further folded position.  FIG. 14  shows assembly  80  in a fully folded position where links  82 ,  84 ,  86  and  88  are stacked into a cubic bundle. The relationships of axes  92 ,  94 ,  96  and  98  with regards to whether they intersect is unchanged throughout the folding process. 
       FIG. 15  shows a plan view of assembly  100  which is comprised of nine links  102 ,  104 ,  106 ,  112 ,  114 ,  116 ,  122 ,  124  and  126  that are joined together in a three-by-three grid arrangement. Each link is pivotally attached to its neighbors by axes that lie in various different planes. For example, link  102  is joined to link  112  by axis  107 . Likewise, link  114  is joined to link  116  by axis  115 . 
       FIG. 16  shows an elevation view of assembly  100 . Axes  107 ,  108 ,  109 ,  117 ,  118  and  119  are shown; all lie in different planes. 
       FIG. 17  shows a perspective view of assembly  100 . It may be seen that links  102 ,  104 ,  106 ,  112 ,  114 ,  116 ,  122 ,  124  and  126  form a common plane having significant thickness. Axes  103 ,  113  and  123  lie on one side of the common plane. Axes  105 ,  115  and  125  lie on the other side of the common plane. Axes  107 ,  108 ,  109 ,  117 ,  118  and  119  lie outside of the common plane. 
       FIGS. 18 and 19  show perspective views of assembly  100  as it is successively folded. 
       FIG. 20  shows assembly  100  in a fully folded state such that links  102 ,  104 ,  106 ,  112 ,  114 ,  116 ,  122 ,  124  and  126  form a cubic bundle. 
       FIG. 21  shows a perspective view of link  130  that is comprised of three planes  131 ,  133  and  135 . Also shown are four axes; axis  132  which borders plane  131 , axis  136  which borders plane  135 , and axes  138  and  134  which border plane  133 . Axes  132 ,  134 ,  136  and  138  are non-intersecting. 
       FIG. 22  shows an elevation view of link  130 . Axis  132  forms an angle  140  with plane  133 . Likewise, axis  136  forms an angle  142  with plane  133 . 
       FIG. 23  shows a plan view of link  130 . It may be seen that link  130  has an essentially square shape. Axis  138  forms a right angle  144  with plane  131 . Axis  136  forms a right angle  146  with plane  135 . 
       FIG. 24  shows a link  150  which is superimposed over link  130  which is shown in dashed line. Link  150  is constructed as a three dimensional volume whereas link  130  is shown as constructed of three thin planes. 
       FIG. 25  shows link  150  in more detail. Link  150  has four axes  152 ,  154 ,  156  and  158 . The geometric relationship between these non-intersecting axes is identical to axes  132 ,  134 ,  136  and  138  as shown in  FIG. 21 . 
       FIG. 26  shows an elevation view of link  150 .  FIG. 27  shows a plan view of link  150 . 
       FIG. 28  shows an elevation view of assembly  200  which is comprised of nine links  202 ,  204 ,  206 ,  212 ,  214 ,  216 ,  222 ,  224  and  226 . The links form a three-by-three grid of square shapes. They are each connected to their neighbors by various axes that lie in different planes. 
       FIG. 29  shows a second elevation view of assembly  200 . Four axes  205 ,  209 ,  213  and  215  are shown in this view, all of which lie outside the main plane defined by assembly  200 . 
       FIG. 30  shows a perspective view of assembly  200  in its unfolded state wherein it forms a flat plane. 
       FIG. 31  shows assembly  200  in a partially folded state. It may be seen that links  202 ,  212  and  222  continue to lie in a common plane. Links  204 ,  214  and  224  also lie in a common plane that forms an angle with the plane of the previous three links. Likewise, links  206 ,  216  and  226  lie in a common plane, also forming an angle with the previous two planes. 
     In  FIG. 32  assembly  200  has be further folded such that the three common planes formed respectively by  202 ,  212 ,  222  and  204 ,  214 ,  224  and  206 ,  216 ,  226  are stacked one over the other. 
       FIG. 33  shows assembly  200  in a further folded position such that the stacked links  202 ,  204  and  206  form an angle with stacked links  212 ,  214  and  216  which in turn form an angle with stacked links  222 ,  224  and  226 . It may be observed that axes  209  and  205  are co-axial relative to each other. Likewise, axes  213  and  215  are co-axial relative to each other. 
       FIG. 34  shows assembly  200  in a fully folded position such that the nine links  202 ,  204 ,  206 ,  212 ,  214 ,  216 ,  222 ,  224  and  226  are stacked one over the other. Thus, assembly  200  folds in a two-stage process with the first stage being illustrated by  FIGS. 30-32 , and the second stage being illustrated by  FIGS. 32-34 . 
       FIG. 35  shows an assembly  300  which is in a fully folded position. 
       FIG. 36  shows assembly  300  in a partially folded position. Assembly  300  is comprised of eighteen links arranged in three rows. The upper row is comprised of links  302 ,  312 ,  322 ,  332 ,  342  and  352 . The middle row is comprised of links  304 ,  314 ,  324 ,  334 ,  344  and  354 . The lower row is comprised of links  306 ,  316 ,  326 ,  336 ,  346  and  356 . Link  312  is connected to link  322  by hinge  313 . Links  312  and  322  are constrained to lie in a common plane because of the position of the assembly. Likewise, links  314  and  324  are constrained to lie in a common plane, and are connected each other by hinge  315 . Similarly, links  316 ,  326  and  332 ,  342  and  334 ,  344  and  336 ,  346  are connected by hinges  317 ,  333 ,  335  and  337  respectively and are constrained to lie in common planes relative to one another. 
       FIG. 37  shows assembly  300  in an unfolded position wherein all the links form a common plane. Hinges  313 ,  315  and  317  share a common axis in this position. Likewise, hinges  333 ,  335  and  337  share a common axis in the unfolded position. 
       FIG. 38  shows assembly  300  in a second alternative unfolded position where links  302 ,  304 ,  306 ,  312 ,  314  and  316  have been rotated along hinges  313 ,  315  and  317 . Additionally, links  342 ,  344 ,  346 ,  352 ,  354  and  356  have been rotated along hinges  333 ,  335  and  337 . In this way, assembly  300  becomes self-supporting and can be used as a divider or wall. 
       FIG. 39  shows an assembly  400  which is comprised of six links  402 ,  404 ,  406 ,  412 ,  414  and  416 . Link  402  is attached to link  412  by hinge  407 . Similarly, each link is attached to its neighboring links by hinges  403 ,  405 ,  408 ,  409 ,  413  and  415 . Assembly  400  is shown in a partially folded configuration so that the approximate shape of a chair is formed. 
       FIG. 40  shows assembly  400  in a partially folded position.  FIG. 41  shows assembly  400  in a fully folded position. 
       FIG. 42  shows an assembly  500  that is in a fully folded position and is comprised of four links  502 ,  504 ,  512  and  514  which are essentially stacked one over the other. In addition to these four links, there are frame elements  522  and  526 . Also shown in  FIG. 42  is hinge  520  which attaches links  502  and  512 . 
     In  FIG. 43 , assembly  500  is shown in a partially unfolded position such that links  504  and  512  lie along side of one another. Links  502  and  512  also lie along side each other in this position. 
       FIGS. 44 and 45  show assembly  500  in positions that are successively further unfolded. Frame elements  522 ,  524 ,  526  and  528  are seen to extend as links  502 ,  504 ,  512  and  514  are unfolded. 
       FIG. 46  shows assembly  500  in a fully unfolded position forming a stable and self-supporting chair. 
       FIG. 47  shows an assembly  600  that is comprised of six links  602 ,  604 ,  606 ,  612 ,  614  and  616  that form the surface of a table. 
       FIGS. 48-50  show assembly  600  as it appears in successively further folded positions. 
       FIG. 51  shows assembly  600  in a fully folded position forming a compact cubic bundle. 
     The scope of the invention will now be set forth in the following claims.