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You are an expert at summarizing long articles. Proceed to summarize the following text: 
BACKGROUND OF THE INVENTION 
       [0001]    Arches have been known for centuries to provide a stable means for spanning a space in a manner capable of supporting significant weight. The curved structure defining the arch eliminates, or at least significantly reduces, tensile stresses over a span thereof by substantially resolving the forces into compressive stresses. Generally, an arch structure is made from materials such as masonry, metal and concrete. 
       SUMMARY OF THE INVENTION 
       [0002]    The invention concerns an arch structure comprised of adjacent segments that are rotatably attached to each other. In particular, the invention concerns an arch structure comprised of at least two segments in which adjacent segments are linked to each other via hinges or equivalent means to form a continuous bendable chain of attached segments, and adjacent segments rotate relative to each other about an axis. The segments have magnets above the hinge or equivalent means on opposed end faces, positioned to oppose magnets on confronting end faces of adjacent arch segments, with like poles facing one another, thereby creating a repulsion force. The repulsion force inhibits the arch segments from being brought together. Due to this effect, the aggregate of the arch segments define an arcuate path (convex upward), maintained by the repulsion forces of the magnets. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0003]      FIG. 1  is a side view of a first exemplary embodiment of an arch structure according to the present invention; 
           [0004]      FIG. 1   a  is a side view of an alternative exemplary embodiment wherein end segments are immovably attached to horizontal abutments; 
           [0005]      FIG. 1   b  is a side view of an alternative exemplary embodiment wherein end segments are rotatably attached to abutments via hinges or equivalent means and the abutments are rotatably attached to a support surface via hinges or equivalent means (support surface not shown); 
           [0006]      FIG. 1   c  is a side view of an alternative exemplary embodiment wherein end segments are rotatably attached to horizontal abutments; 
           [0007]      FIG. 1   d  is a side view of the alternative exemplary embodiment of  FIG. 1   b  illustrating the rotation of the abutments and the segments due to load forces on the arch structure; 
           [0008]      FIG. 1   e  is a side view of the alternative exemplary embodiment of  FIG. 1   c  illustrating the rotation of the abutments and the segments due to load forces on the arch structure; 
           [0009]      FIG. 2  is a top view of two segments from the exemplary embodiment shown in  FIG. 1 ; 
           [0010]      FIG. 2   a  is a top view of two segments from the exemplary embodiment shown in  FIG. 1  with an alternative magnet arrangement to prevent “over-arching”; 
           [0011]      FIG. 3  is a side view of an alternative embodiment of an arch structure according to the present invention wherein each segment is comprised of an upper part and a lower part; 
           [0012]      FIG. 4  is a cross-section view of the alternative embodiment of the arch structure of  FIG. 3 ; 
           [0013]      FIG. 5  is a top view of a portion of two segments from the alternative embodiment of the arch structure of  FIG. 3  illustrating the interleaving of segment transition teeth between adjacent segments; 
           [0014]      FIGS. 6   a  and  6   b  are side views of two segments at differing angles from the alternative embodiment of the arch structure of  FIG. 3  illustrating how the segment transition teeth between adjacent segments maintain a relatively smooth continuous surface as the angle between segments changes; 
           [0015]      FIG. 7  is a side view of another alternative embodiment of an arch structure according to the present invention wherein adjacent segments are connected by a segment support structure; 
           [0016]      FIG. 8  is a side view of an end portion of an arch structure according to another alternative exemplary embodiment of the present invention wherein the end segment is connected to a sub-road surface mechanism comprised of a flat bed with wheels and a flat support surface; 
           [0017]      FIG. 9  is a top view of a portion of the end segment of  FIG. 8  illustrating how the end segment passes through a road; 
           [0018]      FIG. 10  is a side view of an end portion of an arch structure according to another alternative exemplary embodiment of the present invention wherein the end segment is connected to a sub-road surface mechanism comprised of a flat bed with wheels and a flat support surface and a transition portion of the road is supported by a rolling support above the end segment; 
           [0019]      FIG. 11  is a side view of an end portion of an arch structure according to another alternative exemplary embodiment of the present invention wherein the end segment is connected to a sub-road surface mechanism comprised of a flat bed with wheels and a curved support surface. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0020]      FIG. 1  is a side view of a first exemplary embodiment of the invention. The arch structure  1 , as shown in  FIG. 1 , is comprised of several segments  2 , although there may be as few as two segments  2 . The segments  2  have top and bottom surfaces as well as ends, which generally face ends of adjacent segments  2 , and sides. Although the exemplary embodiment shown has segments with flat top and bottom surfaces, it should be understood that these surfaces could be concave, convex, stepped or any other shape. The segments  2  may be made of any material of suitable strength to carry the load that will be placed upon them. For example, the segments  2  may be made of wood, PVC, steel or concrete. Adjacent segments  2  are connected to each other with a hinge  3  that is secured to the bottom surface of the segments  2  by hinge plates  6  that are rotatably attached by a barrel and pin structure  7 . Alternatively, the segments  2  may be connected with ball joints or equivalent structure. The segments  2  may also be connected to each other by their ends or sides by a hinge or equivalent structure. 
         [0021]    On the ends of adjacent segments  2 , which face each other, there are magnets  5  with opposing polarities, which force the segments  2  to remain apart. The magnets  5  may be neodymium magnets, which have a strong magnetic field and are comparatively light-weight. The magnets  5  may also be electromagnets, which are provided electric power when one wants the arch structure to maintain an arch shape. Other types of magnets known in the art may be used for the magnets  5  on the segments  2 , and the magnets  5  may be a combination of different types of magnets. The magnets  5  may be mounted to the segments  2  with an intervening low permeability material. 
         [0022]    The load the arch structure  1  will be required to support before the segments  2  come into contact with each other will determine the number, strength and shape of magnets used. The force between the magnets  5  on the segments may be calculated using Ampère&#39;s law of force or may be empirically determined by measuring the repulsive force between two segments when brought within an operational distance and angle that will be experienced by the segments  2  in the arch structure  1 . It is understood by one in the art that other mechanical repelling means such as springs or a pneumatic or hydraulic system, may be used as an alternative to or in conjunction with the magnets  5 , to provide the repelling force between the segments  2 . 
         [0023]    The end segments  2   y  and  2   z  at the ends of the arch structure  1  are attached to abutments  4 . The abutments  4  may be immovably or rotatably attached by end hinges  32 - 38  to the end segments  2   y  and  2   z,  as illustrated in  FIGS. 1 and 1   b , respectively. Furthermore, the abutments  4  may be stationary, as illustrated in  FIG. 1 . Alternatively, the abutments  4 , may be rotatably attached to the ground or other support structure by abutment hinges  40 - 42 , as illustrated in  FIG. 1   b  and  1   d , in order to accommodate changes in the arch structure  1  length, due to changes in the load on the arch structure  1 . The abutments  4  or the abutment hinges  40 - 42  may be configured as disclosed in Japanese patent JP 2005-188022, which is hereby incorporated by reference. It should be noted, though, that the abutments  4  rotate independently in  FIGS. 1   b  and  1   d  in contrast to the tension legs ( 5 ) in JP 2005-188022, which must rotate in the same direction to the same angle. It should also be noted that the end segments  2   y  and  2   z  may be rotatably attached to the abutments  4  whether or not the abutments  4  are rotatably attached to the ground. In  FIG. 1   b , the abutments  4  are shown with no rotation, and in  FIG. 1   d , the abutments  4  are shown rotated in an outward direction and the angles between the segments  2  are reduced. 
         [0024]    As shown in  FIG. 1   a , the end segments  2   y  and  2   z  may be immovably attached to horizontal abutments  104 . The horizontal abutments  104  may be a road, path or simply the ground. Preferably the end segments  2   y  and  2   z  are attached to the horizontal abutments  104  in a manner that provides a relatively smooth and continuous surface between the end segments  2   y  and  2   z  and the horizontal abutments  104 . Alternatively, as shown in  FIGS. 1   c  and  1   e  the end segments  2   y  and  2   z  may be rotatably attached to the horizontal abutment  104  attached by end hinges  32 . In this case, the horizontal abutment  104  may be provided with a transitional surface such as a ramp (not shown) to provide a relatively smooth and continuous surface between the end segments  2   y  and  2   z  and the horizontal abutments  104 . 
         [0025]      FIG. 2  is a top view of a portion of the first exemplary embodiment of the arch structure  1 . The ends of the segments  2  above the hinges  3  have teeth-like projections  8  extending from each segment  2  such that the teeth-like projections  8  fit together in such a manner as to accommodate the gap between the segments  2  and are shaped in such a manner as to provide a relatively continuous surface as the angle and distance of the gap between the segments  2  vary. On the ends of each projection  8  is a magnet  5  whose polarity is opposite to a parallel magnet  5  on the end of the adjacent segment  2 . In the exemplary embodiment of the invention shown in  FIG. 2 , a first set of magnets  5   a,    5   b  &amp;  5   c  on one end of a first segment  2   a  are configured with opposite polarities to a second set of magnets  5   d,    5   e  &amp;  5   f  on one end of a second segment  2   b,  although other polarity configurations may be used. 
         [0026]    As shown in  FIG. 2   a,  according to one alternative embodiment of the invention, the magnets  5  located on the projections  8  are configured, sized and shaped so that those located on adjacent segments develop a repelling force between them that resists any force separating the segments  2  from each other. In the exemplary embodiment shown in  FIG. 2   a,  magnets  5   a  and  5   c  on segment  2   a  develop a repelling force with magnet  5   e  on segment  2   b.  The repelling force between the magnets  5  on the projections  8  prevents the structure from “over-arching” i.e. prevents the gap between segments  2  from going beyond a certain distance. This may be useful in certain instances such as when a gust of wind applies an upward force on the bottom surface of the segments  5 . It may be understood by one in the art that prevention of “over-arching” may also be accomplished by other structures such as springs or projections from the segments that come into communication with each other when the segments are a predetermined distance apart. These alternative structures may be used alone or in conjunction with the magnets to prevent “over-arching.” 
         [0027]    As illustrated in  FIGS. 3 and 4 , the segments  2  may be comprised of an upper part  50  and a lower part  52  that are structurally connected at or by their sides. Magnets  5  with opposing polarities are attached to ends of the upper parts  50  of the segments  2 , which face each other. Adjacent segments  2  are connected to each other on the lower parts  52  with the hinge  3  secured to the bottom surface of the segments  2  by hinge plates  6  that are rotatably attached by a barrel and pin structure  7 . Alternatively, the segments  2  may be connected with ball joints or equivalent structure. The segments  2  may also be connected to each other by their ends or sides by a hinge or equivalent structure. 
         [0028]    Projecting out from the ends of the segments  2  are several segment transition teeth  62  whose upper surfaces are initially aligned with an upper surface of the lower part  52  and curve in a downward direction. As is illustrated in  FIG. 5 , the segment transition teeth  62  of adjacent segments  2  are interleaved. As is illustrated in  FIG. 6   a  and  6   b,  the segment transition teeth  62  are so shaped and configured so as to provide as smooth and continuous a surface as is practicable between the upper surfaces of the lower parts  52  as the segments  2  rotate relative to each other. 
         [0029]    In  FIG. 7 , another alternative exemplary embodiment of the invention is illustrated. Segment support structures  80  are connected to the bottom or side surfaces of the segments  2  and may only be extant by the sides of the segments  2  or they may span the entire width underneath the segments  2 . Adjacent segment support structures  80  are connected to each other with a barrel and pin structure  7 . On the ends of adjacent segment support structures  80 , which face each other, are the magnets  5  with opposing polarities, which force the segments  2  to remain apart. The magnets  5  may be disposed horizontally underneath the segments  2  in a manner similar to that discussed by previous embodiments of the arch structure. Alternatively, or in addition, the magnets  5  may be disposed vertically along the ends of the segment support structures  80  or magnets  5  may be disposed on the upper part  50 . 
         [0030]    As discussed above, the end segments  2   y  and  2   z  may be attached to the abutments  4 . Alternatively, the end segments  2   y  and  2   z  may be attached to a sub-road surface mechanism  40  below a road  22  leading on to the arch structure  1 . The sub-road surface mechanism  40  may be any arrangement that provides substantially vertical support for the arch structure  1  and allows for substantially, possibly limited, horizontal movement for the arch structure  1 . As illustrated in  FIG. 8  for one end of an exemplary embodiment of the arch structure  1 , the end segment  2   z  is attached to the sub-road surface mechanism  40  comprised of a flat bed with wheels  42  and a support surface  44  along which the flat bed  42  may move. The flat bed  42  may be comprised of one or more electric generators with crankshafts that are mechanically connected to the flat bed wheels, for example via a cam shaft, to harness the axial movement of the wheels. Electricity may thereby be generated from the movement of the arch structure  1 . 
         [0031]    The portion of the end segment  2   z  that intersects with the road  22  may be formed, as illustrated in  FIG. 9 , of closely spaced spokes  26  that penetrate corresponding road apertures  24  in the road  22 . Alternatively, as illustrated in  FIG. 10 , a transition portion  60  of the road  22  may be supported above the end segment  2   z  by a rolling support  64  and connected to the road  22  by a hinge  62 . The rolling support  64  has a suspension system for rolling support wheels  66  to adjust to the changing angles of the end segment  2   z.    
         [0032]    The support surface  44  may be flat and horizontal, as illustrated in  FIG. 8 . Alternatively, the support surface  44  may be variably angled to provide a resistance force that increases or decreases as an increasing load forces the arch structure  1  to spread. One such alternative support surface  44  is illustrated in  FIG. 11 . 
         [0033]    The embodiments of the invention described herein are exemplary in nature, and therefore, the spirit and the scope of the invention are by no means restricted to what is described above or intended to represent every possible embodiment of the invention.

Summary:
This invention concerns an arch structure. In particular, the invention relates to an arch structure comprised of at least two segments which are rotatably linked to each other via hinges or equivalent means to form a continuous bendable chain of attached segments. The segments have magnets above the rotatable or hinged link on opposed end faces, positioned to oppose magnets on confronting end faces of adjacent arch segments, with like poles facing one another, thereby creating a repulsion force. The repulsion force inhibits the arch segments from being brought together and into contact. Due to this effect, the aggregate of the arch segments define an arcuate path (convex upward), maintained by the repulsion forces of the magnets.