Application for forming a sheet structure from a foldable material

Abstract

The present invention supplies practical procedures, functions or techniques for folding tessellations. Several tessellation crease pattern techniques, and the three-dimensional folded configuration are given. Additionally several new forming processes, including mathematical methods for describing the material flow are disclosed doubly-periodic folding of materials that name the doubly-periodic folded (DPF) surface, including vertices, edges, and facets, at any stage of the folding. This information is necessary for designing tooling and forming equipment, for analyzing strength and deflections of the DPFs under a variety of conditions, for modeling the physical properties of DPF laminations and composite structures, for understanding the acoustic or other wave absorption/diffusion/reflection characteristics, and for analyzing and optimizing the structure of DPFs in any other physical situation. Fundamental methods and procedures for designing and generating DPF materials include ways for defining the tessellation crease patterns, the folding process, and the three-dimensional folded configuration. The ways are mathematically sound in that they can be extended to a theorem/proof format.

1 - 23 . (canceled) 
     
     
         24 . A folded material having at least two orthogonal planar cross sections, one of which corresponds to row cross-section (RCS) data and the other of which corresponds to column cross-section (CCS) data, and wherein at least one of the following are true:
 a) the RCS data corresponds to a wave pattern that is not a triangle wave, a hexagonal wave, a square wave, or a sinusoidal wave;   b) the CCS data corresponds to a wave pattern that is not a triangle wave, or a 4-, 6-, or 8-sided regular polygon; or   c) the wave pattern corresponding to the RCS data is a hexagonal wave or a square wave, and the wave pattern corresponding to the CCS data is not a triangle wave.   
     
     
         25 - 28 . (canceled) 
     
     
         29 . A method for providing a folded sheet structure, the method comprising:
 (a) obtaining a sequence of local isometries;   (b) selecting an initial zero-curvature surface;   (c) applying the sequence of local isometries to said initial surface to generate surface information that includes vertex and edge descriptions; and   (d) utilizing the surface information to generate or image a folded sheet structure in accordance with the surface information   
     
     
         30 . The method of  claim 29  wherein a composition of local isometries method is applied and a composition sequence is used to calculate a singular set of the folded sheet structure. 
     
     
         31 - 35 . (canceled) 
     
     
         36 . A method for forming a folded sheet structure from a foldable material, the folded sheet structure having column of edges in a tessellation (CET) data and row of edges in a tessellation (RET) defining a tessellation, the method comprising:
 a) utilizing the tessellation to generate a first die;   b) utilizing the tessellation to generate a second die; and   c) sandwiching a foldable material between the first die and the second die.   
     
     
         37 . The method of  claim 36  further comprising etching or marking at least some of the fold lines of the material before sandwiching the material between the first and second dies. 
     
     
         38 . The method of  claim 36  whereby the dies are articulated according to a uniform folding process.