Patterning technology for folded sheet structures

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 discloseddoubly-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 . A method for providing a pattern for folded sheet structures comprising: 
 (a) entering row and column data and an intersection point thereof into a computer program;    (b) calculating a doubly-periodic folded (DPF) surface pattern from the data entered in step (a);    (c) outputting the DPF surface pattern calculated in step (b) for folding a sheet structure according to said DPF surface pattern.    
   
   
       2 . The method according to  claim 1 , wherein step (c) includes outputting the DPF surface pattern to a folding machine.  
   
   
       3 . The method according to  claim 2 , wherein the folding machine receiving the output in step (c) is a casting machine.  
   
   
       4 . The method according to  claim 2 , wherein the folding machine receiving the output in step (c) is a cutting machine.  
   
   
       5 . The method according to  claim 4 , wherein the cutting machine is a milling machine.  
   
   
       6 . The method according to  claim 2 , wherein the folding machine receiving the output in step (c) is a stamping machine.  
   
   
       7 . The method according to  claim 1 , wherein the DPF surface pattern is output to a display.  
   
   
       8 . The method according to  claim 1 , wherein the DPF surface pattern is printed.  
   
   
       9 . The method according to  claim 2 , wherein the DPF surface pattern is output to a computer numerical control (CNC) machine.  
   
   
       10 . The method according to  claim 1 , wherein the row data entered in step (a) comprises a row of edges in a tessellation (RET).  
   
   
       11 . The method according to  claim 1 , wherein the row data entered in step (a) comprises a row cross section (RCS).  
   
   
       12 . The method according to  claim 1 , wherein the row data entered in step (a) comprises a row of edges (RED) of a folded sheet.  
   
   
       13 . The method according to  claim 10 , wherein the row of edges all have a same fold convexity and are coplanar.  
   
   
       14 . The method according to  claim 12 , the row of edges all have a same fold convexity and are coplanar.  
   
   
       15 . The method according to  claim 1 , wherein step (a) includes at least one vertex of the row data and column data.  
   
   
       16 . The method according to  claim 1 , wherein the row data entered in step (a) comprises incremental vectors in polar coordinates.  
   
   
       17 . The method according to  claim 1 , wherein the column data entered in step (a) comprises a column of edges in a tessellation, augmented to give relative amplitudes and spacing of successive rows of the tessellation (CET).  
   
   
       18 . The method according to  claim 10 , wherein the column data entered in step (a) comprises a column of edges in a tessellation, augmented to give relative amplitudes and spacing of successive rows of the tessellation (CET).  
   
   
       19 . The method according to  claim 12 , wherein the column data entered in step (a) comprises a column of edges in a tessellation, augmented to give relative amplitudes and spacing of successive rows of the tessellation (CET).  
   
   
       20 . The method according to  claim 17 , wherein the column of edges alternate sequentially in fold convexity and are coplanar in a vertically oriented plane.  
   
   
       21 . The method according to  claim 18 , wherein the column of edges alternate sequentially in fold convexity and are coplanar in a vertically oriented plane.  
   
   
       22 . The method according to  claim 19 , wherein the column of edges alternate sequentially in fold convexity and are coplanar in a vertically oriented plane.  
   
   
       23 . The method according to  claim 1 , wherein the column data entered in step (a) comprises a column-cross section (CCS).  
   
   
       24 . The method according to  claim 1 , wherein the column data.entered in step (a) comprises a column strip map.  
   
   
       25 . The method according to  claim 10 , wherein the column data entered in step (a) comprises a column-cross section (CCS).  
   
   
       26 . The method according to  claim 12 , wherein the column data entered in step (a) comprises a column strip map.  
   
   
       27 . The method according to  claim 1 , wherein the row data is entered in step (a) for a plurality of rows.  
   
   
       28 . The method according to  claim 1 , wherein the column data is entered in step (a) for a plurality of columns.  
   
   
       29 . The method according to  claim 27 , wherein steps (a) and (b) are repeated for each one of the plurality of rows, before step (c) is performed only once.  
   
   
       30 . The method according to  claim 28 , wherein steps (a) and (b) are repeated fore each one of the plurality of rows, before step (c) is performed only once.  
   
   
       31 . The method according to  claim 27 , wherein for each one of the plurality of rows, step (a), (b) and (c) are respectively performed.  
   
   
       32 . The mehtod according to  claim 28 , wherein for each one of the plurality of columns, steps (a), (b) and (c) are respectively performed.  
   
   
       33 . The method according to  claim 27 , wherein the DPF surface pattern step (b) includes at least one row of facets, said facets being connected in a row and column direction so that said at least one row of facets is bounded on either side by a row of edges, and the facets are connected successively across column edges.  
   
   
       34 . The method according to  claim 33 , wherein said at least one row of facets comprises a plurality of rows of facets, wherein a row-cross section being an intersection of a plane with a ruled surface, each one the rows of facets being a family of parallel line segments.  
   
   
       35 . The method according to  claim 28 , wherein the plurality of columns are parallel.  
   
   
       36 . The method according to  claim 1 , wherein the calculating of the DPF surface pattern begins with a general DPF pattern which is adjusted according to the row and column data from step (a).  
   
   
       37 . The method according to  claim 11 , wherein the RCS is based on three dimensions comprising x, y and z dimensions.  
   
   
       38 . The method according to  claim 12 , wherein the RED is based on three dimensions comprising x,y and z dimensions.  
   
   
       39 . The method according to  claim 37 , wherein the row data for the RCS is supplied on the XZ plane, and the column data is supplied on the YZ plane.  
   
   
       40 . The method according to  claim 38 , wherein the row data for the RED is supplied on the XZ plane, and the column data is supplied on the YZ plane.  
   
   
       41 . The method according to  claim 10 , wherein the RET is based on three dimensions comprising x,y and z dimensions.  
   
   
       42 . The method according to  claim 41 , wherein the row data for the RET is supplied on the XY plane, and the column data on the YZ plane.  
   
   
       43 . The method according to  claim 39 , wherein an axis of the X dimension is used as a reference line.  
   
   
       44 - 50 . (canceled)