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Unfolding: From Digital to Physical



In this assignment the aim was to construct a powercopy (the same process that was shown in a previous post [http://dtbyemad.blogspot.com/2013/10/powercopy-debugged.html]) that unfolds from a three dimensional geometry to a two dimensional plane that could be fabricated afterwards. The process is a straight forward approach, but it requires deeper understanding of geometry. The constraints of geometry - especially in unfolding operations -  must be clear from the start. To be able to unfold, the surface of the geometry  has to be a developable surface or ruled surface (explained in http://dtbyemad.blogspot.com/2013/10/developable-geometry.html). What follows the unfolding operation is fabrication; the unfolded surface is then laser cut using "museum paper". The paper after it has be cut and etched, it is then assembled in the same sequencing as the digital model. An additional benefit of using powercopies in this project is that, when a single cell is manipulated the unfolded planes correspond, and that is showed below.


Image 1: the process of unfolding starts with the framework, the layout where the powercopy will be generated. The framework is constrained and includes on both sides control handles to manipulate the form. 


Image 2: after the framework is done the layout for the unfolded parts is set, and this can be seen in the image (the dots on the right).


Image 3: in this image the powercopy is created, and this is the initial cell that will help in generating the rest. 


Image 4: this is a close up of the powercopy, and as mentioned previously, the cell includes geometry and surfaces that are ruled to help in the unfolding process (developable surfaces could be used also, but not included in this assignment). 


Image 5: is an image of the overall assembly. Notice the geometrical difference between the cells, and that is one of the advantages of using the powercopy; the cell reconfigures its form based on its location on the framework. 


Image 6: shows the response of the cells to the manipulation of the framework.



Image 7: is the start of the unfolding process, notice that the geometry is flattened on a plane for the fabrication process. The challenge was to define which of the joints between the surfaces that will be used to cut (separated). And this understanding of how geometry is connected helps in avoiding any overlaps between the surfaces when flattened. 


Image 8: Image shows all of the cells flattened into position corresponding to the powercopies on the framework. 


Image 9: shows the response of the unfolded geometry in relation to the changes in the cells. 


Image 10: After the the unfolding of the geometry is complete, the layout is exported to Rhino. In Rhino, each unfolded cell is assigned to a layer; this helps the laser cuter to understand the inputs and to distinguish between the edges to cut and the edges to etch. 



Image 11: Shows a close up of the cell. The deference between the cut and etched edges are clear and defined by the level of darkness of the contours. 


Image 12: the cells are removed from the paper sheet and then folded. Each cell is places in its location on the sheet to be assembled in order. 


Image 13: shows the final folded model of the assembly. What can be noticed is that, the model is warping and mirrored. Both of these issues are better understood in small scale models (physical), as a way to understand the gaps between the translation of geometry between the digital and physical environments. 






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Location: A. Alfred Taubman College of Architecture and Urban Planning, University of Michigan - North Campus, 2000 Bonisteel Boulevard, Ann Arbor, MI 48109, USA

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