Edge-Compositions of 3D Surfaces

Origami-based design methods enable complex devices to be fabricated quickly in plane and then folded into their final 3D shapes. So far, these folded structures have been designed manually. This paper presents a geometric approach to automatic composition of folded surfaces, which will allow existing designs to be combined and complex functionality to be produced with minimal human input. We show that given two surfaces in 3D and their 2D unfoldings, a surface consisting of the two originals joined along an arbitrary edge can always be achieved by connecting the two original unfoldings with some additional linking material, and we provide a polynomial-time algorithm to generate this composite unfolding. The algorithm is verified using various surfaces, as well as a walking and gripping robot design.

[1]  Kang Hao Cheong,et al.  Designing crease patterns for polyhedra by composing right frusta , 2012, Comput. Aided Des..

[2]  Jun Mitani,et al.  A Design Method for Axisymmetric Curved Origami with Triangular Prism , 2011 .

[3]  G. Whitesides,et al.  Foldable Printed Circuit Boards on Paper Substrates , 2010 .

[4]  David Avis,et al.  A Linear Algorithm for Finding the Convex Hull of a Simple Polygon , 1979, Inf. Process. Lett..

[5]  R. J. Wood,et al.  An Origami-Inspired Approach to Worm Robots , 2013, IEEE/ASME Transactions on Mechatronics.

[6]  Erik D. Demaine,et al.  Geometric folding algorithms - linkages, origami, polyhedra , 2007 .

[7]  David W. Currier Automation of Sheet Metal Design and Manufacturing , 1980, 17th Design Automation Conference.

[8]  Avraham A. Melkman,et al.  On-Line Construction of the Convex Hull of a Simple Polyline , 1987, Inf. Process. Lett..

[9]  Tomohiro Tachi,et al.  Origamizing Polyhedral Surfaces , 2010, IEEE Transactions on Visualization and Computer Graphics.

[10]  Robert J. Wood,et al.  Robot self-assembly by folding: A printed inchworm robot , 2013, 2013 IEEE International Conference on Robotics and Automation.

[11]  H Tanaka,et al.  Programmable matter by folding , 2010, Proceedings of the National Academy of Sciences.

[12]  Henry Ericsson Theis Handbook of Metalforming Processes , 1999 .

[13]  Erik D. Demaine,et al.  JOINING UNFOLDINGS OF 3-D SURFACES , 2013 .

[14]  Carlo H. Séquin,et al.  Synthesis of bent sheet metal parts from design features , 1999, SMA '99.

[15]  Matthew I. Campbell,et al.  An Approach to Automate Concept Generation of Sheet Metal Parts Based on Manufacturing Operations , 2008, DAC 2008.

[16]  Cheng-Hua Wang Manufacturability-Driven Decomposition of Sheet Metal Products , 1997 .

[17]  J. O'Rourke,et al.  Geometric Folding Algorithms: Linkages , 2007 .

[18]  Ronald S. Fearing,et al.  RoACH: An autonomous 2.4g crawling hexapod robot , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Jun Mitani,et al.  A Design Method for 3D Origami Based on Rotational Sweep , 2009 .

[20]  David Eppstein,et al.  Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions , 1998, SCG '98.

[21]  Franz Aurenhammer,et al.  A Novel Type of Skeleton for Polygons , 1995, J. Univers. Comput. Sci..

[22]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[23]  David Eppstein,et al.  Ununfoldable polyhedra with convex faces , 1999, Comput. Geom..

[24]  Tomohiro Tachi,et al.  3D Origami Design based on Tucking Molecule , 2008 .

[25]  Jay Patel,et al.  An Approach to Automate and Optimize Concept Generation of Sheet Metal Parts by Topological and Parametric Decoupling , 2010 .

[26]  J. P. Whitney,et al.  Pop-up book MEMS , 2011 .

[27]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[28]  H. Okuzaki,et al.  A biomorphic origami actuator fabricated by folding a conducting paper , 2008 .

[29]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.