One of the more computationally demanding tasks in a process of synthesizing “from scratch” origami crease patterns designed for a given purpose involve a simulation capability to track the progression of the folding process as the pattern folds. This work presents an approach to simulate origami folding based on bar frameworks. The work is related to joint frameworks and projected polyhedral, as they apply to folding. The analysis starts from a representation of a crease pattern as an undirected graph G(E,V) formed by edges E and vertices V. A framework G(p) is an instance of G where the vertex locations are assigned positions according to a vector valued function p(t), where t marks the folding progression and t=0 represents the initial, flat configuration. The strategy presented is based on finding a sequence of instances {p(1), p(2), …} corresponding to an analytic flex p, i.e., functions such that edges in all G(p(t)) have the same length. The method is based on using a finite element description of a bar framework corresponding to a truss-like structure congruent with G(p). Solutions to an eigenvalue problem associated with this structure provide the means to update from p(t) to p(t+1). Two simple (purely geometric) optimization problems adjust the update to compensate for higher order effects, guaranteeing that the length of the edges remain constant. The methodology can be used to achieve configurations close to “flat folding”, provided that no interference of the faces occurs along the way. We expected that physically-motivated constraints (stresses, deformations, etc.) and sensitivity analysis computations will be more easily represented in this framework and therefore this formulation will have an advantage over more standard “origami mathematics” approaches. The approach is illustrated with an example of folding a simple 10-crease pattern.
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ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 17–20, 2014
Buffalo, New York, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4637-7
PROCEEDINGS PAPER
Origami Folding and Bar Frameworks
Alejandro R. Diaz
Alejandro R. Diaz
Michigan State University, East Lansing, MI
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Alejandro R. Diaz
Michigan State University, East Lansing, MI
Paper No:
DETC2014-34149, V05BT08A031; 8 pages
Published Online:
January 13, 2015
Citation
Diaz, AR. "Origami Folding and Bar Frameworks." Proceedings of the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5B: 38th Mechanisms and Robotics Conference. Buffalo, New York, USA. August 17–20, 2014. V05BT08A031. ASME. https://doi.org/10.1115/DETC2014-34149
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