Origami metamaterials : design, symmetries, and combinatorics
2018
In the first part of this thesis we study the geometry of
folding patterns. Specifically, we focus on crease patterns consisting
entirely of four-vertices; these are points where four fold lines come
together. A single four-vertex is the simplest example of a foldable crease
pattern that can be folded without bending the material in between the folds,
and has a remarkable property: despite its single degree of freedom, it has
two distinct folding motions. We make use of this property, and show how to
design arbitrarily large four-vertex crease patterns, which can fold into two
or more shapes. This is in contrast to other design methods, which produce
patterns that can only fold into one specific shape. In
the second part of this thesis, we study single four-vertices, and show a
robust method to obtain four-vertices with three energy minima, which
correspond to three different stable folded configurations. This too is in
contrast to other experimental methods, which can only generate bistable
vertices or patterns.
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