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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Christian Santangelo

Subject Categories

Geometry and Topology | Statistical, Nonlinear, and Soft Matter Physics


Linkages and mechanisms are pervasive in physics and engineering as models for a
variety of structures and systems, from jamming to biomechanics. With the increase
in physical realizations of discrete shape-changing materials, such as metamaterials,
programmable materials, and self-actuating structures, an increased understanding
of mechanisms and how they can be designed is crucial. At a basic level, linkages
or mechanisms can be understood to be rigid bars connected at pivots around which
they can rotate freely. We will have a particular focus on origami-like materials, an
extension to linkages with the added constraint of faces. Self-actuated versions typ-
ically start flat and when exposed to an external stimulus - such as a temperature
change or magnetic field - spontaneously fold. Since these structures fold all at once,
and the number of folding patterns accessible to a given origami are exponential, they
are prone to folding to a configuration other than the desired one. Other work has
suggested methods for avoiding this misfolding, but it assumes ideal, rigid origami. Here, we expand on these models to account for the elasticity of real structures and
introduce methods for accounting for Gaussian curvature in them. We also explore
how to find and set an upper bound on minimal forcing sets, or the minimum set of
folds required to force an origami, and present a graph theory algorithm for finding
them in arbitrary origami. Taken altogether, these origami studies give insight into
how the physical properties of origami influence folding and a new set of tools for
avoiding misfolding. Next, we turn back to a more fundamental study of linkages
and present a new method for finding the manifold of their critical points. We then
demonstrate a design protocol that utilizes this manifold to create linkages with tun-
able motions, before turning to several example structures, including the four-bar
linkage and the Kane-Lubensky chain.


Creative Commons License

Creative Commons Attribution-Share Alike 4.0 License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.