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Geometry Synthesis and Multi-Configuration Rigidity of Reconfigurable Structures


Dorn, Charles Jacob (2022) Geometry Synthesis and Multi-Configuration Rigidity of Reconfigurable Structures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ph2w-9a34.


Reconfigurable structures are structures that can change their shapes to change their functionalities. Origami-inspired folding offers a path to achieving shape changes that enables multi-functional structures in electronics, robotics, architecture and beyond. Folding structures with many kinematic degrees of freedom are appealing because they are capable of achieving drastic shape changes, but are consequently highly flexible and therefore challenging to implement as load-bearing engineering structures. This thesis presents two contributions with the aim of enabling folding structures with many degrees of freedom to be load-bearing engineering structures.

The first contribution is the synthesis of kirigami patterns capable of achieving multiple target surfaces. The inverse design problem of generating origami or kirigami patterns to achieve a single target shape has been extensively studied. However, the problem of designing a single fold pattern capable of achieving multiple target surfaces has received little attention. In this work, a constrained optimization framework is presented to generate kirigami fold patterns that can transform between several target surfaces with varying Gaussian curvature. The resulting fold patterns have many kinematic degrees of freedom to achieve these drastic geometric changes, complicating their use in the design of practical load-bearing structures.

To address this challenge, the second part of this thesis introduces the concept of multi-configuration rigidity as a means of achieving load-bearing capabilities in structures with multiple degrees of freedom. By embedding springs and unilateral constraints, multiple configurations are rigidly held due to the prestress between the springs and unilateral constraints. This results in a structure capable of rigidly supporting finite loads in multiple configurations so long as the loads do not exceed some threshold magnitude. A theoretical framework for rigidity due to embedded springs and unilateral constraints is developed, followed by a systematic method for designing springs to maximize the load-bearing capacity in a set of target configurations. An experimental study then validates theoretical predictions for a linkage structure. Together, the application of geometry synthesis and multi-configuration rigidity constitute a path towards engineering reconfigurable load-bearing structures.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:reconfigurable surface, origami, inverse design, rigidity, unilateral constraints
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Space Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pellegrino, Sergio
Thesis Committee:
  • Bhattacharya, Kaushik (chair)
  • Daraio, Chiara
  • Pellegrino, Sergio
  • Ravichandran, Guruswami
Defense Date:13 September 2021
Non-Caltech Author Email:charlesjdorn (AT)
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0566
Record Number:CaltechTHESIS:09182021-045958776
Persistent URL:
Dorn, Charles Jacob0000-0001-6516-2586
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14367
Deposited By: Charles Dorn
Deposited On:28 Sep 2021 15:59
Last Modified:04 Aug 2022 18:59

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