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Conditions for Rigid and Flat Foldability of Degree-n Vertices in Origami
Journal article

Conditions for Rigid and Flat Foldability of Degree-n Vertices in Origami

  • Zimmermann, Luca Engineering Design and Computing Laboratory, ETH Zürich, Tannenstrasse 3, Zürich 8092, Switzerland
  • Shea, Kristina Engineering Design and Computing Laboratory, ETH Zürich, Tannenstrasse 3, Zürich 8092, Switzerland
  • Stanković, Tino Engineering Design and Computing Laboratory, ETH Zürich, Tannenstrasse 3, Zürich 8092, Switzerland
  • 2019-10-31
Published in:
  • Journal of Mechanisms and Robotics. - ASME International. - 2019, vol. 12, no. 1
Mechanical Engineering
English Abstract
In rigid origami, the complex folding motion arises from the rotation of strictly rigid faces around crease lines that represent perfect revolute joints. The rigid folding motion of an origami crease pattern is collectively determined by the kinematics of its individual vertices. Establishing a kinematic model and determining the conditions for the rigid foldability of a single vertex is thus important to exploit rigid origami in engineering design tasks. Today, there exists neither an efficient kinematic model to determine the unknown dihedral angles nor an intrinsic condition for the rigid foldability of arbitrarily complex vertices of degree n. In this paper, we present the principle of three units (PTU) that provides an efficient approach to modeling the kinematics of single degree-n vertices. The PTU is based on the notion that the kinematics of a vertex is determined by the behavior of a single underlying spherical triangle. The condition for the existence of this triangle leads to the condition for the rigid and flat foldability of degree-n vertices. These findings are transferred from single vertices to crease patterns, resulting in a simple rule to generate kinematically determinate crease patterns that can be designed to fold rigidly. Finally, we discuss the limitations of the PTU with respect to the global rigid foldability of a crease pattern.
Language
  • English
Open access status
closed
Identifiers
Persistent URL
https://folia.unifr.ch/global/documents/202631
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