Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.1K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.1K
Unsymmetric Bending01:18

Unsymmetric Bending

680
Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
680
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

255
When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
255
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

726
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
726
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.8K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
8.8K
Torsion of Noncircular Members01:16

Torsion of Noncircular Members

391
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
391

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Dynamic drives allow independent control of material bits for targeted memory.

Science advances·2026
Same author

Pivoting colloidal assemblies exhibit mechanical metamaterial behaviour.

Nature·2026
Same author

Aging of amorphous materials under cyclic strain.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Hysteretic slit-snapping and multistability in buckled beams with partial cuts.

Science advances·2026
Same author

Dynamic Avalanches: Rate-Controlled Switching and Race Conditions.

Physical review letters·2025
Same author

Using Optical Tweezers to Simultaneously Trap, Charge, and Measure the Charge of a Microparticle in Air.

Physical review letters·2025

Related Experiment Video

Updated: Dec 5, 2025

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
14:52

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

9.2K

Non-Euclidean origami.

Scott Waitukaitis1, Peter Dieleman1, Martin van Hecke1

  • 1Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.

Physical Review. E
|October 20, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces non-Euclidean 4-vertices for origami, overcoming limitations of traditional Euclidean vertices. These new vertices enable more stable and versatile folding designs, preventing misfolding in applications like origami inverters.

More Related Videos

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

22.1K
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
10:23

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

12.0K

Related Experiment Videos

Last Updated: Dec 5, 2025

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
14:52

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

9.2K
Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

22.1K
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
10:23

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

12.0K

Area of Science:

  • Mechanics
  • Materials Science
  • Robotics

Background:

  • Traditional origami relies on Euclidean vertices, which have inherent limitations in folding motion and are prone to misfolding.
  • These limitations restrict the complexity and reliability of origami-based structures and mechanisms.

Purpose of the Study:

  • To introduce and analyze non-Euclidean 4-vertices as a solution to the limitations of Euclidean vertices in origami.
  • To demonstrate how these non-Euclidean vertices enhance folding stability and enable multistability.
  • To design and realize practical origami applications, such as a misfolding-free inverter and a tristable vertex.

Main Methods:

  • Theoretical analysis of non-Euclidean 4-vertex geometry and folding mechanics.
  • Incorporation of hinge elasticity into the vertex model to explore multistability.
  • Design and physical realization of an origami inverter and a tristable vertex based on the new vertex design.

Main Results:

  • Non-Euclidean 4-vertices overcome the degeneracy and misfolding issues associated with Euclidean vertices.
  • The elasticity of hinges in non-Euclidean 4-vertices leads to higher-order multistability.
  • A functional origami inverter that avoids misfolding and a physically realized tristable vertex were successfully demonstrated.

Conclusions:

  • Non-Euclidean 4-vertices offer significant advantages over traditional Euclidean vertices for advanced origami applications.
  • This work paves the way for more robust, stable, and complex origami designs in fields like robotics and deployable structures.
  • The developed vertex design enables precise control over folding states and enhances the reliability of origami mechanisms.