## Pi Mu Epsilon Conference - April 14-15, 2023

#### Event Title

Rigid Origami and No-hands Folding

#### Location

Pellegrene Auditorium, Saint John’s University

#### Event Website

https://www.csbsju.edu/mathematics/pi-mu-epsilon-conference/conference-details

#### Start Date

15-4-2023 10:30 AM

#### Description

As mentioned in the first talk, origami has enjoyed increased attention in math and science over the past 10 years. One aspect that has especially blossomed is rigid origami, where we insist that the origami model can be smoothly folded and unfolded with the faces of paper between the creases remaining flat (or rigid, as if they were made of metal or wood). Engineers especially like rigid origami as a way to design interesting mechanisms that work at large scales (think solar panel arrays) and tiny scales (think folded capsules and stents in the human body).

To actuate a rigid origami mechanism without the aid of human hands, we apply driving forces to the crease lines, such as with springs. We say these driving forces make the origami model self-fold. In doing this we often confront a problem where it is not possible to predict the way the springs will make the model fold from the unfolded state. In this talk we will develop a mathematical model of self-folding and describe how to design a driving force such that a given crease pattern will uniquely self-fold to a desired mode without getting caught in a bifurcation. We'll use linear algebra to find necessary conditions for self-foldability and see how it works on actual examples. This is joint work with Tomohiro Tachi (University of Tokyo), my students at Western New England University, and was partially supported by NSF grants EFRI-1240441 and DMS-1906202.

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Apr 15th, 10:30 AM

Rigid Origami and No-hands Folding

Pellegrene Auditorium, Saint John’s University

As mentioned in the first talk, origami has enjoyed increased attention in math and science over the past 10 years. One aspect that has especially blossomed is rigid origami, where we insist that the origami model can be smoothly folded and unfolded with the faces of paper between the creases remaining flat (or rigid, as if they were made of metal or wood). Engineers especially like rigid origami as a way to design interesting mechanisms that work at large scales (think solar panel arrays) and tiny scales (think folded capsules and stents in the human body).

To actuate a rigid origami mechanism without the aid of human hands, we apply driving forces to the crease lines, such as with springs. We say these driving forces make the origami model self-fold. In doing this we often confront a problem where it is not possible to predict the way the springs will make the model fold from the unfolded state. In this talk we will develop a mathematical model of self-folding and describe how to design a driving force such that a given crease pattern will uniquely self-fold to a desired mode without getting caught in a bifurcation. We'll use linear algebra to find necessary conditions for self-foldability and see how it works on actual examples. This is joint work with Tomohiro Tachi (University of Tokyo), my students at Western New England University, and was partially supported by NSF grants EFRI-1240441 and DMS-1906202.

https://digitalcommons.csbsju.edu/math_pi_mu_epsilon/2023/keynote/1