Folding Simulation of Rigid Origami with Lagrange Multiplier Method

TL;DR

This paper introduces a novel method combining loop closure constraints with Lagrange multipliers to simulate the sequential folding of rigid origami with multiple degrees of freedom, including elastic effects.

Contribution

It develops a new algorithm for modeling complex origami folding sequences and equilibrium states with rotational springs, advancing origami simulation techniques.

Findings

Successfully simulates sequential folding processes.

Accurately finds equilibrium configurations with elastic energy.

Validates the method with multiple origami examples.

Abstract

Origami crease patterns are folding paths that transform flat sheets into spatial objects. Origami patterns with a single degree of freedom (DOF) have creases that fold simultaneously. More often, several substeps are required to sequentially fold origami of multiple DOFs, and at each substep some creases fold and the rest remain fixed. In this study, we combine the loop closure constraint with Lagrange multiplier method to account for the sequential folding of rigid origami of multiple DOFs, by controlling the rotation of different sets of creases during successive substeps. This strategy is also applicable to model origami-inspired devices, where creases may be equipped with rotational springs and the folding process involves elastic energy. Several examples are presented to verify the proposed algorithms in tracing the sequential folding process as well as searching the equilibrium configurations of origami with rotational springs.