A Unified Framework for Kinematic Simulation of Rigid Foldable Structures

TL;DR

This paper introduces an automated, unified framework for kinematic analysis of rigid foldable structures inspired by origami, capable of handling complex configurations with minimal manual effort.

Contribution

It develops a general method to generate the Pfaffian constraint matrix for arbitrary RFS, integrating loop constraints through a novel graph-based and screw theory approach.

Findings

Successfully models diverse RFS deploy and fold motions

Eliminates manual, error-prone constraint calculations

Provides a visual tool for motion analysis

Abstract

Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a general method that consolidates their loop constraints has been lacking. We present an automated approach that generates the Pfaffian constraint matrix for arbitrary rigid foldable structures (RFS). From a minimally extended data schema, the tool constructs the facet-hinge graph, extracts a minimum cycle basis that captures all constraints, and assembles a velocity-level constraint matrix via screw theory that encodes coupled rotation and translation loop closure. The framework computes and visualizes deploy and fold motions across diverse RFS while eliminating tedious and error-prone constraint calculations.