A unified framework for kinematic simulation of rigid-foldable structures

Abstract

Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a generalized pipeline that systematically translates their geometric definitions into mathematical loop-closure constraints has been lacking. We present an automated approach that constructs the Pfaffian constraint matrix directly from pattern-level geometric data for a broad class of rigid-foldable structures (RFSs). From a minimally extended data schema, the tool first constructs the facet–hinge graph and extracts a minimum cycle basis to capture all constraints. Subsequently, it employs screw theory to assemble a velocity-level constraint matrix, which encodes coupled rotation-translation loop closure. The framework computes and visualizes deployment and folding motions across diverse RFSs, while eliminating tedious, error-prone constraint calculations.