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 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.