Fast Assembly of Curved Structures from Flat Configuration

Abstract

Imagine deploying an emergency shelter that transitions seamlessly from a flat configuration to a lifted structure, or a folded robot that is sent through a tunnel and subsequently activated to expand into a larger form at the endpoint, with a single, collective pull of strings. This scenario raises two critical questions: (i) how to decompose the structure into a flat state that encodes the 3D geometry, and (ii) where to place strings through the unit modules to achieve complete actuation. Although these questions have been explored individually, comprehensive solutions remain scarce. To address this challenge, this thesis presents a computational approach for designing freeform structures that can be rapidly assembled from initially flat configurations by a single string pull. Target structures are decomposed into rigid, spatially varied quad tiles optimized to approximate a user-provided surface, forming a flat mechanical linkage. A two-step algorithm is then applied to determine a physically realizable string path that controls only a subset of tiles, enabling smooth actuation from flat to assembled configuration. First, the minimal subset of tiles required for string control is computed by considering both the structure’s geometry and inter-tile interactions. Second, a valid string path is identified through these tiles that minimizes friction, thereby transforming the flat linkage into the target 3D form upon tightening a single string. The resulting designs can be manufactured in flat form using computational fabrication techniques: such as 3D printing, CNC milling, or molding, thereby simplifying both production and transportation. Validation is provided through a series of physical prototypes and application case studies, ranging from medical devices and space shelters to large-scale architectural installations.