Transformable Surface Mechanisms by Assembly of Geodesic Grid Mechanisms

The scissors-like grid shells composed of members bent in the out-of-plane direction have structural advantages: the ease of deployment as a one-degree-of-freedom system and the stability as it is modeled as a shell once the scissors’ transformation is fixed. However, it is impossible to generate a freeform doubly curved surface from a single grid while maintaining the geodesics. In this paper, we propose an approach based on assembling multiple units of grid systems to obtain a variety of transformable surfaces.We first provide a geometric model of bending active scissors system along the geodesics by interpreting the structures as surfaces that change the intrinsic metric according to the scissors’ transformation. Then, we clarify the compatibility conditions between multiple patches and show approaches for designing patterns that satisfy compatibility. Based on the model, we show a simulation of surface transformation using a bar-and-hinge model. In particular, we propose a method for inversely generating a mechanism that deploys to a given target surface.