Rigidly Foldable Quadrilateral Meshes From Angle Arrays

We present a design technique for generating rigidly foldable quadrilateral meshes (RFQMs), taking as input four arrays of direction angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforcing the fold-angle multiplier condition at each vertex, it is possible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree-of-freedom (DOF). Furthermore, the design technique is computationally simple, reducing for some cases to a simple linear-programming problem. The resulting mechanisms have applications in architectural facades, furniture design, and more.