Rigidly Foldable Quadrilateral Meshes From Angle Arrays

Abstract

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.

Topics in the mathematical design of materials

“…The mathematical understanding of RFFQM has progressed notably since the 1990s [28,29]. Algorithms are developed to parameterize the configuration space of RFFQM [30,31], which inspire new ideas on flat crease pattern design for the achievement of abundant shape-morphing capabilities with practical use in engineering.…”

Evolving, complex topography from combining centers of Gaussian curvature

“…A tiling usually differs from a single intersection in that it requires more global restrictions-we have to arrange different unit cells in a compatible way. In an origami community, the global restriction, called global compatibility, is the key idea to design tilings like rigidly and flat-foldable origami [32,33]. The global compatibility is automatically satisfied for symmetric patterns in Fig.…”

Making Light Work of Metal Bending: Laser Forming in Rapid Prototyping

“…Oftentimes, the desired structures need to be made of materials that have a non-negligible thickness [7,8]. Folding rigid materials is typically done by attaching rigid facets with compliant hinges [9], but this places restrictions on what can be produced, a term called rigid foldability [10]. One of the most common rigid folding patterns is the Miura-ora pattern (Figure 1a,b), as it allows large area structures to be compactly stored before deployment, which is valuable for space applications [5,7,11,12].…”