Packaging of thick membranes using a multi-spiral folding approach: Flat and curved surfaces

Abstract

Elucidating versatile configurations of spiral folding, and investigating the deployment performance is of relevant interest to extend the applicability of deployable membranes towards large-scale and functional configurations. In this paper we propose new schemes to package flat and curved membranes of finite thickness by using multiple spirals, whose governing equations render folding lines by juxtaposing spirals and by accommodating membrane thickness. Our experiments using a set of topologically distinct flat and curved membranes deployed by tensile forces applied in the radial and circumferential directions have shown that (1) the multi-spiral approach with prismatic folding lines offered the improved deployment performance, and (2) the deployment of curved surfaces progresses rapidly within a finite load domain. Furthermore, we confirmed the high efficiency of membranes folded by multi-spiral patterns. From viewpoints of configuration and deployment performance, the multispiral approach is potential to extend the versatility and maneuverability of spiral folding mechanisms.

On a Class of Polar Log-Aesthetic Curves

“…In future work, we aim at studying the formulations for space curves and their real-world applications. Also, we aim at studying the formulation of compounded aesthetic curves in industrial design, path planning, and navigation systems, e.g., to assemble complex silhouettes and match a specific curvature profile in polar coordinates [36,37,38,17,14,30,27,28,29]. To the best of our knowledge, our closed-form characterizations are the first presented in the literature, whose use is potential to design aesthetic curves in CAD/CAE and planning problems.…”

“…In this paper we focus our attention on a class of curves defined by spirals, which are relevant for applications in efficient coverage path planning [7,8,3,9], folding membranes into compact structures [10,11,12,13,14], and to devise new interpolation patterns for metaheuristics [15,16], among many other applications. For instance, in [7], an archimedean spiral curve is used to generate spiral paths within a circle, and then the generated paths are analytically mapped to a bounding rectangle; and in [9], the archimedean spiral is deformed into a squircircle (a shape intermediary between a circle and a square) for efficient coverage planning.…”

“…Furthermore, in [8], an archimedean-like formulation is used to sample path points for coverage, whose configuration is filtered and optimized. Generally speaking spiralbased paths (robotics) and spiral-based folding configurations (membranes applications) are desirable due to the fact of avoiding frequent or aggressive changes in acceleration, allowing the smooth deployment of mobile robots [9,17] and membrane structures [10,11,12,13,14].…”

Wrapping Deployment Simulation Analysis of Leaf-Inspired Membrane Structures

“…Guang and Yang [23] identified the different geometrical characteristics of this kind of origami along this study line. Multiple spirals were used by Parque et al [24] to form a new pattern to deploy flat and curved membranes with small thicknesses. Apart from these conceptual studies, wrapping membrane structures were investigated with the aid of physical models.…”

Solar sail with superconducting circular current-carrying wire

“…The deployment is usually performed by uniaxial mechanisms, such as a telescopic boom, the extendable masts, the deployable booms, the inflatable booms, the centrifugal force that renders a spin-type deployment mechanism (See Refs. [19][20][21][22] and references therein). We cite these works, but the recent literature on the subject is not limited by them.…”