Rigid Origami Vertices: Conditions and Forcing Sets

We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way

Computational design of steady 3D dissection puzzles

Dissection puzzles require assembling a common set of pieces into multiple distinct forms. Existing works focus on creating 2D dissection puzzles that form primitive or naturalistic shapes. Unlike 2D dissection puzzles that could be supported on a tabletop surface, 3D dissection puzzles are preferable to be steady by themselves for each assembly form. In this work, we aim at computationally designing steady 3D dissection puzzles. We address this challenging problem with three key contributions. First, we take two voxelized shapes as inputs and dissect them into a common set of puzzle pieces, during which we allow slightly modifying the input shapes, preferably on their internal volume, to preserve the external appearance. Second, we formulate a formal model of generalized interlocking for connecting pieces into a steady assembly using both their geometric arrangements and friction. Third, we modify the geometry of each dissected puzzle piece based on the formal model such that each assembly form is steady accordingly. We demonstrate the effectiveness of our approach on a wide variety of shapes, compare it with the state-of-the-art on 2D and 3D examples, and fabricate some of our designed puzzles to validate their steadiness

Definición paramétrica de Estructuras Recíprocas Transformables con Nodos de tres barras

This article researches the determination of the equilibrium conditions of Variable Geometry Surfaces defined by Reciprocal Frame Structures by means of a study of the acting force field and the locus that describe the elements of these structures through the different states of transformation. It is established, through the development of a mathematic-parametric formulation, geometric and structural properties of an equal cylindrical three-bar Reciprocal Frame Node, with the objective of deducing the balance mechanism for obtaining the stabilization systems of Variable Geometry Surfaces made up of Transformable Reciprocal Frame Structures. The aim of this research is the application of the said stabilization system by means of a newly created structural-geometric software, to the design and calculation of different transformable geometry typologies of architectural surfacesEn este artículo, se aborda la determinación de las condiciones de equilibrio de Superficies de Geometría Variable definidas por Estructuras Recíprocas mediante el estudio de un campo de fuerzas actuantes y del lugar geométrico que describen los elementos de tales estructuras a través de los diferentes estados de transformación. Se establecen las propiedades geométricas y estructurales de un Nodo Recíproco de estas estructuras con tres barras cilíndricas iguales, mediante el desarrollo de una formulación matemático-paramétrica, con el objetivo de deducir el proceso de equilibrio para la obtención analítica de sistemas de estabilización de Superficies de Geometría Variable conformadas por Estructuras Recíprocas Transformables. La finalidad de la investigación presentada aquí es la aplicación de dicho sistema de estabilización mediante un software geométrico-estructural de nueva creación, al diseño y cálculo de distintas tipologías de superficies en la configuración de arquitecturas de geometría transformable

A New Approach To Expandable Structures: Crossed Expandable Frames (X-Frames)

The use of expandable structures in the field of building began in the 1960s, based on the pioneering work of Emilio Pérez Piñero. They underwent significant developments at the end of the 20th century, with typologies based on scissors or bundle modules. Until now, this typology has not been further enhanced, despite some very interesting contributions. These studies are usually based on straight bar expandable structures, although there are some interesting proposals based on the deployability of parallel arc systems, even in real buildings. However, other possible types of expandable structures have not been explored to date. In this paper, a new system for expandable structures is proposed, which opens new and interesting design possibilities based on the same folding principle. The system consists of deploying elements such as arches or frames with multiple intersections. Solutions for cylindrical vaults with horizontal axis joints and more complex geometries such as conoids are proposed, as well as domes with vertical and horizontal axis joints. Finally, other structures with special kinematic compatibility difficulties, such as concentric domes or toroids, are also studied.MINECO; BIA2016-79459-

Folding Flat Crease Patterns With Thick Materials

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flat-foldable crease patterns into new crease patterns with similar folded structure but with a facet-separated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local self-intersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.National Science Foundation (U.S.) (Origami Design for Integration of Self-assembling Systems for Engineering Innovation (ODISSEI Grant No. EFRI-1240383))National Science Foundation (U.S.) (NSF Expedition Grant No. CCF-1138967

ORIGAMI-SCISSOR Hinged Geometry Method

The diamond origami-scissor hinged pattern marks a new type of thick origami that can not only fold and unfold, but also expand and contract (project below). This was done by applying the ‘form generation method of relative ratios’ for two-bar scissors to the thick origami. This research tests whether this method can be extended and generalized to other types of origami. The origami-scissor hinged geometry method is here applied to the waterbomb of thick panels making a waterbomb origami-scissor hinged pattern. While the waterbomb origami of thick panels has one degree of freedom, the waterbomb origami-scissor hinged pattern has two degrees of freedom as it can independently fold and unfold as an origami, and expand and contract as a scissor hinged structure. This creates a new research branch of expandable thick origami. The ‘form generation method of relative ratios’ (FGMORR) [Rivas-Adrover 17] has been applied to the ‘origami of thick panels’ [Chen et al. 15] because this method to make thick origami can be extended and generalized to different types of origami, and therefore the origami-scissor hinged geometry method can also be applied to all these different types of origami. A critical condition is that the thick origami has to be made of equal or proportional thicknesses so that when translating that geometry with scissors the end nodes match. Another condition is that the pantographs that mark the creases and join different origami faces must have an equal morphology and bilateral symmetry. Automation of this method will be investigated with Grasshopper for Rhinoceros. Origami-scissor hinged patterns provide an extra degree of freedom, therefore origami patterns that could be folded can now also contract and occupy much smaller volumes. This would be useful in applications where a high ratio of deployed-to stowed volume is required such as space applications, earthbound transportable applications, and to create adaptable spaces and transformable environments in permanent architecture

Simulación aero acústica de un plano aeronáutico

En los últimos años el ruido producido por las aeronaves ha estado bajo mucho escrutinio debido al creciente número de aeropuertos y aerolíneas a nivel mundial. El ruido generado por las superficies de control y los sistemas sustentadores, es comparado con el ruido producido por los motores1. Un alerón es un punto de comienzo adecuado para estudiar y entender el fenómeno Aero acústico, debido a la sustentación adicional que este otorga y debido a su geometría simple. Los objetivos de este proyecto de grado están en simular Aero acústicamente un perfil NACA 0012 con un alerón tipo ala morphing, para así estudiar la influencia del alerón, para posteriormente validar estos resultados con un estudio experimental realizado por Thomas F. Brookes et al2, en el artículo “Aeroacoustics measurements in a wing-flap configuration”