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Three-Dimensionality in Reciprocal Structures: Concepts and Generative Rules
Abstract
Reciprocal systems based on superimposition joints, i.e. where un-notched bars sits on the top or in the bottom of each other, could be regarded as being intrinsically three-dimensional because of their natural out-of plane development. This paper presents seven of these three-dimensional configurations, conceived and
built by the students of the Master of Science in ‘‘Architectural Design’’ at Aalborg University. They have been developed as an integral part of a 2-week workshop, organized and run by the authors during the fall semester 2011. Since physical models are instruments that trigger the exploration of new typologies because of the direct interaction they provide with the designer the students were called to deal with the issue of three-dimensionality in reciprocal systems through scale models and actual scale prototypes.
... 8 The result of this specific organization is that the geometry is not easy to control and predict. 1,3,[9][10][11][12][13][14] The specific organization of beams inside moduli, as well as the one of moduli next to other moduli, induces a cyclic arrangement that makes also the analytical calculation of internal forces complicated. Several methods have been developed to determine or approach internal forces, [15][16][17] but reciprocal structures can nevertheless be easily calculated by a classical FEM approach, and even commercial softwares. ...
... According to (9), the total volume of the floor subjected to a total external load F is equal to: ...
Building with raw timber allows to reduce the price of construction and to make it more competitive with respect to concrete or steel construction. For a few years now, the combination of parametric design and robotic tools make possible the fast and precise milling of timber logs for their accurate connection. However, the spans are quickly limited by the logs length. In this context, reciprocal structures are relevant, since they allow to build large spans structures with short beams. Finally, the architectural interest of reciprocal structures is not to prove. However, the choice of the most efficient reciprocal frame, as well as its structural relevance in terms of mass and stiffness is, most of the time, ruled by subjective considerations. This paper focuses on rectangular floors composed of reciprocal moduli and has three objectives: (1) to develop a general mass and stiffness optimization method for reciprocal floors, which is not only necessary to limit the price, but also to reduce their thickness, (2) to define design rules for reciprocal floors, in particular for the choice of the best engagement ratio, and (3) to compare the structural efficiency of reciprocal floors with the one of “traditional” floors with parallel logs. Coming from a dimensionless transformation of the equilibrium equations, the results of this article will thus give the designers keys to better design reciprocal structures, evaluate their structural performances and relevance, and justify their choices.
... This consists of temporary works that are fully reusable, fitting very well with the current tendencies for sustainable architecture or bioconstruction. The scientific literature contains several examples of three-dimensional reciprocal constructions which express this resurgence (12)(13)(14)(15)(16). Another advantage of this type of structure is that prefabricated parts can be used, with simple or complex geometry, which are easy to assemble on-site (17). ...
The elements in conventional structures are perfectly ranked, so that load transmission is logical and follows the usual structural orders. Nevertheless, in reciprocal structures each element has to support all of the others in a less intuitive pattern of load transmission. The purpose of this paper is to understand exactly how load is transmitted between elements, quantifying this analytically by developing a new method which is applicable to a flat structure composed of a basic unit with any number of nexors. It is based on determining the increase in load to which the members in a reciprocal structure are subjected by calculating the coefficient k, or “transference coefficient”. The k coefficient value, and therefore the load transferred between members, falls with the number of nexors, with the proximity of point loads to exterior supports, and with the size of the central space in the structure.
... Among the first studies on reciprocal structures, works by John Chilton [21,22], Olga Popovic Larsen [23,7], Olivier Baverel [24] and their collaborators stand out. The preferences of these researchers and their leading followers, such as Dario Parigi, Alberto Pugnale and Paul Kirkegaard [25,26] primarily concern nonplanar reciprocal structures, which distinguishes them from the interests of researchers from previous centuries. ...
The article concerns structural grillages made of short reciprocally supported beams. The history of reciprocal structures, as well as origin of the renewed interest in them have been characterised in the introductory part of the article. The main part presents the methodology of forming the grillages from short beams and the results of a static analysis. It has aimed at comparing the values of maximum bending moments and deflections of the grillages, due to the load acting perpendicular to the plane of the grillage. The first series of tests has included the grillages differing in the beams configuration, which supported the identical square slab. The second series has included the grillages of analogous configuration, but supporting the square slabs of different sizes. The results prove that the configuration of the beams does not have a significant impact on the values of bending moments and deflections, which are mainly determined by the overall dimensions of the grillage. The conclusion is that configuration of grillage based on reciprocity of beams let to replace rigid joints with articulated ones, which does not affect the load-bearing capacity and facilitates construction of the grillage.
... Another framing system that emerged in the logic of overlapping is the structure system called "reciprocal" and "nexorades" in the international literature (Geno et al., 2022;Baverel, 2000). The most basic principle of this structural system is that the short elements in the space to be covered provide strength by transferring loads to each other (Parigi and Pugnale, 2014). In this structure, which is generally used in the roof cover function, planes with different curvatures are formed. ...
Interior Architecture education is an educational discipline in which the experience-based learning that takes place in studios is at the center of the design concept. In this paper, it is planned to experience the basic design principles and elements that are required to be understood in the basic design course within the interior architecture education process, and to contribute to awakening and stimulating the minds of the students for various inventions thorugh raising awareness of nature-based learning. As a result of the pilot study designed for this purpose, an application-based flowchart is presented as a model for designing new patterns for basic design courses. In the creation of the model, the concept of pattern is researched in different disciplines within a broad framework in line with the principles of consistency and inclusiveness. The stages of creating the model include the stages of analyzing the pattern systematics based on abstraction in interior architecture basic education and reconstructing the systematic in a way that will increase the capacity to be used in the creation of new patterns. In line with these stages, it is aimed to define basic design elements such as point, line, plane, volume and basic design principles such as contrast, emphasis, repetition, balance, and rhythm in the formation principles of natural elements, and to systematize the same principles strategically to be used in the shaping of design patterns.
... The etymology of 'reciprocal' is from the Latin word 'reciprocus' while recus means backward, procous means forwards. Therefore, reciprocity means back and forth, providing an exchange for mutual benefit [1]. ...
This study aims to develop missing geometric knowledge for demountable reciprocal frames (RF). While designing a demountable RF, one should know the initial, in-process and final form of the RF. These processes require some specific geometric knowledge. There are some deficiencies about geometric properties in the previous studies about demountable RFs. In this study, the positions and the orientations of the nexors are found by using the Denavit-Hartenberg parameters. This information gives where the joints are placed, how they are oriented and take position according to one another. Besides, the influence of engagement length on the fan height and the base edge are analyzed. Thereby one will be able to find out how much space the RF covers with the known base edge. With the geometric knowledge obtained from this study, demountable RFs having different engagement lengths can be produced with the same nexors.
... The etymology of 'reciprocal' is from the Latin word 'reciprocus' while recus means backward, procous means forwards. Reciprocity is, therefore, meaning that back and forth, providing an exchange for mutual benefit (Parigi and Pugnale, 2014). ...
Reciprocal Frame (RF) is a three-dimensional grillage structure that consists of mutually supported elements. In RF, whatever the composition that is built, the geometry should always have two members that are connected at a time. Moreover, at least three members should be connected to create a grid, but there is no limit for the maximum. In the research that has been done until today, the geometry of RF, form-finding issues, connections, structural behavior, fabrication methods were studied, but there is very limited number of studies about kinetic RF. In this study RF structures for single loop 3-, 4-, and 5-nexor configurations are analyzed in terms of their motion capabilities. The kinematic diagrams are drawn and their mobilities are calculated. Zero, single, and multi Degrees of Freedom (DoF) configurations are obtained. It has been found that the configurations with revolute joint series get minimum value and also it is not necessary to use as many joints as possible or joints with as many DoF as possible in the configuration to get maximum mobility value.
... The etymology of 'reciprocal' is from the Latin word 'reciprocus' while recus means backward, procous means forwards. Reciprocity is, therefore, meaning that back and forth, offering the return of behaviors (being support and be supported) which provides a mutual benefit (Parigi and Pugnale, 2014). ...
Reciprocal Frame (RF) is a three-dimensional grillage structure that consists of mutually supported elements. In RF, whatever the composition that is built, the geometry should always have two members that are connected at a time. Moreover, at least three members should be connected to create a grid, but there is no limit for the maximum. In the research that has been done until today, the geometry of RF, form-finding issues, connections, structural behavior, fabrication methods were studied, but there is very limited number of studies about kinetic RF. In this study RF structures for single loop 3-, 4-, and 5-nexor configurations are analyzed in terms of their motion capabilities. The kinematic diagrams are drawn and their mobilities are calculated. Zero, single, and multi Degrees of Freedom (DoF) configurations are obtained. It has been found that the configurations with revolute joint series get minimum value and also it is not necessary to use as many joints as possible or joints with as many DoF as possible in the configuration to get maximum mobility value.
... In other words, the position of each beam determines, and is at the same time determined not only by the position of the immediately adjacent beams, but also by all the beams of the structure [7]. The result of this specific organization is that the shape of a reciprocal structure is neither easy to control or predict [12]. During the last two decades, many researchers [2,[13][14][15][16][17][18] focused on different algorithms of form-finding to explore the The complexity may not only lie in the form finding of the structures, but also in the specific connections between the beams, which could all be different. ...
To decrease the impact of the construction sector on climate change, sufficiently economic processes must urgently be developed to encourage the use of minorly transformed timber, such as tree trunks. However, the question remains how to inexpensively incorporate tree trunks with irregular morphology into structural systems from design to fabrication. It is only within recent years that robotic tools and parametric design software have made it possible to both quickly and affordably build with elements of geometry as variable as tree trunks. The objective of this article is to describe an automatic process, from parametric design to robotic fabrication, that makes it possible to build a full-scale structure from reshaped tree trunks. This research brings to light the scientific and technical challenges that must be undertaken before industrialization can be realized, therefore the geometric parametrization required of trunk-to-trunk connections is detailed herein. Finally, the authors describe a case study from design to fabrication of a full-scale 10 m × 5 m reciprocal structure prototype made from fourteen tree trunk elements fabricated as described above using robotic arms. It is seen that reciprocal structures can span large distances with logs of limited length, but their structural complexity brings additional challenges to the design and construction processes. This study highlights not only the need for future development to accelerate the processes of automatic scanning and cutting of timber logs, but also for mechanical characterization of logs using non-destructive methods and better prediction of transmission of stresses in wood-wood assemblies.
... Por otro lado, el empleo de un material eficiente como la madera está muy alineado con las nuevas tendencias en arquitectura sostenible. Aparecen así, en la bibliografía científica, varios ejemplos de construcciones recíprocas tridimensionales que demuestran este nuevo renacer (3)(4)(5)(6)(7). ...
During the last decades reciprocal structures have found a new purpose linked to the execution of temporary and recyclable projects in relation with current trends in sustainable architecture. The objective of this work is to analyze the behaviour of
timber bridges with reciprocal structure. A numerical model was made and the structural behavior of a traditional Chinese bridge and Leonardo's removable bridge were compared. The model was verified by measuring the deformation of a real bridge built in a workshop. In addition to the mechanical behavior, the load transmission mechanism, the influence of friction, lateral stability and robustness were studied. The Chinese bridge works mainly in compression, getting closer to the behavior of a funicular arch and transmitting a horizontal load on the supports around three times greater than the Leonardo bridge. The latter works fundamentally on bending and subjected to stresses and deformations closer to its ultimate limits.
... Porém, ainda é necessário aplicar o conceito desenvolvido em outras geometrias, com nexors curvos, uma vez que a geometria da conexão deve ser determinada com base na geração da estrutura com auxílio de métodos de form-finding. O artigo apresentado porParigi et al. (2014) apresenta uma proposta de conexão, sendo uma extensão dos estudos de Pellegrino e Calladine sobre um tipo específico de articulação para a montagem de ERs. Apesar dos resultados iniciais positivos sobre a avaliação do número de articulações internas e externas, ainda é "[...] necessário trabalhos adicionais para completar as especificações de todas as possíveis condições de restrições, como a inclusão de articulações deslizantes [...]"(PARIGI et al., 2014, p. 58, tradução nossa).Os principais tópicos que sintetizam esta lacuna são:(a) dificuldade em prever o comportamento estrutural das conexões e de realizar análises precisas em cada uma; e (b) em geral, as conexões são resolvidas depois do processo de geração das ERs, sem aproveitar a oportunidade de utilizá-las como um dos parâmetros iniciais do projeto. ...
Estruturas recíprocas (ERs) são datadas do período neolítico, produzidas originalmente em madeira e compostas por elementos de dimensões reduzidas. Trata-se de um sistema estrutural que apresenta a capacidade de se adaptar a formas livres, complexas e com grande potencial estético, como indicado por diversas pesquisas contemporâneas. No entanto, acredita-se que essas estruturas poderiam fazer melhor uso das tecnologias digitais disponíveis de projeto, análises, fabricação e montagem. Este artigo tem o objetivo de identificar as atuais lacunas em que se pode concentrar esforços de pesquisa no sentido de tornar a tecnologia das ERs mais viável. Foi feita uma revisão sistemática da literatura (RSL) em sete bases de dados diferentes. Encontrou-se um total de 180 artigos, dos quais 49 foram selecionados para análise. Dentre eles, 27 identificaram lacunas existentes, que foram compiladas em cinco categorias: (a) dificuldades na concepção geométrica/estrutural; (b) necessidade de aprimoramento de ferramentas digitais; (c) dificuldade no projeto, análise, fabricação e montagem de conexões; (d) dificuldade de compreensão da real contribuição dos protótipos para aplicações em grande escala; e (e) necessidade de incorporar o processo de montagem no projeto de ERs. Foi possível concluir que o desenvolvimento de novos mecanismos de análise estrutural aliados à criação de novos detalhes construtivos pode contribuir para a expansão do uso das ERs.
... Douthe and Baverel (2009) compared the structural behavior of reciprocal domes with conventional triangular grid structures and addressed the design process of these structures using "dynamic relaxation" in 2014. Parigi (2013) compared the behavior of two-and three-dimensional reciprocal frames to study the impact of geometric parameters on the distribution of internal forces [6]. Besides, Parigi and Sassone (2011) conducted research on pinned connections to fabricate movable reciprocal frame structures [7]. ...
... The minimum number of component in this basic module is only three bars (Fig. 2). Based on that basic module, Parigi et al. (2014) further developed seven advanced modules which they called as bug, matrix, neural network, monkey saddle, hypar, star frame, and wave. The difference between those morphologies are mainly the results of the parametric relationship between bar configuration, bar composition, bar dimension, and bar slope angle. ...
There are several statements mentioning the possibilities of combining reciprocal and tensegrity structure. One of those is called reciprocal-tension (rection). This research was aimed to propose rection as a new structural system that also differs from both reciprocal and tensegrity. It defined rection structure and its characteristic, basic configuration and structural behaviour. Three simulations were conducted to test the hypothesis using dynamic relaxation method. The result showed that rection structure had the characteristics of (1) bar under bending stress, that do not touch each other, that hangs to each other reciprocally, and (2) self-equilibrated and pre-stressed system for enough rigidity. The research also concluded that the basic configurations of rection structure consist of upward fan reciprocal and positive double curvature configuration. Structural analysis also had been done on a 1:1 scale experiment and dynamic relaxation simulation.
... The minimum number of component in this basic module is only three bars (Fig. 2). Based on that basic module, Parigi et al. (2014) further developed seven advanced modules which they called as bug, matrix, neural network, monkey saddle, hypar, star frame, and wave. The difference between those morphologies are mainly the results of the parametric relationship between bar configuration, bar composition, bar dimension, and bar slope angle. ...
Bamboo applications become popular recently by the community due to the rise of environmental awareness, including for post-disaster building. Two aspects of post-disaster buildings were considered: i.e. its performance and its recyclabil-ity. This research explore ability of bamboo as tensile structure, and also as knock-down structure. Bamboo radial compression (barcom) connection was explored by these aspects. Barcom joint is one of the solutions to be effectively used for gaining the tensile strength of bamboo by converting tensile load parallel to fiber into radial compression perpendicular to fiber. Barcom joint was tested to acquire its load capacity and its future improvement. The load test showed that the barcom connection could reach up to 21.61 kN. To improve this capacity, either better wire or special washer design could be proposed. The adaption in previous built structure (i.e. Three Mountain Building in Serangan island, Bali and knock-down bamboo geodesic dome in Colombia) was used as a case-study. In the construction of Three Mountain Building, barcom joint was used to hang the bamboo rafters and acts as tension-like member. Meanwhile, the use of barcom joint in Colombia was intended to connect the bamboo with the steel bowl connector which could be dismantled and reused again many times.
... The five categories explained above are entirely based on physical prototyping rather than computational modeling, nevertheless it is a valuable classification of these systems based on their configurational behavior, and a good starting point for computational modelling and form finding. The change from configurations with 1D elements to 2D and 3D elements effects both the form finding process as well as the structural behavior of these systems, which requires a different simulation and form finding process in each case [2,11]. ...
ABSTRACT
In this research a computational method is developed to study the form-finding process of non-standard reciprocal systems with 2D elements based on the current methods on the morphology of reciprocal systems with 1D elements. The developed form-finding methods will be used in a performance based form exploration process for geometrical and structural performance enhancement. The proposed computational framework will explore new potentials for variations in the assembly design of these systems through the introduction of new geometric parameters both at the component level and the assembly level within the form exploration process. The proposed method integrates parametric assembly design with structural analysis in a stochastic optimization process to explore the design space while minimizing the total weight of the structure. The results of the form exploration process will be stored for the post processing phase in which the solution space is explored to study the variation of the emerging assemblies. In this paper the proposed method is explained and implemented via two case studies towards the further exploration of the concept.
... Some isolated cases seem to appear more by chance than by any systematic analysis with different geometries and settings. There also exist very interesting exceptions, such as the works of Baverel and Pugnale (2014) and others (Kohlhammer and Kotnik 2011;Parigi and Pugnale 2014;Sánchez et al. 2010). ...
Reciprocal structures are constructed by using a wide variety of patterns. These designs are a good source of inspiration when working with laminar constructions (sheets). Using the same formal schemes, laminar constructions feature better bending of their elements along the shape of the model and the application of extra pressure on the connection joints. Many of the geometric constructions made at the University of the Basque Country and presented in this paper show structural, constructive and formal improvements in many reciprocal structures assembled using sheets instead of linear elements.
... In a few cases, reciprocal systems grow in space without belonging to the previous categories; these can be considered as full 3D spatial structures. A design workshop on this topic was organized at Aalborg University in 2011, and the results are described in (Parigi and Pugnale 2014). It should be underlined that assemblies of reciprocal fans can be obtained from regular polyhedra too. ...
The concept of transferring forces in a reciprocal way has always been related to the use of timber beams, that is, elongated elements. However, planar components can also be considered; circular tiles, squares, triangles and more articulated or irregular geometrical shapes are all valid alternatives. This report proposes an initial exploration of reciprocal systems based on planar elements in order to guide further morphological studies. It also presents some prototypes, which were developed by the students of the Ecole des Ponts in Paris during two design workshops run in 2012 and 2013.
Due to their non-hierarchical nature, the geometry of reciprocal assemblies cannot be described conveniently with the available CAD modelling tools or by hierarchical, associative parametric modellers. The geometry of a network of reciprocally connected elements is a characteristic that emerges, bottom-up, from the complex interaction between all the elements’ shape, topology and position, and requires numerical solution of the elements’ geometric compatibility. A computational method, the “Reciprocalizer”, has been developed by the authors to predict and control the geometry of large networks of reciprocally connected elements, and it has been now perfected and included in a larger procedure that can be regarded as an extremely flexible and capable design tool for the generation of free-form reciprocal structures. The design tool has been applied for the design and realization of a free-form structure composed of 506 round, un-notched wooden elements with a diameter of 22 mm. This paper focuses on the geometry of reciprocal systems and the unique issues of fabrication posed by such assemblies.
This paper discusses teaching of technical subjects in architecture, presenting two experimental activities, recently organized at Aalborg University -a two week long workshop and a one day long lecture. From the pedagogical point of view, the activities are strategically placed between conventional disciplinary courses and architectural design studios. On the one hand, this allows a better mix of theoretical lectures, exercises and design practice; on the other hand, narrow topic related to structural design may be deepened on the basis of a research-based approach to design.
The objective of this paper is to discuss the generation of configurations of nexorades using genetic algorithm. The process of genetic algorithm allows one to create a nexorade from an initial simple configuration. An important application of nexorades is for shelters of various sizes and shapes for temporary or permanent purposes.
The objective of this paper is to propose a simple method using dynamic relaxation algorithm to find the form and perform a structural analysis of reciprocal frame systems, also called nexorades. After a brief historical note, details of the parameters that govern the design of nexorades are introduced together with details of the assembly. These parameters induce strong geometrical constrains on this kind of structures so that a form-finding step is required. It is suggested here to introduce a fictitious mechanical behaviour to solve this problem. The dynamic relaxation algorithm is used with a model that takes into account the eccentricity between the elements. Its implementation is explained and its versatility is illustrated through several examples covering various fields of applications going from form-finding problems to non-linear structural analysis of structures. In a last example the structural behaviour of nexorades is compared with more conventional triangulated structures.
In 1989 I made a drawing of a net on a cube, consisting of 12 lines/elements. They were connected in a way that, a couple
of months later, I recognised them in 899v in Leonardo’s Codex Atlanticus. I don’t know which moment impressed me the most: my own discovery of a very simple and powerful connecting system or the
discovery of the Leonardo drawings, which implied that my own discovery was in fact a rediscovery. What we see in Leonardo’s
drawings are some examples of roof constructions built with a lot of straight elements. These drawings can be ‘translated’
into the following definition: On each element we define four points at some distance of each other – two points somewhere
in the middle and two points closer to the ends. To make constructions with these elements we need only connect a middle point
of one element to an end point of another one in a regular over-under pattern. Out of the simple definition of the elements,
I designed many different patterns for my so-called “+ - - +” structures: domes, spheres, cylinders and other models were
made.
p. 1895-1906 Spatial Reciprocal Frames (S.R.F) are three dimensional structures created with beams that hold each other up through simple support bindings. The construction principle is antique in origin and citations to its use have been found in the manuscripts of medieval treatise writers, such as Villard de Honnecourt, and in the documents of renaissance architects including those of Sebastiano Serlio and Leonardo da Vinci's Atlantic Code. This building concept allows the dismantling of the framework and its subsequent reassembly into different forms. Moreover, these geometrical and functional flexibilities consent the S.R.F. to meet ecological building standards of environmental regulations. The irregular arrangement of their modular support points and their ability to be dismantled make them suitable even in unusual situations; for example, to provide the covering an exposition pavilion as well as archaeological field with a temporary roof. Their use today appears to present particular interest for the planning of temporary buildings that can be dismantled and their materials recuperated. What is more, they hold specific implications for ecosustainable building systems; in particular, for their potential reuse in the creation of both large and small structures that can be repeatedly readapted for changing uses. In such cases, the resulting constructions may be of distinct forms and dimensions, there need not be waste of the previously used materials, or the consumption of additional ones. Indeed, a key characteristic of these structures is that they are able to reform junctions with different geometries that can then be dismantled and reformed again using differently positioned support points that are not necessarily coplanar. The same elements (i.e. the beams) can then be used to create junctions formed of three, four, five or even more connecting beams with a static system equilibrium that changes depending upon the variation of the stipulated heights of the base support points. This geometrical and structural flexibility also renders the S.R.F. subject to particular interest with regards to the LEED (Leadership in Energy and Environmental Design) certification, in which protocols are assigned a higher value of ecosustainability when the structure can be reused at the end of its functional life in such a way that it can be reassembled into alternative forms and compositions for purposes that differ to its initial use. The structure lends itself as being particularly well suited for the covering of large spaces and can be built using highly diverse materials, including, steel, lamellar wood and even reinforced concrete that can be readily employed. Such flexibility makes it appealing when special solutions are required, as is the case when creating of temporary and reversible protections for archaeological excavations sites, where the ability to dismantle the system is of particular importance, as is the ability to stipulate the position of the base support points with total geometrical flexibility, both in the horizontal and in the vertical plane, in a way that the structure does not interfere with the historical remains. A renowned company from Bergamo, a world leader in the production of cement, also contributed to the project. They gave us the possibility to make and test some prototypes of demountable elements for the creation of temporary roofs and buildings. As the sponsor Italcementi produces concrete, we built the model using a high resistance concrete of reinforced fibre (HRC). The prototype was of an appropriate dimension and weight such that it could easily be positioned during the trials. The cases reported here are essentially the studies and laboratory prototypes that have been perfected through the course of the research conducted within the Faculty of Engineering at the University of Bergamo between 2006 and today; the results of which have permitted the elaboration of a project that has been submitted to the competition for the construction of the Italian Pavilion at the Shanghai 2010 World Expo. This paper summarises the geometrical research carried out at the University of Bergamo on the S.R.F. and describes the setting-up of a physical Finished Elements Model (FEM) created to test the structural potential of the system. The results of the research have permitted the elaboration of a project that has been submitted to the competition for the construction of the Italian Pavilion at the Shanghai 2010 World Expo and demonstrates the practical and viable use of S.R.F. in a contemporary architectural context. Finally, this paper will now summarise some concepts in order to demonstrate the preliminary results of our studies and their possible outlook and future development on the way of a necessary continuity between reciprocal structures and tensegral structures.
Due to their non-hierarchical nature, the geometry of reciprocal assemblies cannot be described conveniently with the available CAD modelling tools or by hierarchical, associative parametric modellers. The geometry of a network of reciprocally connected elements is a characteristic that emerges, bottom-up, from the complex interaction between all the elements’ shape, topology and position, and requires numerical solution of the elements’ geometric compatibility. A computational method, the “Reciprocalizer”, has been developed by the authors to predict and control the geometry of large networks of reciprocally connected elements, and it has been now perfected and included in a larger procedure that can be regarded as an extremely flexible and capable design tool for the generation of free-form reciprocal structures. The design tool has been applied for the design and realization of a free-form structure composed of 506 round, un-notched wooden elements with a diameter of 22 mm. This paper focuses on the geometry of reciprocal systems and the unique issues of fabrication posed by such assemblies.
The geometry of reciprocal structures is extremely difficult to predict and control, and it cannot be described with the available CAD software or by hierarchical, associative parametric modellers. The geometry of a network of reciprocally connected elements is a characteristic that emerges, bottom-up, from the complex interaction between all the elements shape, topology and position, and requires numerical solution of the geometric compatibility. This paper presents a design tool, the "Reciprocalizer", that is able to solve the geometry of reciprocal structures. The tool has been tested in the generation of both regular configuration, and non-regular configurations that are able to adapt to virtually any possible free-form geometry.
The reciprocalizer: a design tool for reciprocal structures The reciprocalizer: an agile design took for reciprocal structures in this same issue. Parigi, Dario, and Kirkegaard Poul H. 2014b. Design and fabrication of free-form reciprocal structures
- Parigi
- H Dario
- Parigi
- H Dario
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Parigi, Dario, and Kirkegaard Poul H. 2013. The reciprocalizer: a design tool for reciprocal structures. In Proceedings of Civil Comp Press, Cagliari, Italy, 3–6 September 2013. Parigi, Dario, and Kirkegaard Poul H. 2014a. The reciprocalizer: an agile design took for reciprocal structures. Nexus Network Journal 16, 1 in this same issue. Parigi, Dario, and Kirkegaard Poul H. 2014b. Design and fabrication of free-form reciprocal structures. Nexus Network Journal 16, 1 in this same issue.
14 The elemental fan (the 'bug') Fig. 15 Three-dimensionality Fig. 13 The generative rule References Baverel, Olivier, Hoshyar Nooshin, and Y. Kuroiwa. 2004. Configuration processing of nexorades using genetic algorithms
- Fig
Fig. 14 The elemental fan (the 'bug') Fig. 15 Three-dimensionality Fig. 13 The generative rule References Baverel, Olivier, Hoshyar Nooshin, and Y. Kuroiwa. 2004. Configuration processing of nexorades using genetic algorithms. Journal of the International Association for Shell and Spatial Structures 45(2): 99–108.
The reciprocalizer: an agile design took for reciprocal structures
- Dario Parigi
- Kirkegaard Poul
Parigi, Dario, and Kirkegaard Poul H. 2014a. The reciprocalizer: an agile design took for reciprocal
structures. Nexus Network Journal 16, 1 in this same issue.
44 The built prototype of the 'wave'
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Fig. 44 The built prototype of the 'wave'