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Reciprocal Frames (RF) are a type of structural system that can be used to build temporary structures with large spans. This is possible due their ease of assembly and the use of relatively short, light-weight elements. However, a challenge is presented when this kind of structure is applied to complex surfaces. In this case, the only way to figure out each connection is through an algorithmic geometric model. Only a few algorithms have already been developed for generating complex RF structures, but they still have some limitations. In this paper we present a new approach represent RF geometry, based on symmetry theory, combining pinwheel patterns with wallpaper symmetry groups. In future works, this will be combined with structural performance analysis and the use of digital fabrication methods for producing the structures' connections. [ABSTRACT FROM AUTHOR]

Face à la diminution des ressources et afin de réduire l’impact carbone du secteur de la construction, il est important d’envisager la fin de vie des bâtiments. Il faut considérer les constructions et leur structure comme des éléments pouvant être démontés ou désassemblés pour être recyclés ou réutilisés. Cette recherche s’intéresse aux assemblages non-séquentiels, permettant une réversibilité pour répondre à ces enjeux. Pour démontrer l’intérêt de ces assemblages, un prototype de Nexorade échelle 1 a été construit et illustre l’article. La première partie définit l’assemblage non-séquentiel et ses cinématiques possibles. La recherche du pavage et de la géométrie sont évoquées dans la seconde partie. L’article continue sur la génération de la nexorade et son analyse mécanique mettant en évidence l'intérêt d’incliner les poutres de la nexorade, pour réduire la flèche de 35%. La séquence d’assemblage est développée dans la partie 5. Enfin, la construction du pavillon est détaillée, permettant le passage d’un modèle numérique à la fabrication du prototype. Pour conclure cet article, les auteurs discutent des résultats obtenus sur les assemblages non-séquentiels et sur l’inclinaison des poutres. Des extensions possibles et futures recherches sont suggérées.

Abstract This article proposes a new computational method for the form-finding of nexorades, also called reciprocal frames in the literature. The method is based on the translations of members forming the initial layout. It is shown that the two geometrical quantities defining nexorades - eccentricity and engagement length - depend linearly on the transformation parameters. The method introduced in this article is thus based on linear algebra, so that fitting problems can be formulated as simple quadratic optimisation problems under linear constraints. The proposed method is therefore fast, simple to implement, robust and can be applied to various grid patterns. Furthermore, the proposed framework preserves planar facets. This paper proposes thus a new structural system where the nexorade is braced by planar facets. The feasibility of this structural system and of the computational framework introduced in this article is demonstrated by the fabrication of a 50 m2 timber pavilion. Highlights • A new form finding approach for nexorades is proposed. • The form finding is based on translation of members. • The influence of design parameters is discussed with numerous examples. • The resulting structures can be covered with planar panels which can be used as bracing components. • An experimental prototype demonstrates the potential of the form finding technique. [ABSTRACT FROM AUTHOR]

Nexorades or reciprocal frames can be seen as a practical way to reduce the complexity of connections in spatial structures by connecting reciprocally the members by pairs. This reduction of the technological complexity of the connections is however replaced by a geometrical complexity due to numerous compatibility constraints. The purpose of this article is to make explicit these constraints for elementary structures and to solve analytically the resulting system of equations. Applications to regular polyhedrons are presented and a practical realization (a 3 m high dodeca-icosahedron) is shown. In the brief conclusion, perspectives for complementary analytical developments for spatial structures are drawn forth. [ABSTRACT FROM AUTHOR]

Among the family of space structures is a typology called nexorades or reciprocal frame structures. Nexorades can have various configurations and shapes. This article focuses on a simple configuration to obtain results that are easy to read and communicate. The aim is to get a better understanding of the structural behavior of nexorades to facilitate their design.Two analytical methods are proposed to calculate the bending resistance and the stiffness of a nexorade. The influence of the connections between members on the structural behavior and the robustness is studied. A comparison is made with flat grids. [ABSTRACT FROM AUTHOR]

There are many ways of covering a surface. This paper describes the solution adopted for a prototype of an archaeological excavation shelter in Bibracte, France. A nexorade or reciprocal frame system covered with fabric has been designed by French architect Paul Andreu and French engineers Bernard Vaudeville and Simon Aubry (RFR first stage and T/E/S/S second stage). The shelter was built in 2008 and is currently in use. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

The paper presents new results about the geometry of topological interlocking masonries and some possibilities they present to build without formwork. Construction without the use of formwork may be an important issue concerning both productivity increase and decreasing of waste generated on a construction site. Due to the development of computational design and robotics in the construction industry, it makes sense to (re)explore innovative design and process of complex masonry structures. The design of this kind of masonry is standard for planar structures, and in this paper, a generalisation is proposed for the parametric design of curved structures. To achieve this, a criterion for translationally interlocked structure based on quadrilateral meshes is exhibited. The application of this criterion is then extended to masonry structures derived from other patterns. Physical prototypes of topological interlocking masonry are also presented. One of these designs seems to allow construction without formwork. • The context of the work concerns the development of robotics in construction. • The focus is set on complex masonry structures, and topological interlocking systems. • A new design criterion, for translational interlocked free-form structures is proposed. • This criterion is used to design masonry structures constructible without formwork. • Experimental prototype results are discussed. [ABSTRACT FROM AUTHOR]