Estructuras desplegables de barras rectas y su optimización mediante diseño paramétrico. Caracterización geométrica y límites funcionales"

Abstract

A growing interest in experimentation with deployable structures emerged in the middle of the last century, driven by the research of designers such as Buckminster Fuller and Emilio Pérez Piñero. These pioneers used scale models as their main tool to develop their research. The drawing of these structures was an arduous task due to the movement of their parts, nodes and rods. Recently, the emergence of specific Algorithm Aided Design (AAD) software, also known as Parametric Design tools, has effectively solved this Challenge. Therefore, this study hypothesizes on the use of parametric design tools applied to the study of four systems of articulated straight bar deployable structures (EDBRA), to obtain breakthrough results dealing with geometric characterization of these structures and their functional limits. The proposed method would even allow geometrically evaluating the kinematic behaviour of different structural systems other than those considered in this study, without appealing to preliminary physical modelling of the structures. In this study we will also define the geometrical functional limits of the structures, separating between their behaviour as a mechanism, variable, dynamic, and their behaviour as a structural element, static stable. Among others, we define for the first time the deployability coefficient or the kinetic range, determinants in the characterization of the kinetics of the systems. With the purpose of supporting this thesis, the present research produces four lines of results. They are concerned with four identified parameters and a final protocol. First of all, the number of modules of each system and their capacity to cover the space in each case is identified, as a function of the folding angle of the system, under idealized simulation conditions (with the rods simplistically represented as lines and the nodes as points). We then simulate the structures with real dimensions and analyse how the eccentricity introduced by the dimension of the nodes affects the kinetics of the systems, considering the constant cross-section of the bars. Subsequently, it is analysed how the variation of the cross-section of the bars affects the kinetics of the systems. Based on the results of the last two steps, the kinetic range of each system is established, defined as a complex Surface in ℝ3 that takes as variables the opening angle of the system, the eccentricity and the radius of the cross section of the rods. Eventually, by applying this kinetic range, a graphical method governed by algorithms is proposed, which allows predicting the limits of the kinetic performance of a deployable system, for any configuration of the three geometrical variables. These results provide a new vision when it comes to mechanical-structural system design, predicting its geometrical response in folding and unfolding for the dimensions resulting from the structural calculation.