Form Finding And Shape Change Analysis Of Spine Inspired Bio-Tensegrity Model - Oh, Chai Lian (2017)
Biotensegrity mimicking the living organisms possesses excellent characteristics that duly demonstrate most of the properties in biological systems such as efficiency, self-stabilization, multi-modularity and multi-functional. Moreover, biotensegrity as a model emulated from the forms and functions of hierarchical biological system reveals its great potential in shape change ability. Therefore it is highly suitable to study biotensegrity as a new alternative choice for possible application where shape change ability is desired such as flexible arm in construction industry. However, there are limited studies on form finding of biotensegrity configurations and mathematical models on shape change of biotensegrity. Mimicking biological system by their shape, pertinent anatomical dimensions and natural curvature of human spine to seek its potential in shape change beneficial to application like automated robotic tools is the overall aim of this study. Specifically, this basic study aims to (1) formulate mathematical procedures for finding self-equilibrated configurations of spine biotensegrity structure (SBS) models (2) formulate computational strategy for simulating the shape change of novel SBS models, and (3) evaluate the characteristics of the novel SBS models. The methodology for this study consists of three phases. In the first phase, assemblage and mathematical formulation procedure for form finding of self-equilibrated four-stage class 1 biotensegrity models inspired by human spine or spine biotensegrity (SBS) models are established. The form-finding procedure involves method of solving the system of equilibrium equations through the use of Moore-Penrose generalized inverse, determination of self-equilibrium stress modes via eigenvector basis decomposition and optimization of coefficients for the linear combination of linearly independent selfequilibrium stress modes. Advantageous features of human spine like the slenderness and natural curvature in the geometry, as well as the stabilizing network consist of spinal column and muscle are incorporated in the mathematical formulation of the configuration of the SBS models. Additionally, two specific approaches in modification of nodal coordinates are implemented to improve the efficiency for form-finding of self-equilibrated SBS models, i.e. by means of adjustment of twist angles and modification of initial nodal coordinates. After successful searching of the configuration of self-equilibrated SBS models, the ability of the models to undergo shape change to achieve the prescribed state is investigated in the second phase. Specifically, unconstrained nodes of SBS model are chosen as monitored nodes where these nodes are required to reach a set of target displacements in prescribed magnitudes and directional modes. The shape change of SBS models towards target state is achieved by means of forced elongation of cable. Computational strategies for the shape change consist of two stages: the derivation of incremental equilibrium equations and optimization of the cables forced elongation by sequential quadratic programming. In the third phase, the structural characteristics of SBS models such as the deformed configurations and changes of axial force at the end of shape change analysis are investigated. The following four cases of target displacements are studied in order to investigate the characteristics of SBS models after shape change: uni-, bi-, tri-directional and twisting modes. The current study has successfully formulated mathematically the self-equilibrated configuration of SBS models inspired by human spine. A total of three novel selfequilibrated configurations of SBS models were searched. This study has also proposed a set of procedures involving incremental calculation for shape change analysis of SBS models. Numerical simulations of the regular tensegrity and SBS models have proven the superior convergent characteristic of the proposed algorithm for shape change analysis. The results reveal that the proposed approach for shape change analysis has a very strong ability for a self-equilibrated model to search their desired target coordinates in multi-directional modes through optimization of the forced elongation in cables. It is also found that the SBS models are capable to undergo bending, axial and torsional deformation. Active changes in forces in element groups even within the far-away element groups of SBS models are observed during the shape change analysis. In conclusion, the findings of this basic study have paved the way for realization of spine inspired flexible arm with magnitude shape change ability.