# Multi-Directional Shape Change Analysis of Biotensegrity Model Mimicking Human Spine Curvature
## 5 Conclusions  
This paper presented a shape change analysis of three variations of biotensegrity models inspired by the form of the human spine, SB1-3 in the cases of uni-, bi- and tri-directional modes. The formulation of incremental equilibrium equations and the exploitation of the optimization tool, particularly the sequential quadratic programming method, were presented. The proposed shape change algorithm is capable of simulating the shape change of spine biotensegrity models via four states, the initial state, the deformed state, the shape change state and the target state, which allows for the advancement of the monitored nodes to approach to the target coordinates. The algorithm successfully solves the nonlinear programming problem, searches for the optimized forced elongation for cables and ensures non-slackened cables during the shape change analysis under specific constraints. A highly successful rate (99.62%) in achieving the objective function was observed in a total of 54, 35 and 168 analysis cases dealing with uni- (99.96%), bi- (99.98%) and tri-directional modes (98.92%), respectively. The convergence results can be further enhanced after the allowance of relaxing tolerance of 2% in the algorithm.  
Generally, no significant variation in the results of the total computational steps, NOF and displacement of the monitored nodes corresponding to the type of SB models was observed. The capability of the spine biotensegrity models to undergo bending and axial deformation and combinations of these deformations was proven in the study. The results of deformed configurations suggest that the spine biotensegrity models (SB1, SB2 and SB3) have more flexibility to undergo bending deformation in comparison with axial deformation. Apices (i.e., AP1, AP2 and AP3) in the spine biotensegrity models act as joints to permit the bending, extension, contraction and rotation in the shape change process. The contribution of the apices in shape change depends on the target displacement magnitude and the distance of the apice from the monitored nodes. Understanding the potential deformations of the spine biotensegrity models during the shape change process is essential for further extension to the simulation of shape change control. Towards the above mentioned direction, member and external obstacle collision avoidance, as well as the application of multiple series of monitored nodes, should be explored in future studies. Furthermore, the extension of the modeling of the human spine to incorporate parts connected to the spine, as well as more constraints on the movement of the human spine in the formulation of shape change analysis strategy, should also be considered.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12052377/s1](https://www.mdpi.com/article/10.3390/app12052377/s1)]([https://www.mdpi.com/article/10.3390/app12052377/s1](https://www.mdpi.com/article/10.3390/app12052377/s1)), Video S1: Shape Change of Biotensegrity Model Mimicking Human Spine.  
Conceptualization, K.K.C. and T.N.; methodology, T.N., K.K.C. and C.L.O.; software, C.L.O.; validation, T.N. and K.K.C.; formal analysis, C.L.O.; investigation, C.L.O.; resources, K.K.C., T.N. and J.-Y.K.; data curation, T.N., K.K.C. and C.L.O.; writing--original draft preparation, C.L.O.; writing--review and editing, K.K.C., C.L.O. and T.N.; visualization, C.L.O.; supervision, K.K.C. and T.N.; project administration, K.K.C., T.N. and J.-Y.K.; funding acquisition, J.-Y.K. All authors have read and agreed to the published version of the manuscript.  
The APC was funded by the National Research Foundation of Korea (NRF) and the Ministry of Education (NRF-2019R1A2C1007548).  
Not applicable.  
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2019R1A2C1007548).  
The authors declare no conflict of interest.