# Multi-Directional Shape Change Analysis of Biotensegrity Model Mimicking Human Spine Curvature
## 4 Numerical Examples
### Deformed Modes
However, no significant bending was observed at the segments between AP1 and AP3. The deformation characteristics of all of the spine biotensegrity models except series XnYn were governed primarily by axial deformations at target displacement magnitude of 600 mm, accompanied by expansion and contraction. Along with the axial deformation, most of the spine biotensegrity models allow for slight bending around AP3 (Figure 17f,g). In a way different from the other series, series XnYn demonstrates double curvature bending deformation (Figure 17h). Despite the fact that monitored nodes are only prescribed at the top, the deformation of nodes at AP1 was clearly observed during the shape change process. Similar to the human spine, the struts (i.e., vertebrae) and cables (i.e., muscle) of the spine biotensegrity model act in an interrelated manner. The far-away members can act immediately when the signal was given even to local points to advance to a set of targets. Figure 18 shows the final state for cases of shape change analysis involving the tri-directional mode. SB models in series XY200Z reach their target coordinates mainly by means of bending deformation about AP1 and AP2 (Figure 18a). On the contrary, almost all SB models in series XY400Z reach the target coordinates by means of axial deformation (Figure 18b). In series Zp, all SB models in series XY200 Zp and XY400Z reach the target coordinates by means of axial deformation (Figure 18c,d). The vertical clearance between the two groups of nodes (the upper and lower nodes) becomes significant when both x and y or z target displacement magnitudes increase. On the other hand, all SB models in series XY200 Zn reach the target coordinates primarily by means of bending deformation. In cases with z target displacement magnitude of 200 mm, all SB models in series XpYn and XnYn generally bend around AP2 whereas series XpYp and XnYp demonstrate noticeable bending around both AP1 and AP2. When the z target displacement magnitude increases, bending deformation around all apices, AP1, AP2 and AP3, is observed (Figure 18e). Bi-axial bending is also observed in most of the cases (Figure 18f), except series XnYn, which shows only uni-axial bending. Generally, the majority of all SB models in series XY400 Zn show axial deformation with slight bending around AP3 in most of the cases with z-displacement magnitude of 200 mm, while, for cases of magnitudes of target displacement equal to 400 mm and 600 mm, bending around AP1 and AP2 is generally seen. It is noted that all SB models demonstrate expansion and contraction in the final configuration. The proposed spine model incorporates the freedom of movement inherent in humans but does not necessarily exhibit the same movements experienced by humans. Depending on the settings of the analysis model, it may show cases of shape change that exceed the limits of human spine movement, as shown in Figures 15-18. Nevertheless, the findings derived from the use of the simplified spine biotensegrity model considered in this study provide useful insight into the influence of the incorporation of human spine topology on the deformation characteristics of the model. Figure 17: Deformed configuration (**a**–**h**) at the final step for cases with the bi-directional mode. Figure 18: Deformed configuration (**a**–**f**) at the final step for cases with the tri-directional mode.