###### Abstract  
This paper presents a study on form-finding of four-stage class one self-equilibrated spine biotensegrity models. Advantageous features such as slenderness and natural curvature of the human spine, as well as the stabilizing network that consists of the spinal column and muscles, were modeled and incorporated in the mathematical formulation of the spine biotensegrity models. Form-finding analysis, which involved determination of independent self-equilibrium stress modes using generalized inverse and their linear combination, was carried out. Form-finding strategy for searching the self-equilibrated models was studied through two approaches: application of various combinations of (1) twist angles and (2) nodal coordinates. A total of three configurations of the spine biotensegrity models with different sizes of triangular cell were successfully established for the first time in this study. All members in the spine biotensegrity models satisfied the assumption of linear elastic material behavior. With the established spine biotensegrity model, the advantageous characteristics of flexibility and versatility of movement can be further studied for potential application in deployable structures and flexible arm in the robotic industry. biotensegrity; form-finding; tensegrity; spine; prestress; equilibrium; generalized inverse +
Footnote †: journal: Applied Soft  
This study is aimed at form-finding of possible biotensegrity models inspired by the form of the human spine. Advantageous features of a human spine such as slenderness and natural curvature of the geometry, as well as the stabilizing network consisting of spinal column and muscles were incorporated in the configuration of the spine biotensegrity model. This study was carried out as a first step towards the next phase of study on the shape changeability of the spine biotensegrity models that can be beneficial for applications such as automated robotic tools (i.e., for inspection and automation in manufacturing) or deployable structures (Figure 1). Shape change of regular tensegrity models studied by the authors can be found in [8]. The form-finding analysis employed Moore-Penrose generalized inverse in the solution of rank-deficient system of equilibrium equations. An algorithm incorporating iterative process to determine the self-equilibrated configuration of spine biotensegrity model through the modification of nodal coordinates was proposed. The human spine is one of the unique models in the biological system with the ability to sustain high loads and at the same time demonstrate a superior combination of multidirectional movements. Despite being spongy, the tapered spinal vertebrae body efficiently maintains body weight and withstands external impacts. In addition to the special architecture with sagittal curvature of spinal column, the spine can avoid distress (i.e., exhaustion) by re-establishing new equilibrium positions. The dexterity in avoidance of distress in the system is mainly due to the harmonization of the passive (i.e., spinal column), active (i.e., surrounding muscles and tendons) and control (i.e., neural centers) subsystems [9]. It is noted that the spine always maintains the stability of the system even after disturbance by a self-structural reorganization. Based on the above descriptions, a spine has a distinctive characteristic of flexibility and versatility in accommodating different movements. Coupling the advantage of tensegrity (i.e., lightweight and flexibility) and the versatility of a human spine, a novel biotensegrity model can be realized. In addition, the principle of biotensegrity is highly suitable for explaining the mechanism of compressive passive subsystem (i.e, spinal column) and tensional active subsystem (i.e., surrounding muscles and tendons) in the spine. According to [PERSON], a spinal system re-structures to form many new postures in order to sustain the stability of the system once the tensional forces in the network have been disturbed [10].