# Multi-Directional Shape Change Analysis of Biotensegrity Model Mimicking Human Spine Curvature
## 1 Introduction  
The principle of biotensegrity is an application of the concept of tensegrity in explaining the anatomy and physiology of biological systems which has been studied since 1980s. Biotensegrity consisting of compressive (i.e., vertebrae) and tensional (i.e., fascial, muscle, tendon) components exhibits stable form, prestressed condition at rest and effective transmission of forces within the system. Extensive research investigations on biotensegrity based biomechanical models, particularly cellular, molecular, organ and tissue, organisms and fascial biotensegrity, as well as the principle of biotensegrity in cellular mechanical signal transduction (mechanotransduction), were reported [1, 2]. To date, biotensegrity as a model emulated from the forms and functions of complex biological systems has been suggested for several potential applications such as in medical technology [3], health care practices [4] and engineering applications [5]. Characteristics, such as the ability to self-assemble and perform global deformations upon loadings while at the same time maintaining their stability, have been attracting increasing interest on the shape change of tensegrity. The deformation of tensegrities to achieve shape change is basically generated based on the member length actuation, change in prestress and alteration of the structural stiffness of tensegrities. Most of the previous studies implemented static or quasi-static deployment analysis owing to the complicated mechanical properties of the tensegrities [6]. The shape change of tensegrity was solved as a quasi-static problem during the sufficiently slow deployment process [7; 8; 9]. The solutions to the quasi-static problems of tensegrities are commonly proposed by employing numerical, analytical and optimization algorithms. [PERSON], et al. [10] derived a non-linear finite element formulation for the quasi-static deployment of clustered tensegrities based on a co-rotational approach. [PERSON], et al. [11] investigated a control methodology to connect two half bridges through the changes of cable length employing a combination of stochastic search and quasi-static analyses. The deployment of the footbridges was solved based on the distance between a pair of nodal coordinates of two mid-span connectors. [PERSON] et al. [7] carried out both quasi-static and dynamic analyses for a clustered tensegrity beam and a four-stage tensegrity tower incorporating sliding cable elements. Using an energy-based approach for system equilibriums and a nonlinear finite element model, the trajectory and stress distribution of two foldable tensegrity-membrane systems during deployment was investigated [12]. [PERSON] and [PERSON] [8] applied quasi-static assumptions for determining the member length actuation of a cantilever tensegrity based on the variation in the structural load-carrying stiffness. [PERSON] and [PERSON] [13] developed general analysis methods for n-strut cylindrical Class-1 and Class-2 deployable tensegrity booms, with the assumption of quasi-static motion. A shape control method employing a dynamic relaxation-based motion tracking algorithm suitable for both quasi-static and dynamic process was proposed in [9]. Nonetheless, a study on shape change analysis of biotensegrity, especially for deployable structures, has not been found. Instead, many have studied the shape change of biotensegrity for robotic and automation applications. A class 2 biotensegrity underwater robot was designed and fabricated with stiffness approximating that of the real fish [14]. The flipping of the fish tail was performed by tuning the bending stiffness of the robot body, which was formulated based on the virtual work method. Using the force density method to solve the inverse kinematics, a modular tensegrity robot inspired by the vertebrae morphologies to grasp objects was developed [15]. An investigation on the motion patterns of a flexible biotensegrity manipulator mimicking the shrinking behavior of octopus tentacles was also conducted [16].