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The aim of this article is to obtain a stable tensegrity structure by using the minimum knowledge of the structure.

Three methods have been formulated based on the eigen value decomposition (EVD) and singular value decomposition theorems. These two theorems are being implemented on the matrices, which are computed from the minimal data of the structure. The required minimum data for the structure is the dimension of the structure, the connectivity matrix of the structure and the initial force density matrix computed from the type of elements. The stability of the structure is analyzed based on the rank deficiency of the force density matrix and equilibrium matrix.

The main purpose of this article is to use the defined methods to find (1) the nodal coordinates of the structure, (2) the final force density values of the structure, (3) single self-stress from multiple self-stresses and (4) the stable structure.

By using the defined approaches, one can understand the difference of each method, which includes, (1) the selection of eigenvalues, (2) the selection of nodal coordinates from the first decomposition theorem, (3) the selection of mechanism mode and force density values further and (4) the solution of single feasible self-stress from multiple self-stresses.

This paper aims to propose a study on the static behavior of prismatic tensegrity structures and an innovative form for determining the effect of mechanical properties and geometric parameters on the minimal mass design of these structures.

The minimal mass design in this paper considers a stable class-two tensegrity tower built through stable models. Using the proposed structures, comprehensive parametric studies are performed to examine the mass (in which the masses of joints are ignored), the mass ratio between a class-two tensegrity tower and a single element, both having the same diameter and length and afterward determine a reliable mass saving structure under various circumstances.

The simulations show that the mass ratio versus the number of units is a nonlinear regressive curve and predicts that the proposed model outperforms the standard model when the variation parameter considered is a vertical force. The difference in mass between these structures is visible when the gap gradually decreases while the number of units increases. On the geometrical aspect, the gap between the masses is not significant.

This paper helps to understand the influences of geometric parameters and the mechanical properties on the design of cylinder tensegrity structures dealing with a compressive force.