## 4 Results
\((m=8)\) and the compatibility matrix \(\mathbf{B}\big{(}\in\mathbb{R}^{6\times 8}\big{)}\) is as follows:  
\[\mathbf{B}=\left[ \begin{array}{cccccccc}0&-1&0&1&0&0&0\\ 0&0&-1&0&1&0&0&0\\ 0&0&0&0&0&1&0&-1\\ -1&0&0&0&0&0&1&0\\ 0&0&-0.707&0.707&0&0&0.707&-0.707\\ -0.707&-0.707&0&0&0.707&0.707&0&0\end{array} \right]\]  
Matrices \(\mathbf{L}\big{(}\in\mathbb{R}^{8\times 8}\big{)}\) and \(\mathbf{M}\big{(}\in\mathbb{R}^{6\times 6}\big{)}\) are respectively:  
\[\mathbf{L}=\text{diag}\Big{[} \begin{array}{cccccccc}4&2&2&2&2&0&0&0\end{array}  \Big{]};\ \mathbf{M}=\text{diag}\Big{[} \begin{array}{cccccccc}4&2&2&2&2&0\end{array}  \Big{]}.\]  
There are three zero eigenvalues in \(\mathbf{L}\), which means three mechanisms (\(M\)) are identified (Figure 3):  
\[\mathbf{x}_{7}=\Big{\{} \begin{array}{cccccccc}0.51&0.11&0.43&0.11&0.43&0.19&0. 51&0.19\end{array} \Big{\}},\]  
\[\mathbf{x}_{8}=\Big{\{} \begin{array}{cccccccc}-0.33&0.57&0.25&0.57&0.25&-0. 01&-0.33&-0.01\end{array} \Big{\}},\]  
\[\mathbf{x}_{9}=\Big{\{} \begin{array}{cccccccc}0.04&0.18&-0.35&0.18&-0.35&0. 58&0.04&0.58\end{array} \Big{\}}.\]  
Figure 3: Mechanisms of unsupported “X” truss: (**a**) \(\mathbf{x}_{7}\), (**b**) \(\mathbf{x}_{8}\), (**c**) \(\mathbf{x}_{9}\). The zero eigenvalue in \(\mathbf{M}\) is responsible for the existence of the self-stress state (\(S\)) defined by the same eigenvector as for the supported truss:  
\[\mathbf{y}_{6}=\Big{\{}\ \ 0.35\ \ \ 0.35\ \ \ 0.35\ \ \ 0.35\ \ \ -0.5\ \ \ -0.5\ \ \Big{\}}.\]  
In this case, three eigenvalues of the matrix \((\mathbf{K}_{L}+\mathbf{K}_{G})\) are zero:  
\[\mathbf{O}=\text{diag}\Big{[}\ \ 3.41\ \ \ 2.71\ \ \ 2.71\ \ \ 2.12\ \ \ 1.29\ \ \ 0\ \ \ 0\ \ \ 0\ \Big{]},\]  
It means the mechanisms are finite--a distance between any pair of nodes do no change. There are four structures with similar features wrongly termed \"tensegrity\" in the literature:  
* the truss (\(T\)) with five elements \((n=5)\) and four d.o.f. \((m=4)\)[79; 80] (Figure 4a),
* the truss (\(T\)) with 14 components \((n=14)\) and 13 d.o.f. \((m=13)\)[16; 81; 82; 83; 84; 85] (Figure 4b),
* the modified truss (\(T\))[20] from example presented later [6; 20] with ten components \((n=10)\) and nine d.o.f. \((m=9)\) (Figure 4c),
* the truss (\(T\)) with ten elements \((n=10)\) and seven d.o.f. \((m=7)\)[86] (Figure 4d). In the first three cases (Figure 4a-c) there is one zero eigenvalue in matrix \(\mathbf{M}\), which is responsible for the existence of one self-stress state (\(S\)) shown in Figure 4a-c. The system of compression members (thick red line) is discontinuous (\(D\)) and included inside the set of components in tension (\(I\)), which are cables (\(C\)). The truss shown in Figure 4d has three zero eigenvalues in matrix \(\mathbf{M}\) responsible for the existence of three self-stress states (\(S\)). These states need to be considered together. Superposition and normalization of self-stress states were performed, as shown in Figure 4d. For this truss the system of compression members is inside the set of tensioned elements (\(I\)), which are cables (\(C\)) but it does not satisfy the condition of discontinuity. According to the [PERSON]'s definition [13], it is a class 2 tensegrity system--a system with two compressive elements connected at the nodes. Figure 4: Self-stress values for fourtrusses (**a–d**) with tensegrity features. For these trusses there are no zero eigenvalues in matrix \(\mathbf{L}\), which means that the system lacks the mechanisms. From the perspective of structural mechanics, the mechanism is one of the most important tensegrity features--the uniqueness of tensegrity structures is based on the fact that states of self-stress stabilize existing mechanisms. Because of the absence of the mechanism, these trusses are only structures with tensegrity features.