# Parametric Analysis of Tensegrity Plate-Like Structures: Part 1--Qualitative Analysis
## 3 Classification of Tensegrity Structures  
In terms of structural mechanics, self-stress states and infinitesimal mechanisms stabilised by these states are the two most important features of tensegrity structures. Based on the definitions known from the literature, tensegrity structures demonstrate six characteristic features [58]:  
* \(T\) -- the structure is a truss,
* \(S\) -- there is a self-stress state,
* \(C\) -- tensile elements are cables and have no rigidity in compression,
* \(M\) -- there is an infinitesimal mechanism stiffened by the self-stress state,
* \(I\) -- the set of struts is contained within the continuous net of tensile elements,
* \(D\) -- compressed elements form a discontinuous set so its extremities do not touch each other.  
The structure has to meet the first three obligatory features (\(T\), \(S\), \(C\)) and at least one of the others (\(M\), \(D\), \(I\)) to be considered a structure with tensegrity features. If a structure meets all the above requirements, it can be classified as a \"pure\" tensegrity structure [3; 45; 57; 70; 71]. That classification was revised by [PERSON] [70] (60-62) and extended to four classes, namely:  
* ideal tensegrity--structures which meet all requirements (\(T\), \(S\), \(C\), \(M\), \(D\), \(I\)) and all self-stress states (including the superposed one) must ensure the stability of the structure,
* \"pure\" tensegrity--structures satisfy the first five requirements, that is, \(T\), \(S\), \(C\), \(M\), \(D\), and all self-stress states ensure the stability of the structure,
* structures with tensegrity features of class 1--structures meet the conditions of the first four features (\(T\), \(S\), \(C\), \(M\)) and at least one self-stress state that ensures the stability of the structure,
* structures with tensegrity features of class 2--structures meet only the obligatory requirements (\(T\), \(S\), \(C\)) and additionally either feature \(I\) or \(D\).  
The classification is shown concisely in Table 1. Features \(S\) and \(M\) (the presence of self-stress states and infinitesimal mechanisms) can be determined directly by the spectral analyses of the truss matrices, while the features \(D\), \(I\), and \(C\) (struts do not share ends and are located inside the continuous net of tensile elements with zero compression rigidity) are recognised indirectly by the identified self-stress state.  
The proposed classification systematises and precisely defines tensegrity structures and ensures the correct use of the term \"tensegrity\" in all applications. In engineering practice, such systematisation facilitates the analysis and design of tensegrities because it is a consequence of different behaviours of tensegrity structures under the influence of external action.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(T\) & \(S\) & \(C\) & \(M\) & \(I\) & \(D\) \\ \hline ideal tensegrity & **+** & **+** & **+** & **+** & **+** & **+** \\ “pure” tensegrity & **+** & **+** & **+** & **+** & **+** & **-** \\ structures with tensegrity features of class 1 & **+** & **+** & **+** & **+** & **-** & **-** \\ structures with tensegrity features of class 2 & **+** & **+** & **+** & **-** & **+** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Tensegrity classification, based on [70].