For a tensegrity framework with bars, cables (unilateral tension members) and struts (unilateral compression members), this paper presents a sequence of four mathematical concepts for detecting its rigidity. In order from the strongest to the weakest, these concepts are called infinitesimal (or static) rigidity, prestress stability, second-order rigidity and rigidity. Emphasis is placed on pre-stress stability, which lies between infinitesimal rigidity and second-order rigidity.
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