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This paper presents a closed-form analysis of a series of planar tensegrity structures to determine all possible equilibrium configurations for each device when no external forces or moments are applied. The equilibrium position is determined by identifying the configurations at which the potential energy stored in the springs is a minimum. The degree of complexity associated with the solution was far greater than expected. For a two-spring system, a 28th degree polynomial expressed in terms of the length of one of the springs is developed where this polynomial identifies the cases where the change in potential energy with respect to an infinitesimal change in the spring length is zero. Three and four spring systems are also analyzed. These more complex systems were solved using the Continuation Method. Numerical examples are presented.

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