A kinematic analysis of a stacked planar compliant tensegrity mechanism

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tensile members (strings). Compliant tensegrity mechanisms (CoTM) introduce springs alongside strings and rods, allowing these structures to be more adaptable and robust. The kinematic and stability analyses of such mechanisms will facilitate better behavioral understanding for control of such structures. Such structures are known to display nonlinear behaviors including multiple equilibria. Previously, a simple planar model of such a CoTM has been studied. This can be furthered upon by viewing the mechanism as a single link within a kinematic chain. However, a nomenclature methodology for kinematic chain of CoTM modules is lacking. The equilibrium analysis of CoTM is non-trivial as the equilibrium equations are nonlinear in variables (angles occuring as sine and cosine). Mathematically, for a small number of equations, the solutions can be obtained using polynomial elimination methods. The computational complexity increases exponentially with the number of equations along with the number of equilibrium solutions. The presented work analyzes single module and chain of planar CoTM comprising of two rigid bodies connected by a rigid link and two springs through revolute joints. The computational complexity of a planar CoTM link increases drastically as the zero free-length (ZFL) constraint of the springs in relaxed. Stability of the solutions is evaluated by observing the eigenvalues of the Jacobian of the equilibrium equations. After analyzing the system for one link, a two-link chain system is analyzed. Analysis is done based on knowledge gained from analyzing a single link and solving for all solutions of the mechanism and then determining stability of the found equilibrium solutions.

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