Nonlinear Behavior of Planar Compliant Tensegrity Mechanism with Variable Free-Lengths

Traditional tensegrity mechanisms comprise compressive (rigid rods) and tensile members (cables). Compliant tensegrity mechanisms (CoTM) include springs alongside cables. Introduction of spring elements allows these structures to be more adaptable and robust. The kinematic and stability analyses of such mechanisms will facilitate better understanding of their behaviors for developing control and design methodologies. The analysis of CoTM often involves making the zero free-length (ZFL) assumption, i.e., the free-length of the spring is zero, which disqualifies the analysis for most real-word applications. The paper illustrates the drastic increase in computational complexity for finding static solutions as the assumption of ZFL for spring elements are relaxed for a simple planar compliant tensegrity mechanism comprising two rigid triangular platforms connected by a compressive member and two spring elements. The resulting nonlinear behavior of obtained static solutions shows intersecting manifolds of equilibrium orientation angles where the number of solutions vary from minimum of 4 to beyond 10 as the spring free-lengths are varied.