Building multi-stable structures based on Baranov truss part II: analysis, design and applications

Abstract Part I of this study established a distance-geometry based framework for programmable multi-stability in planar linkages, showing how elasticity can be embedded directly into bilateration closure equations to transform discrete compatibility into continuous energy landscapes. Part II develops this framework into a generalized design tool. We first extend the method to handle multiple non-rigid links, where energy landscapes reveal rich patterns of bifurcation and branch connectivity. We then explore design extensions: tessellation of Baranov trusses in series to generate modular architectures, incorporation of joint compliance to capture torsional flexibility and generalization to higher-order Baranov groups such as the 7/B1 truss. Across these examples, we demonstrate how Assur groups provide modular building blocks for constructing scalable multi-stable structures, whose stability and transitions can be programmed through geometry and stiffness allocation. The resulting framework moves beyond isolated trusses to architected assemblies, offering systematic strategies for designing deployable, adaptive and multi-functional structures.