A Virtual Work Framework for Class- k and 2.5D Tensegrity Simulation with Clusters

This paper presents KC3 Tensegrity Sim, an open-source Python simulation framework for modeling class-k tensegrity structures with clustered cable routing and cylindrical 2.5D geometries. In this work, a 2.5D tensegrity structure refers to a planar tensegrity topology whose nodes are constrained to lie on a prescribed three-dimensional cylindrical surface while retaining the connectivity of the original planar pattern. Rather than proposing virtual work as a new theoretical method, this study applies a virtual-work equilibrium formulation to integrate three modeling capabilities that are not jointly supported in existing tensegrity software: class-k connectivity, clustered cables routed through multiple nodes, and cylindrical surface-wrapping constraints. The framework represents tensegrity systems through declarative configuration files, assembles the corresponding equilibrium residuals numerically, and solves for static equilibrium configurations in 2D, 3D, and cylindrical 2.5D settings. The framework is validated against a physical tensegrity structure and is intended to support early-stage design and configuration analysis of clustered and cylindrical surface-constrained tensegrity mechanisms, including wearable and morphing robotic structures.