Statics and dynamics of pulley-driven tensegrity structures with sliding cable modeling

This article introduces the concept of Pulley-Driven Clustered Tensegrity Structures (PD-CTS) and develops nonlinear and linearized static and dynamic equations using the Lagrangian method. The generalized coordinates utilized in this framework comprise the nodal coordinates of the tensegrity structure and the string sliding distances. The governing equations are specifically constructed, considering situations with and without boundary constraints. The developed method can be applied to nonlinear and linearized static and dynamic analysis of any PD-CTS, covering various research domains such as load analysis, form-finding, large deformation analysis, modal analysis, and dynamic response to various inputs. The substructure method is used to lower the order of the equations to reduce computational costs and facilitate the study of actuation strategies of tensegrity structures. The effectiveness of the suggested methods is validated through the analysis of two case studies: a 2D T-bar and a 3D tensegrity tower. Furthermore, the methodologies established in this paper can also be employed to examine deployable cable net structures and pulley-driven robotic systems.