Design and optimization of mass-efficient tensegrity Michell truss with variable anchorage length

Abstract

This research introduces a method for designing a cantilever tensegrity structure using Michell’s spiral theory, focusing on optimizing the anchorage length for minimal mass. The structural topology is first established by deriving geometric parameters, including spiral properties and complexity order. The equilibrium equation is derived using the method of joints, and a recursive expression is developed to calculate axial forces in all members. The minimum mass configuration is achieved by optimizing the anchorage length under buckling and yielding constraints across various complexity orders. Additionally, a dynamic equation is derived via the Lagrangian approach, treating nodal coordinates as generalized coordinates. The dynamic response of the Michell structure under base excitation is analyzed. Results reveal that structures with low-complexity order exhibit greater stability, with reduced deformation and more efficient force transmission compared to higher complexity order. This indicates the importance of complexity order selection in designing dynamically robust Michell structures. The research provides an efficient foundation for the mass optimal design of lightweight, high strength structures suitable for application in robotics, aerospace, and earthquake resistant construction.