Cable Actuated Tensegrity Structures for Deployable Space Booms with Enhanced Stiffness

Open Access
Yildiz, Kaan
Graduate Program:
Aerospace Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
June 13, 2018
Committee Members:
  • George A Lesieutre, Dissertation Advisor
  • George A Lesieutre, Committee Chair
  • Robert Graham Melton, Committee Member
  • Namiko Yamamoto, Committee Member
  • Joseph Paul Cusumano, Outside Member
  • tensegrity structures
  • space structures
  • deployment
  • optimization
  • effective stiffness
  • deployable booms
  • form finding
  • force finding
  • transformation
  • cylindrical tensegrity booms
Spacecraft having extended configurations must be stowed for launch compactly, with final stiffness adequate to maintain shape and stability under dynamic disturbances. The proposed research focuses on deployable booms, one-dimensional beam-like structures comprising a lightweight, structurally-efficient assemblage of finer-scale structural members. In particular, tensegrity structures are considered for their potential to provide a new kind of deployable boom for space applications. Tensegrity structures (or ``tensegrities'') comprise a self-equilibrating assemblage of 1-D compression members (struts) and tension members (tendons or cables) connected via frictionless ball joints at member ends (nodes). Tensegrities can also carry external loads very efficiently. In a classical tensegrity structure, struts are connected only to cables; however, in a generalization of the concept, struts can meet at nodes, and can be classified based on the maximum number of struts connected at a single node. A classical tensegrity is thus ``Class-1'', and one in which two struts meet at a node would be ``Class-2''. Existing approaches to the analysis and design of tensegrity structures are reviewed, including: various methods of form-finding such as numerical and semi-analytical; as well as methods of force finding (from a given geometry). The behavior of tensegrity structures under external loads is studied using a nonlinear finite element model in which unique characteristics such as the effect of pre-stress and cable slackness are taken into account. Effect of pre-stress is observed as stiffening while cable slackness reduces the overall stiffness. Free vibration properties are investigated, and substantial effects of pre-stress levels on vibration modes associated with infinitesimal mechanisms are revealed. Vibration modes associated with infinitesimal mechanisms are governed by pre-stress levels. The results indicate that corresponding natural frequencies increase proportionally with the square root of the pre-stress levels. Furthermore, effective beam stiffness properties are determined for use in preliminary design; these stiffnesses depend on pre-stress levels. Axial and torsional rigidities are found to increase substantially as pre-stress levels are increased; however, bending and shear rigities do not increase as much as the axial and torsional rigidities. A primary concern regarding the use of classical tensegrity structures for space applications is inferior stiffness, due mainly to the small cross-sectional areas of tendons. Structural stiffness can be increased by allowing strut-to-strut connections, but this decreases packaging efficiency. Two examples of deployable ``cylindrical'' tensegrity booms are investigated in detail: one, a Class-1 tensegrity, the three-strut Snelson type configuration, which is also known as ``SVD'' (Saddle-Vertical-Diagonal) configuration; and the other, a Class-2 tensegrity comprising pairs of mirror-image ``triplex'' configurations. Strut lengths are fixed, and deployment is achieved conceptually via actuation of cable lengths. Generalization to n-strut cylindrical tensegrities is achieved, and example deployments are simulated. The primary focus of the dissertation is a concept for a deployable cylindrical tensegrity boom that begins as a Class-1 tensegrity having high packaging efficiency and, through a multi-stage deployment process, ends as a Class-2 tensegrity having higher stiffness. Realizing this structural concept requires consistent connectivity, augmented by additional cable actuation to achieve the transition at an appropriate stage of deployment. An initial physical realization of this concept (configuration and deployment process) is demonstrated. As a result, it is found that axial and torsional rigidities are increased by factors of 4.5 and 3 for the selected tensegrity boom example, respectively. Whereas the improvements in bending and shear rigidities are obtained as 36$\%$ and 63$\%$, respectively. Another important benefit of the transformation is also identified as the increase in the total height of the boom. Sizing and prestress optimization of tensegrity booms, with consideration of member buckling and yielding, are achieved by implementing a heuristic optimization algorithm, Particle Swarm Optimization (PSO). A trade-off study was conducted with the number of bays varied, and its influence on several properties including bending and torsional stiffnesses, mass and stiffness-to-mass ratios is discussed. The results show that the bending stiffness-to-mass ratio of the optimized tensegrity booms are greater than the bending stiffness-to-mass ratio of most of state of the art deployable boom concepts. A multi-stage optimal deployment path in terms of stiffness is also obtained for a selected case by evaluating effective beam stiffness parameters. The proposed deployment strategy involving a transformation between Class-1 to Class-2 tensegrities promises significant improvements in the structural efficiency of deployable tensegrity booms. The final stiffness-to-mass ratio is found to be greater compared to state of the art deployable boom concepts. This deployment strategy has the potential to increase the claims on tensegrity structures to be one of the best candidates for deployable structures. Alongside parallel advances in cable actuation, tensegrity structures can replace the conventional deployable structures in real space missions.