Form-Finding of Tensegrity Basic Unit with Equal Cable Length

Abstract

Tensegrity is a lightweight, self-stressing, and self-stabilizing structure made up of cables and bars, with each member bearing either tension or compression but not affected by shear stress. This design allows for optimal utilization of the material properties of the members. In a tensegrity basic unit, the bar members are of equal length, while the cable members come in three lengths: lower-end surface horizontal cable, upper-end surface horizontal cable, and stayed cable. The tensegrity basic unit with equal cable length simplifies this further by ensuring that all cables are the same length, resulting in a structure with only two member lengths, i.e., bar length and cable length, enhancing interchangeability. In order to find the form without the action of external forces, the force density coefficient ratio is introduced. By performing a force balance analysis on any node of the unit, the equilibrium equation of the structure is determined, incorporating the additional constraint of equal cable length. Two methods are employed to ascertain the force density coefficient ratio of each member in the unit: the theoretical derivation method based on the stable configuration condition of the tensegrity basic unit with equal cable length, and the method of solving the characteristic equations of the force density matrix. A program is developed to validate the form-finding method using basic units with three, four, five, and six bars as examples. The results show that the model accurately represents the physical structure, confirming the reliability of the form-finding methods.