A modified dynamic relaxation form-finding method for general tensegrity structures with inextensible tensile members

In tensegrity structures, there may exist tensile members with very low elongation. This type of tensile member is almost inextensible under the effect of tensile force and cannot effectively utilize length change to calculate axial force, posing challenge in form-finding. In this paper, a modified dynamic relaxation (DR) form-finding method for general tensegrity structures with inextensible tensile members is presented. The method considers the compressive members as rigid bodies and establishes pseudo-dynamic equation that incorporate both forces and torques. The existence of inextensible tensile members constrains on the motion of rigid bodies, the mobility analysis via screw theory can decompose the wrenches acting on the rigid bodies into their degrees of freedom space. Through iterative processes, rigid compressive members movement towards equilibrium poses under the action of unbalanced wrenches within the permissible range of mobilities. Numerical examples demonstrate the effectiveness of the proposed method in form-finding of classic tensegrity, general tensegrity, and clustered tensegrity.