Abstract：To study the topological morphology of tensegrity structures with specified node coordinates, a topology shape finding method is proposed to form the scheme matrix by directly coding the connectivity matrix. Based on the morphology analysis of tensegrity structures, the number of components that connected to node is taken as the constraint index. The placement of element can be determined by reasonably selecting certain elements in the scheme matrix. The topology finding of tensegrities is completely realized by combining the stability judgement condition with the relationship established from the variables (0, -1) and the structural geometric stability. Several tensegrity structures with high symmetry of topological morphology are found in two spatial tensegrity structure examples using the symmetric index, demonstrating the feasibility and validity of the proposed algorithm in searching the topological morphology of tensegrities with specified nodes. For the case of a spatial tensegrity structure comprising of 26 elements, 17 topological morphologies with different number of struts are found, and the critical value of force density symmetric index is determined as 0.3846. For the space tensegrity structure with 36 components, 5 topological configurations with same number of struts are obtained. It is worth noting that the feasible configurations meeting the specific requirements of practical projects can be achived by adjusting the weight ratio of different design parameters in the performance-evaluation index.
