Geometric Drawing Method for Form-finding and Force-finding to Triangular Prism Tensegrity with End Surfaces not Paralleled

Abstract

The triangular prism tensegrity with arbitrary triangle bottom and end surfaces not paralleled is the most common type tensegrity structure. A geometric drawing method with four steps’ process for form-finding was given based on the properity of tensegrity structure, and the degree of freedom for form-finding was analysied. The force-finding method with ten steps’ process was given after form-finding, and the self-balancing internal forces was obtained by measuring the lengths of correspondant line segements. The geometric drawing method was carried out in CAD software by an example, and the example tensegrity structure obtained by the method was analysed by finite element method software, the correctness of the method was verified. The form-finding method is the geometric implementation of the force density method, and the process is intuitive and controllable, it is suitable and operational for triangular prism of tensegrity structures of any shape.