Acta Mech Sin (2010) 26:559–565 DOI 10.1007/s10409-010-0351-6 RESEARCH PAPER Design methods of rhombic tensegrity structures Xi-Qiao Feng · Yue Li · Yan-Ping Cao · Shou-Wen Yu · Yuan-Tong Gu Received: 7 December 2009 / Accepted: 20 January 2010 / Published online: 13 May 2010 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2010 Abstract As a special type of novel flexible structures, tensegrity holds promise for many potential applications in such fields as materials science, biomechanics, civil and aerospace engineering. Rhombic systems are an important class of tensegrity structures, in which each bar constitutes the longest diagonal of a rhombus of four strings. In this paper, we address the design methods of rhombic structures based on the idea that many tensegrity structures can be con- structed by assembling one-bar elementary cells. By analyz- ing the properties of rhombic cells, we first develop two novel schemes, namely, direct enumeration scheme and cell-sub- stitution scheme. In addition, a facile and efficient method is presented to integrate several rhombic systems into a larger tensegrity structure. To illustrate the applications of these methods, some novel rhombic tensegrity structures are con- structed. Keywords Tensegrity · Structural design · Assembling method · Flexible structure The project was supported by the National Natural Science Foundation of China (10732050), Tsinghua University (2009THZ02122), and the National Basic Research Program of China (973) (2010CB631005). X.-Q. Feng (B ) · Y. Li · Y.-P. Cao · S.-W. Yu AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China e-mail: fengxq@tsinghua.edu.cn Y.-T. Gu School of Engineering Systems, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia 1 Introduction As a novel type of structures, tensegrity consists of a set of discontinuous compression components and a set of contin- uous tensile components [1]. In 1962, Fuller [2] coined the name “tensegrity” as a contraction of two words, tensile and integrity. In his patent, tensegrity was described as “Islands of compression inside an ocean of tension”. Later, Pugh [3] proposed the following definition: “A tensegrity system is established when a set of discontinuous compression compo- nents interacts with a set of continuous tensile components to define a stable volume in space”, which has been widely accepted nowadays. In practice, tensegrity structures are usu- ally modeled as a set of weightless discontinuous bars (or struts) and continuous strings (or cables) connected by fric- tionless ball joints. The bars can withstand both compression and tension, while the strings can only carry tensile forces. Both bars and strings are prestressed and subjected to an axial load [4, 5]. In the past decades, tensegrity structures have attracted considerable attention from a diversity of fields, e.g., mathe- matics [6], civil engineering [7], aerospace engineering [8, 9], and materials science [10]. Recently, much effort has been directed towards the applications of tensegrity in the model- ing of such biological systems as cells and tissues [11–14] and the design methods of tensegrity structures [15–21]. Many natural and artificial materials and structures can be regarded as generalized tensegrity [1, 9, 18, 22]. With the increase in the scale and complexity of the systems involved in their appli- cations, a crucial issue naturally arises as to how large-scale tensegrity structures with specific geometry and mechanical properties can be designed. Among others, a basic idea is to construct a tensegrity structure by assembling elementary modules together in a certain manner. Most of the previous assembling design methods use two-dimensional X-frame 123