This paper hands in a review of the basic issues about the statics of tensegrity structures. Definitions and notation for the most important concepts, borrowed from the vast existing literature, are summarized. All of these concepts and definitions provide a complete mathematical framework to analyze the rigidity and stability properties of tensegrity structures from three different, but related, points of view: motions, forces and energy approaches. Several rigidity and stability definitions are presented in this paper and hierarchically ordered, from the strongest condition of infinitesimal rigidity to the more wide concept of simple rigidity, so extending some previous classifications already available.Important theorems regarding the relationship between these definitions are also put together to complete the static overview of tensegrity structures. Examples of different tensegrity structures belonging to each of the rigidity and stability categories presented are described and analyzed. Concluding the static analysis of tensegrity structures, a review of existing form-finding methods is presented.

Many water companies have a limited knowledge of the structural condition of their assets. Underground assets have been installed for a long time, so they are old and are failing, leading to leaks, breaks, and consequential damage to third parties. A common practice is the removal of pipe sections for condition assessment, causing service interruption and resulting in the assessment of a small percentage of the network as well as high replacement costs. Systematic condition assessment of pipes could help to prevent network problems as well as in proposing an efficient investment plan. This can be performed by using robotic inspection devices. Toward this end, this paper reviews existing robotic tools and analyzes open problems to be addressed for a successful robotic inspection device. C

The main objective of this paper is twofold. First, to conclude the overview about tensegrity frameworks, started by the same authors in a previous work, covering the most important dynamic aspects of such structures. Here, the most common approaches to tensegrity dynamic modeling used so far are presented, giving the most important results about their dynamic behavior under external action.Also, the main underlying problems are identified which allow the authors to give a clear picture of the main research lines currently open, as well as the most relevant contributions in each of them, which is in fact the second main objective of this paper. From the extensive literature available on the subject, four main areas have been identified: design and form-finding methods which deal with the problem of finding stable configurations, shape changing algorithms which deal with the problem of finding stable trajectories between them and, also control algorithms which take into account the dynamic model of the tensegrity structure and possible external perturbations to achieve the desired goal and performance.Finally, some applications of such structures are presented emphasizing the increasing interest of the scientific community on tensegrity structures.

a b s t r a c tThis paper presents a novel form-finding algorithm for tensegrity structures that is based on the finite element method. The required data for the form-finding is the topology of the structure, undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The form-finding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two-and three-dimensional examples are presented that demonstrate the excellent performance of the proposed algorithm.

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