# Tensegrity Applications to Architecture, Engineering and Robotics: A Review
## 1 Introduction  
Tensegrity is a principle that is said to have been discovered for the first time about 75 years ago, although some authors claim that it was created by [PERSON] more than 100 years ago [1]. In fact, the authors of the present work have found a picture from 1921 (Figure 1) where [PERSON]'s tensegrity prototypes can be seen with the first example of a Simplex [2, 3], which was patented some decades later. Figure 1: [PERSON]’s tensegrity prototypes showing the first example of a Simplex (figure on the left-hand side) in 1921. Reprinted with permission from Refs. [2, 3]. Tensegrity governs the behavior of many structures within the engineering scope [4]. Throughout the years, many definitions have been given to this principle. On an informal basis, tensegrities are prestressed and self-stable pin-connected frameworks built up from two kinds of elements, bars and tendons [5]. Bars, also called struts, will always carry compression, whereas tendons (cables, wires, strings or membranes) can only work under tension. The former are usually made of wood, bamboo or metal (steel, aluminum, titanium, etc. ), while the latter can be built from steel wires, elastic cords and bands, ropes, elastic membranes, adaptive fabrics, etc. One of the precursors of tensegrity, [PERSON], defined tensegrity as \"_islands of compression in an ocean of tension_\". In fact, what he said on a TV interview was that \"what nature has is islands of spherical compression in a sea of comprehensive tension\" [6]. As is well known, he was responsible for coining these kinds of structures as \"Tensegrity\" resulting from the contraction of the two words \"tensional\" and \"integrity\" [7]. One of the problems that we have come across when collecting all the information for this review is the misperception of the concept. The term \"tensegrity\" has been used to refer to structures composed of compressed and tensioned elements regardless of their self-stress condition. In fact, most bar-tendon configurations that one might conceive are not in equilibrium, and once constructed would collapse and change their shape unless they are sustained by external supports. Therefore, the global stability needs to be checked, which is often ignored, and, as a consequence, leads to structures that cannot remain stable once they have been realized [8; 9]. That is why only prestressed bar-cable configurations in stable equilibrium can be called tensegrity structures [10; 11]. Another distinguishing characteristic of these structures, in its purest conception, is that two compressed elements cannot be connected one to another. If two bars join at the same node, it will be considered as a k = 2 tensegrity structure; if 3 bars meet, k = 3 tensegrity, and so on [12]. Since their \"official\" discovery in the late 1940s by [PERSON], tensegrity structures have captured the attention of many engineers, architects, and artists due to their unique advantages and peculiar properties, one of which is that the bars do not touch each other [13]. Some of their singular features are:  
* Self-equilibrium: the stability of the structure depends on its own configuration and topology, not on external supports. * Lightweight and efficiency: tensegrity structures use longitudinal members arranged in an unusual pattern to achieve strength with small mass. * Deployability: due to the fact that the compressed members are connected by ball joints, they are easy to fold. * Small compression volume: the structure has a certain degree of compliance in all degrees of freedom. * Low control cost [5; 10]. Due to all these advantages, tensegrity-based structures have been offering a very interesting field of study in a wide range of engineering scopes. However, these unique structures have struggled when trying to make their way into all the different architecture and engineering fields. Some of the difficulties they have had to face include a problem of bar congestion--when some designs become larger, the struts start colliding with each other [14].