Drafting new strategies and frontiers – CHAP ONE

Drafting new strategies and frontiers

Design topology and multi-objective optimization in form-finding of freeform tensegrity.

Dedicated to the work of my parents and to the dreams of my children. A self published essay of Alberto Campesato.


Chapter One




1.1 –  Tensegrity: past, present and undergoing research

 Inspired by the the work of a young artist called Snelson, and anticipated by Clerk Maxwell in 1864,  in the sixties R. Buckminster Fuller coined a new term referred to an intriguing structural principle: tensegrity. Since then a broad range of research and work has expanded our understanding of such systems, stimulating the quest for deployable lightweight systems. Suddenly, in the last decades new discoveries and definitions appeared, thanks to unprecedented numerical methods and symbolic computation softwares. A large discussion should go in the ambiguous definition of such system, but undoubtedly at Motro goes the merit to disengaged the patent based definition from the principle: “Tensegrity system is a system in stable self-equilibrated state comprising a discontinuous set of components inside a continuum of tensioned components”. Differently, Snelson gave a more comprehensive definition calling them endoskeletal prestressed structures, referring to the internal set of compressed elements holding the systems together with the outer network of cables . At the word endoskeleton we prefer the terms exoskeleton, recalling instead that in particular configurations, tensegrity systems create an hollow body where all carrying elements surround an empty, usable, volume. In what follows therefore, we talk of exoskeletal prestressed structures, later broadly recalled as “ intelligent tensegrity skins”.

Tensegrities have been often disregarded in the market of structural systems for a series of non-trivial issues, limiting their design or applicability compared to traditional truss structures that instead quickly encountered technological development and market demand. Indeed tensegrities systematically challenged the design both for static and dynamic configurations, drifting workable time into tedious manufacturing and assembling processes for their realisation.

Departing from these considerations, we committed to achieve concrete results for market applications. Such effort is not simply motivated by their intrinsic scalability, or unparalleled lightweight and material efficiency [16]. Indeed their natural deployability gained them a central role among deployable structures for space application. What mostly interested us is the inherent complexities that can be easily  embedded within such structural skin (Fig. 1).

Fig. 1. (a) tensegrity model; (b) geodetic tensegrity dome; (c) deployable tensegrity masts for space application.

Needless to say, a larger investigation from static behavior (Hernàndez and Mirats [7]) to dynamic response (Mirats and Hernàndez [11]); from the deployable configurability and dynamic control (Mirats and Hernàndez [11]; Adam and Smith [2]) to form finding design (Chandana et al. [5]) and design optimization (Masic et al. [10]) ; from biological similarities in modeling natural organism (Ingber [8]) to structural-material efficiency (Lieber [9]), gives the idea of potential implications in a more widespread use.

 To clarify the underneath principle, Hanaor distinguished pin-jointed skeletal structures composed of bar and cables in two major classes: not prestressable (statically determinate structure and mechanism) and prestressable (trusses structure and precisely tensegrity). Tensegrity stiffness depends on the state of self-stress -or prestress- keeping the integrity of the structural system from falling apart. Negligible masses and force fields acting at the nodes of the system do not influence their state of internal equilibrium either their stability. They do not require in general the presence of external forces (e.g. gravity) or any physical environment for the self-equilibrium being stable in any position and geometrically scalable. Therefore higher is the prestress applied, higher is the stiffness of the system responding to external actions. Deformability of elements in tension causes loss in stiffness of the system (Motro et al.  [12]).

The resolution of the prestressability problem is indeed one of the major challenges in the process of form finding. Further, results in the theory of rigidity and stability of frameworks achieved in the eighties by Connelly [6], Roth and Whiteley [15] helped to define new classes of mathematical objects –tensegrity frameworks– successfully resolving some simplified tensegrity topology using symbolical computational software.

 Referring to the work of Motro [13], we understood that tensegrity design has limitations firstly in the design phase: sets of equations are integrated till convergence at an optimized configuration, using dynamic relaxation methods. Secondly in the necessity of “mounting struts” that geometrically locate in space nodes throughout the assembling, preventing an easy free form construction. As outlined in prior works at the IASS 2010 Shanghai [3] and IASS 2015 Amsterdam [4], an approach focused in using an integrated design methodology to form find stable configurations suggest the possibility to avoids or contains such limitations. Therefore, integrating both design topology (form finding innovative configurations) and optimization topology (optimizing an existing one) within a unique design step, we use a combination of two software toolsets. Briefly, the input geometry is engineered into a sounding tensegrity system containing all the requirements for fast construction and assembly. We use a Rhino-script plugin to translate a desired model to a proto-topology input; then a standalone tailored software to optimize it.

1.2  –  A short introduction on living systems, chemistry and their virtual convergence. A prelude to nonlinear solutions: organism & biomimetic

Few know tensegrity has been used within the field of molecular biology to model virus structures (Caspar and Klug, 1962) and their behaviors undergoing external environmental changes. The interest has later moved to cytoskeleton: scaffold contained within the cytoplasm of living cell, that are protein polymer based cellular structures (Ingber, 1993). Surprisingly some mechanism of motion depending on the substrate the living cell moves on, was only understood once the model of tensegrity was introduced and explained. In recent years efforts have aimed to establish links between tensegrity systems, muscular-tendons-ligaments apparatus in vertebrates and mechanisms of locomotion to better comprehend living systems.

A puzzling problem such as the explanation of mechanisms behind human brain folds has been recently linked to simple mechanical instability associated with buckling. The relative expansion of the brain outer cortex with respect to the soft tissue underneath, causes the characteristic folding configuration based on the particular shape (Tuomas Tallinen et al. [17]). Interestingly, such natural folding lines due to mechanical instability occur in the attempt to balance material property limitations, responding geometrically to a buckling problem. Like in origami, folding lines create stiffer discontinuous sets of elements breaking the continuity of the outer -more flexible- layer. Recalling the Fuller definition of tensegrity such as “Islands of compression inside an ocean of tension” it cannot go unnoticed striking resemblances between cortical convolutions patterns and folding lines in tensegrity “envelops” we studied.

Fig. 2. Brain folds. Tuomas Tallinen et al.

Looking at other disciplines we were inspired by the work of Prigogine -Nobel in chemistry in 1977- showing the existence of oscillating chemical reactions, spatial structure of non equilibrium, chemical waves. All conditions generated far from the thermodynamics equilibrium, where instability (and non-linearity) drives the progression of the thermodynamic equilibrium and its final product. Such are “dissipative structures” increasing the production of entropy -instead of diminishing- in proximity of the equilibrium. Enzymes, ensuring the rich multiplicity of catalytic reactions and enabling life in all forms.

In static analysis otherwise, tensegrity is described and studied by nonlinear sets of equations and inequalities to be simultaneously solved together with the prestressability conditions. Resolving them results in the equilibrium, stability and rigidity of the system, non mentioning the system`s existence in the real world (non trivial solutions). Curiously such nonlinear search -compared to linear ones- leads to a richer set of solutions within wider spaces of possible configurations, challenging the notion of equilibrium. In such search-space each member of the system behaves -ideally- linearly: purely in tension or compression with zero momentum at the nodes.

We believe searching for new forms and systems that engineers the future obligatorily bring us to explore the “dynamic” equilibrium of systems. Considering systems statically and kinematically indeterminate able to withstand -under particular condition of prestress- stable configurations -such as tensegrities- opens opportunities in further explore the realm of equilibrium. Inspired by the work of Poincaré [i] and his approach, we have to develop alternative ways to freely design tensegrity. In such a perspective searching alternative methodologies to design, manufacture and activate tensegrity become an imperative goal in our studies. In what follows we present results and further speculations hopefully giving some extent of the possibilities at hand.

[i] Poincaré in the so called “problem of the three bodies” had to move away from conventional methods to resolve problems limited by the non-integrability of systems of non equilibrium. 

1.3  –  Engineering systems today: smart textile and biomimetic 

We were intrigued by the tensegrity inherent ability to contain within the envelope itself the whole structural framework needed for stability, enabling large scale structures with little weight and small size parts. The possibility of drawing a continuous pattern of forces with a minimum discontinuous path of compressed members within a continuum of tensioned members, offered the opportunity to experiment alternatives using the latest technologies available. Among others we considered 3D printing and injection moulding manufacturing versus standard construction methods of cables-struts systems, commonly seen in tensegrity structures. Improvements in manufacturing and assembling capability using an integrated methodology -from design to production- virtually brought us to rethink such  class of systems. A unique “structural” envelop possibly embedding multiple layers of utility: power supply, actuators, feedback sensors for static and kinematic response. Only recently such an opportunity has been more widely accepted with the emergence of e-textile technologies for smart “skin”. In such and similar directions Nottingham University together with EPSRC Centre for Innovative Manufacturing is working on multifunctional marketable components.   

Where common structural systems need costly and non-trivial processes to move from designing to manufacturing, our approach to tensegrity design is focused on ready-to-build design solutions, with unlimited  applicability. Issues imposed by the nature itself of tensegrity are therefore mitigated.

Standard lightweight controllable systems either require specific design to implement kinematic behaviors, or suffer in control problems to safely and precisely maneuver throughout the intended trajectory. Tensegrities on the other side are well accustomed -even if not trivial tasks- to be activated because of their nature of self-equilibrated “mechanism”. As system kinematically and statically indeterminate they may offer multiple self-stress states and mechanisms for a given framework: showing stable stiffness configuration where a proper self-stress function is applied to comply stabilization of infinitesimal mechanisms [7]. As such, they can outperform standard systems being able to better fit open-end solutions, or additionally capable to capture into their “envelope matrix” biomimetic principles. For example the ability -how we suggest in the followings- to tune the structural pattern around nodes through a gradient material matrix. A transitions from areas in tension to areas in compression within a unique envelope skin. We recall that biomimetic systems are engineered apparatus making use of embedded means to achieve higher functionality and superior resilience imitating principles and elements of nature. In such a perspective we think fields such as robotics (ex. Paul et al. [14]), lightweight exoskeleton (ex. ActiveLink-Panasonic with PowerLoader Light Ninja) and anthropomorphic prosthetic, or even responsive architecture (ex. Tristan D’Estree Sterk with ORAMBRA) could benefit from similar approaches or systems. Showing some results in such direction we intend to serve as an inspiring story of where future structural skins could further adventure.

1.4  –  A brief market analysis in robotic, prosthetics and lightweight system industry. Potential outcome and opportunities

The industrial robotic market is currently accountable for a +5% growth registered in 2012 with over 168.000 units globally sold in 2013 only (+5% compared to 2012). The average price per robot is estimated in 60.000 USD. USA and Japan markets dominate the run for industrial automation in manufacturing. Other markets escalating the economical expansion -Asia- or in moderate recession -Europe- are otherwise pursuing partial recovery thanks to industrial automation conversion. On the other side the marketplace for robotics is opening towards professionals and small businesses, diversifying and aggregating the offer in few larger competitors and small service suppliers.

In parallel the market of prosthetic -with a yearly growth of +3%- accounts a value of which 2.1 billions goes only into products, components and supplies. It is a consolidated market with growing drivers and growing number of players (fragmentation trend likely due to emerging 3D printing technologies) with locked value chains.

Both markets have a trend toward lightweight solutions targeting niche segments of customers. We believe a subsequent conjunction of the two mentioned markets – industrial robotics automation and prosthetic device- is soon going to generate a new segment of “enhancement personal device” for mobility and productivity. Compared to the existing offer, we think a favorable positioning should aim to lightweight low-cost solutions with limited payload and unparalleled performances. Of particular interest is the sub-segment of industrial robotics for beverage, electronics, medical and pharmaceutical sectors (35% of the global market of industrial robots depends on 5 Kg payload handling capacity). In the prosthetic field instead the sub-segment for upper extremity prostheses accounts already 41% among limb amputations. Capturing such an opportunity will drive innovation in terms of differentiated product, business model and customer relationship (“customer centered” markets). In such a perspective a differentiated offer minimizes usual investment costs, associated with lightweight high-end solutions, till today at the expense of small business competitiveness or customer affordability. Additionally it positively effects long term impact in non-competitive economies -third country without effective labor policies- that currently struggle with inadequate means widening marketplace opportunities. Offering to present and future customers an affordable new class of lightweight systems -with high performance and low cost- is a priceless asset strengthening core businesses and market expansion [1].

©️ 2010-2020 Alberto Campesato.


[1] ACCED A. Campesato Consulting Engineered Design. Business Plan. https://accedtech.files.wordpress.com/2016/03/bp-4.pdf . Accessed 2016/02/01. Please request if not available.

[2] Adam, B., & Smith, I.F.C. (2008). Active tensegrity: A control framework for an adaptive civil-engineering structure. Computers and Structures, 86, 2215-2223.

[3] Campesato, A. (2010). Tensegrity CAD: a new methodology in computer aided design to form find tensegrity systems. Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2010, Shanghai Spatial Structures – Permanent and Temporary, November 8-12 2010, Shanghai, China.

[4] Campesato, A. (2015). The possibility of unparalleled structural systems. Experiments towards novel models of tensegrity. Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam. Spatial Structures – Future Visions, August 17-20 2015, Amsterdam, The Netherlands.

[5] Chandana, P., Hod, L., & Valero Cuevas, F.J. (2005).  Evolutionary form-finding of tensegrity structures. Proceedings of the 2005 Conference on Genetic and evolutionary computation, June 25-29, 2005, Washington DC, USA. 

[6] Connelly, R. (1980). The rigidity of certain cabled networks and the second order rigidity of arbitrarily triangulated convex surfaces. Advances in Mathematics, 37, 272–299.

[7] Hernández, J.S., & Mirats Tur, J.M. (2008). Tensegrity frameworks: static analysis review. Mechanism and Machine Theory, 43(7), 859-881.

[8] Ingber, D.E. (1998). The Architecture of Life. Scientific American, January, 48-57.

[9] Lieber R.L. (2002). Skeletal Muscle Structure, Function and Plasticity. Lippicott Williams & Wilkins.

[10] Masic M. et al. (2006). Optimization of tensegrity structures. International Journal of Solids and Structures, 43, 4687-4703.

[11] Mirats Tur, J.M., & Hernández, J.S. (2009). Tensegrity frameworks: dynamic analysis review and open problems. Mechanism and Machine Theory, 44, 1-18.

[12] Motro, R., Najari, S., & Jouanna P. (1986).  Tensegrity systems. From design to realization. Proceedings of the First International conference on Lightweight structures in architecture 1986.

[13] Motro, R. (2009). Structural morphology of tensegrity systems. Asian Journal of Civil Engineering (Building and Housing), 10, 1-19.

[14] Paul, C., Valero-Cuevas,  F., & Lipson, H. (2006). Design and control of tensegrity robots for locomotion. IEEE Transactions on Robotics, 22(5),  944–956.

[15] Roth, B., & Whiteley, W. (1981). Tensegrity frameworks. Transactions of the American Mathematical Society, 265, 419–446.

[16] Sultan, C. (2009). Tensegrity: 60 years of art, science, and engineering. Advances in Applied Mechanics, 43.

[17] Tuomas Tallinen et al.. (2016). On growth and form of cortical convolutions. Nature Physics; Available on-line 2016/02/01.

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