Tensegrity

Tensegrity is an architectural principle in which both compressive and tensile forces are employed to create a static structure. The word is an amalgamation of tension and integrity.

Sculpture

Tensegrity is not typically employed in architecture, though there are a few examples. More commonly, tensegrity manifests as sculptures. Kenneth Snelson (Wiki, Personal Website) is perhaps the best known creator of tensegrity structures, and either created or played a pivotal role in the development of the concept.
I became seriously interested in tenesgrity in 2013 and have been building the physical structures as well as developing methods to perform the calculations necessary to build them since then. Shown here are several tensegrity structures that I have constructed based on simulations.

Simulation

Constructing tensegrity models requires calculation of the strut and tendon lengths. My current approach is to model the system as a spring-mass system with stiff and weak springs corresponding to struts and tendons, respectively.

Initial strut and tendon configuration. The layout of the struts (shown in orange) is selected by the rough placement of the strut endpoints (shown in black), and the tendons (shown in blue) are then added.
The strut-tendon system is converted into a spring-mass system, where the masses are taken to be the endpoints of the struts, and springs of two stiffnesses are added: weak springs in place of each tendon, and strong springs in place of each strut. Here the masses are omitted and the springs are shown in red to indicate tension, green to indicate compression, and the width of the line is proportional to the magnitude of the spring stiffness.
The spring-mass system is allowed to evolve in time. The system at rest in static equilibrium can be constructed as a tensegrity. Pictured is an intermediate stage in which the system has evolved for a time. Note that in both the initial configuration and in this state, the springs corresponding to struts are in compression and the tendons in tension. This is necessary to produce a valid tensegrity.

The following video illustrates the entire process:

Polyhedra-Induced Tensegrities

Tensegrity structures come in many forms. One way of creating the structures is based on a derivation from polyhedra. The edges of the polyhedron are converted to struts, and adjacent struts are connected if the vertices of their parent edges were either the same, or adjacent vertices.


What follows are some examples of tensegrities derived from various polyhedra with various configurations.

Tetrahedron


Octahedron


Icosahedron


Truncated Tetrahedron