This blog was first published in March 2010 as a record of my study into Tensegrity structures and forms. Most recently (Jan/Feb 2012) I have had the opportunity to correspond with a number of fellow enthusiasts and have realised that symmetrical geometry inherent within the complexity of tensegrity structures is not as widely recognised as I perceived it might be.
Initially being just a record of my work in progress at that time my blog was not well organised, essentially just a collection of observations. During the next few months I will reorganise the content to better explain my discoveries pertinent to Tensegrity Symmetry, my analysis of the various structures the underlying geometric regularities and how from this we can evolve a simpler understanding of the basic geometry mathematics.
Tensegrity structures at first appear to be quite complex and certainly the current understanding of the mathematics behind the Tensegrity forms seem to support this. But is it really that complex?... after all many if not the majority of Tensegrity structures exhibit a number of constants relating to lengths of compression members and similarly the groupings of tendons containing common properties. When we consider the relationships between these structural elements in the final construction it is quite reasonable to expect that there must be an underlying geometric symmetry that helps defines the end product.
My work will attempt to uncover these geometric consistencies which I collectively call "Tensegrity Symmetry" comprising both axis/rotational and geometric symmetry.
Axis/Rotational Symmetry:
Axis/Rotational symmetry refers to axis projections that can be derived within translational tensegrites i.e. those formed from platonic geometry to a tensegrity structure.
In later articles I explore this in detail; essentially when we recognise relationships conforming to platonic forms that easily translate to tensegrities (morphing) we can determine axis lines projected from the centre of the platonic edges to the centroid. It follows that each strut transitioning to a tensegrity structure will retain a midpoint relationship with these axis.
The struts will also be perpendicular to the line of the projected axis and revolve around this axis equally (assuming same strut lengths) according to the length of tendons used.
Geometric Symmetry:
Geometric Symmetry refers to identifiable geometric planar geometry such as circles, triangles and squares that are integral to the formation of the tensegrity structure.
In the example on the left is an abstract from a recent study that I did for Marcelo Pars Icosahedron Tensegrity. As you can see the end of the struts are equally coincident with the circumference of a planar circle. It also transpires that this circle is exactly parallel to the plane defined by the external tendons. The axis as shown is centred about both the planar circle and the external defined planes.
These relationships remain constant for all dimensional variants within the parameters defined by this structure.
By analysing tensegrity in this manner and identifying geometric symmetry it is then simply the application of very basic geometry mathematics to determine either the tendon or strut lengths.
For more details on this icosahedron see http://www.tensegriteit.nl/e-icosahedron.html
The majority of tensegrity structures I will explore are based on architectural designs derived by others. My main purpose is close examination of these structures to determine geometric symmetry and relationships to further the understanding of tensegrity. In the example above the originator of this design was unaware of these particular geometric relationships prior to this study.
Building or Modelling:
So if you are constructing physical Tensegrity models or even creating them using 3D cad then by knowing the basic geometric forms in conjunction with the Axis/Rotational Symmetry it is going to be so much easier to do this than delving into the complexity of the underlying mathematics.
Initially being just a record of my work in progress at that time my blog was not well organised, essentially just a collection of observations. During the next few months I will reorganise the content to better explain my discoveries pertinent to Tensegrity Symmetry, my analysis of the various structures the underlying geometric regularities and how from this we can evolve a simpler understanding of the basic geometry mathematics.
Tensegrity structures at first appear to be quite complex and certainly the current understanding of the mathematics behind the Tensegrity forms seem to support this. But is it really that complex?... after all many if not the majority of Tensegrity structures exhibit a number of constants relating to lengths of compression members and similarly the groupings of tendons containing common properties. When we consider the relationships between these structural elements in the final construction it is quite reasonable to expect that there must be an underlying geometric symmetry that helps defines the end product.
My work will attempt to uncover these geometric consistencies which I collectively call "Tensegrity Symmetry" comprising both axis/rotational and geometric symmetry.
Axis/Rotational Symmetry:
In later articles I explore this in detail; essentially when we recognise relationships conforming to platonic forms that easily translate to tensegrities (morphing) we can determine axis lines projected from the centre of the platonic edges to the centroid. It follows that each strut transitioning to a tensegrity structure will retain a midpoint relationship with these axis.
The struts will also be perpendicular to the line of the projected axis and revolve around this axis equally (assuming same strut lengths) according to the length of tendons used.
Geometric Symmetry:
In the example on the left is an abstract from a recent study that I did for Marcelo Pars Icosahedron Tensegrity. As you can see the end of the struts are equally coincident with the circumference of a planar circle. It also transpires that this circle is exactly parallel to the plane defined by the external tendons. The axis as shown is centred about both the planar circle and the external defined planes.
These relationships remain constant for all dimensional variants within the parameters defined by this structure.
By analysing tensegrity in this manner and identifying geometric symmetry it is then simply the application of very basic geometry mathematics to determine either the tendon or strut lengths.
For more details on this icosahedron see http://www.tensegriteit.nl/e-icosahedron.html
The majority of tensegrity structures I will explore are based on architectural designs derived by others. My main purpose is close examination of these structures to determine geometric symmetry and relationships to further the understanding of tensegrity. In the example above the originator of this design was unaware of these particular geometric relationships prior to this study.
Building or Modelling:
So if you are constructing physical Tensegrity models or even creating them using 3D cad then by knowing the basic geometric forms in conjunction with the Axis/Rotational Symmetry it is going to be so much easier to do this than delving into the complexity of the underlying mathematics.
