Skew lines are defined in mathematics as lines that are neither perpendicular nor parallel. A skew polyhedron is a polyhedron where the edges do not meet at its vertices. Such a geometric form may be considered as either (a) the polyhedron that it would form if the edges did meet at the vertices, or (b) the truncated polyhedron that is described by both the geometric figure outlined by the edges, and the polygon outlined by the edge ends in their skew formation.

Read here about skew lines in tensegrity structures and tensegrity mathematics.

Schenk wrote, tensegrity prisms have regularly been analysed in tensegrity literature, as they allow for analytical equilibrium solutions. Tensegrity prisms are here taken to be tensegrities where the vertices form two equilateral polygons on parallel planes (where all vertices in a plane lie on a circle). For regular tensegrity prisms the perpendicular through the centre of one end of the prism is parallel to, and coincident with, a perpendicular through the centre of the other end. For a prism to be strictly skew, the perpendiculars are still parallel, but are not coincident. Burkhardt describes a non-linear programming approach to designing skew tensegrity prisms, and several observations are made.

This paper describes the properties of skew tensegrity prisms. Schenk explains the observation that the twist angle is the same for both cases, and shows that the analytical equilibrium solutions from the regular tensegrity prisms also apply to their skewed counterparts. By showing that the analytical equilibrium solutions of regular tensegrity prisms still hold for their skewed counterparts -- making use of the fact that the equilibrium of a tensegrity structure is preserved under an affine transformation -- it validates and explains previous numerical results.

## Skew

## Table of Contents

Skewlines are defined in mathematics as lines that are neither perpendicular nor parallel. A skew polyhedron is a polyhedron where the edges do not meet at its vertices. Such a geometric form may be considered as either (a) the polyhedron that it would form if the edges did meet at the vertices, or (b) the truncated polyhedron that is described by both the geometric figure outlined by the edges, and the polygon outlined by the edge ends in their skew formation.Read here about skew lines in tensegrity structures and tensegrity mathematics.

## Analysis of Skew Tensegrity Prisms

Analysis of Skew Tensegrity Prisms by Schenk

Link: http://www.scribd.com/doc/29350474/Analysis-of-Skew-Tensegrity-Prisms-by-Schenk

Schenk wrote, tensegrity prisms have regularly been analysed in tensegrity literature, as they allow for analytical equilibrium solutions. Tensegrity prisms are here taken to be tensegrities where the vertices form two equilateral polygons on parallel planes (where all vertices in a plane lie on a circle). For regular tensegrity prisms the perpendicular through the centre of one end of the prism is parallel to, and coincident with, a perpendicular through the centre of the other end. For a prism to be strictly skew, the perpendiculars are still parallel, but are not coincident. Burkhardt describes a non-linear programming approach to designing skew tensegrity prisms, and several observations are made.

This paper describes the properties of skew tensegrity prisms. Schenk explains the observation that the twist angle is the same for both cases, and shows that the analytical equilibrium solutions from the regular tensegrity prisms also apply to their skewed counterparts. By showing that the analytical equilibrium solutions of regular tensegrity prisms still hold for their skewed counterparts -- making use of the fact that the equilibrium of a tensegrity structure is preserved under an affine transformation -- it validates and explains previous numerical results.

<object id="doc_200595056346234" name="doc_200595056346234" height="600" width="100%" type="application/x-shockwave-flash" data="http://d1.scribdassets.com/ScribdViewer.swf" ><param name="movie" value="http://d1.scribdassets.com/ScribdViewer.swf"><param name="wmode" value="opaque"><param name="bgcolor" value="#ffffff"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><param name="FlashVars" value="document_id=29350474&access_key=key-1cshp56kqcfzk27k254c&page=1&viewMode=list"><embed id="doc_200595056346234" name="doc_200595056346234" src="http://d1.scribdassets.com/ScribdViewer.swf?document_id=29350474&access_key=key-1cshp56kqcfzk27k254c&page=1&viewMode=list" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="600" width="100%" wmode="opaque" bgcolor="#ffffff"></embed></object>

Link: http://www.scribd.com/doc/35190357/Analysis-of-Skew-Tensegrity-Prisms-by-Schenk

<object id="doc_951094859519783" name="doc_951094859519783" height="600" width="100%" type="application/x-shockwave-flash" data="http://d1.scribdassets.com/ScribdViewer.swf" ><param name="movie" value="http://d1.scribdassets.com/ScribdViewer.swf"><param name="wmode" value="opaque"><param name="bgcolor" value="#ffffff"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><param name="FlashVars" value="document_id=35190357&access_key=key-lh6lo5y8psulvtvftwy&page=1&viewMode=list"><embed id="doc_951094859519783" name="doc_951094859519783" src="http://d1.scribdassets.com/ScribdViewer.swf?document_id=35190357&access_key=key-lh6lo5y8psulvtvftwy&page=1&viewMode=list" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="600" width="100%" wmode="opaque" bgcolor="#ffffff"></embed></object>

Link: http://www.scribd.com/doc/35313117/Skew-Tensegrity-Prisms-Response-to-Burkhardt-by-Schenk

<object id="doc_850500263979962" name="doc_850500263979962" height="600" width="100%" type="application/x-shockwave-flash" data="http://d1.scribdassets.com/ScribdViewer.swf" ><param name="movie" value="http://d1.scribdassets.com/ScribdViewer.swf"><param name="wmode" value="opaque"><param name="bgcolor" value="#ffffff"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><param name="FlashVars" value="document_id=35313117&access_key=key-c2ovby90jhkp7aldfd1&page=1&viewMode=list"><embed id="doc_850500263979962" name="doc_850500263979962" src="http://d1.scribdassets.com/ScribdViewer.swf?document_id=35313117&access_key=key-c2ovby90jhkp7aldfd1&page=1&viewMode=list" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="600" width="100%" wmode="opaque" bgcolor="#ffffff"></embed></object>

## Links and References

See also Weaving.Portal To MathematicsPeople: Burkhardt, Connelly, Kenner, Hart, Whiteley