From graphs to tensegrity structures: Geometric and symbolic approaches
نویسندگان
چکیده
منابع مشابه
From graphs to tensegrity structures: Geometric and symbolic approaches
A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to decide whether it can be the underlying graph of a tensegrity in R (typically d = 2, 3) with vertices in general position. Furthermore, our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices, for what we propose both a geometric and a...
متن کاملFinding tensegrity structures: Geometric and symbolic approaches
Two examples of a particular kind of form-finding problems are studied; given a set of fixed points, we ask for the position of an extra point such that a given framework admits a self-stress and hence a tensegrity structure can be built from it. We present two different approaches to solve these problems: The first method is geometric and hence more visual. A symbolic method is proposed as a s...
متن کاملSymbolic Stiffness Optimization of Planar Tensegrity Structures
During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is...
متن کاملProximity Structures for Geometric Graphs
In this paper we study proximity structures like Delaunay triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define several Voronoi diagrams, Delaunay triangulations, relative neighborhood graphs, Gabriel graphs and then study their complexities when G is a general geometric graph or G is some speci...
متن کاملDesigning tensegrity structures
Tensegrity structures are nice-looking and statically strong architectural complexes composed of a set of disjoint struts tied together by cables and nothing more. These structures are known for their aesthetic and structural qualities, which are explored in architecture and art. Their perceived lightness is their distinct visual feature: the heavy elements (the struts) are well disjoint, yet t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2006
ISSN: 0214-1493
DOI: 10.5565/publmat_50206_02