منابع مشابه
Rigidity of Graphs and Frameworks
The first reference to the rigidity of frameworks in the mathematical literature occurs in a problem posed by Euler in 1776. Consider a polyhedron P in 3-space. We view P as a ‘ panel-and-hinge framework’ in which the faces are 2-dimensional panels and the edges are 1-dimensional hinges. The panels are free to move continuously in 3space, subject to the constraints that the shapes of the panels...
متن کاملFrameworks, Symmetry and Rigidity Supported by a London Mathematical Society Scheme 7 Grant
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R d. This leads to a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including the constrained point-line systems that appear in CAD, body-pin frameworks, and hybrid syste...
متن کاملCombinatorics and the Rigidity of Frameworks
A wide variety of physical structures, e.g. scaffolding (rigid), or a DNA molecule (non-rigid), may be modeled as a collection of rigid rods connected to one another by idealized ball joints. For a given structure, the basic question that arises is whether it is rigid and, if not, how to describe its motion. We would like to describe some of the applications of combinatorics to this area. By a ...
متن کاملThe Rigidity of Frameworks: Theory and Applications
DOI: http://dx.doi.org/10.1090/noti1575 P icture a swarm of robots flying to move a piece of rubble from a disaster site, an engineer designing the roof of a stadium, or a protein docking an inhibiting drug. What these scenarios, pulled from robotics, computer-aided design (CAD), and structural biology, have in common is that each is governed by a finite system of geometric constraints that can...
متن کاملConing, Symmetry and Spherical Frameworks
In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning [28], (b) the further transfer of these results to spherical space via associated rigidity matrices [19], and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetryderived orbit rigidity...
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ژورنال
عنوان ژورنال: International Journal of Computational Geometry & Applications
سال: 2010
ISSN: 0218-1959,1793-6357
DOI: 10.1142/s0218195910003505