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Results tagged with rigidity
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user 353
3
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Is the following two-dimensional graph likely to be globally rigid?
But -- generic global rigidity is a property just of the graph $G$ (generic global rigidity means global rigidity for any embedding of the graph where the positions of the vertices are algebraically independent … I won't give a definition of the rigidity matrix (sometimes "stress matrix") here -- you can find it in most of the papers on rigidity that I've cited. …
- 13.6k
1
vote
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Isostatic graphs and the Henneberg conjecture
Question 2 can be addressed computationally by computing the ranks of generic rigidity matrices corresponding to the sequence of graphs. … First, I wrote some ugly code to compute a 4 dimensional rigidity matrix. …
- 13.6k
6
votes
Accepted
Which criteria guarantee an orthogonal circuit in $\mathbb R^3$ to be rigid?
In this answer, I will follow you in calling your structures "circuits", despite the fact that this conflicts with the term used for a minimal dependent set of constraints in rigidity theory. … A circuit that is generic in the usual sense of rigidity theory (e.g. one where the segments and angles between segments are chosen so that they are algebraically independent) is at least as rigid as your …
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9
votes
Accepted
Alexandrov's generalization of Cauchy's rigidity theorem
The following is Theorem 27.2 of Igor Pak's book Lectures on Discrete and Polyhedral Geometry (which in general is a very nice resource for these sorts of questions):
Let $P,Q\subset\mathbb{R}^d$ …
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