Extending a flexible unit-bar framework to a rigid one

✍ Scribed by Hiroshi Maehara

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 494 KB
• Volume: 108
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90671-2

✦ Synopsis

We prove that (1) a flexible unit-bar framework G in R" can always be extended to a rigid unit-bar framework in R", and (2) G is 'congruent' to a subgraph of a rigid unit-bar framework in R" if and only if the Euclidean distances between joints of G are all algebraic numbers. Meanwhile, it is proved that a previous result on a framework in R* [for any real algebraic number r > 0, there is a rigid unit-bar framework in R* having two vertices with distance r apart] extends to any dimension.