Henneberg moves on mechanisms

A bar-and-joint framework in the plane with degree of freedom 1 is called a mechanism. It is well-known that the operations of 0-extension and 1-extension, the so called Henneberg moves, can always be performed on a framework so that its degree of freedom is preserved. It was conjectured by the firs...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2015-10, Vol.56 (2), p.587-591
Main Authors: Jackson, Bill, Jordán, Tibor, Servatius, Brigitte, Servatius, Herman
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
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Summary:A bar-and-joint framework in the plane with degree of freedom 1 is called a mechanism. It is well-known that the operations of 0-extension and 1-extension, the so called Henneberg moves, can always be performed on a framework so that its degree of freedom is preserved. It was conjectured by the first and second author in 2012 that for a mechanism in generic position these operations can be performed without restricting its motion. In this note we provide a counterexample.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-014-0217-3