On Spaces of Infinitesimal Motions and Henneberg Extensions

TL;DR

This paper studies the structure of infinitesimal motion spaces in rigidity theory, proving theorems that advance understanding of Henneberg extensions and their relation to graph rigidity.

Contribution

It provides new structure theorems for infinitesimal motion spaces and addresses special cases of a longstanding conjecture in rigidity theory.

Findings

Established structure theorems for infinitesimal motion spaces

Deduced results related to Henneberg extensions and graph rigidity

Contributed to resolving parts of a long-standing conjecture

Abstract

We investigate certain spaces of infinitesimal motions arising naturally in the rigidity theory of bar and joint frameworks. We prove some structure theorems for these spaces and as a consequence are able to deduce some special cases of a long standing conjecture of Graver, Tay and Whiteley concerning Henneberg extensions and generically rigid graphs.