Title | ||
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Exceptional Stewart-Gough Platforms, Segre Embeddings, And The Special Euclidean Group |
Abstract | ||
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Stewart-Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart-Gough platform is rigid with 40 assembly configurations (over the complex numbers), while exceptional Stewart-Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart-Gough platforms called Segre-dependent Stewart-Gough platforms which arise from a linear dependency of point-pairs under the Segre embedding and compute an irreducible decomposition of this family. We also consider Stewart-Gough platforms which move with two degrees of freedom. Since the Segre embedding arises from a representation of the special Euclidean group in three dimensions which has degree 40, we consider the special Euclidean group in other dimensions and compute spatial Stewart-Gough platforms that move in 4-dimensional space. |
Year | DOI | Venue |
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2018 | 10.1137/17M1114284 | SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY |
Keywords | DocType | Volume |
Stewart-Gough platform, architecturally singular, Segre embedding, special Euclidean group, numerical algebraic geometry | Journal | 2 |
Issue | ISSN | Citations |
1 | 2470-6566 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Jonathan D. Hauenstein | 1 | 269 | 37.65 |
Samantha N. Sherman | 2 | 1 | 0.76 |
Charles W. Wampler | 3 | 410 | 44.13 |