Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group

Dataset

Description

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. The Segre embedding arises from a representation of the special Euclidean group in three dimensions which has degree 40. We also consider the special Euclidean group in other dimensions.

Attributes

Attribute NameValues
Creator
  • Jonathan Hauenstein

Contributor
  • Samantha Sherman

  • Charles Wampler

Publisher
  • Jonathan Hauenstein

Departments and Units
Record Visibility and Access Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0R20Z94

This DOI is the best way to cite this dataset.


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