English

Universality of Polyhedral Linkages

Combinatorics 2025-02-25 v1 Metric Geometry

Abstract

Planar linkages are a rich area of study motivated by practical applications in engineering mechanisms. A central result is Kempe's Universality Theorem, which states that semi-algebraic sets can be realized by planar linkages. Polyhedral linkages are generalizations of planar linkages to higher dimensions, where the faces are required to be rigid. In this paper, we generalize Kempe's Universality Theorem to polyhedral linkages with an embedded construction in dimension three and above.

Keywords

Cite

@article{arxiv.2502.16855,
  title  = {Universality of Polyhedral Linkages},
  author = {Robert Miranda},
  journal= {arXiv preprint arXiv:2502.16855},
  year   = {2025}
}

Comments

15 pages, 13 figures

R2 v1 2026-06-28T21:55:00.527Z