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PreprintCC BY 4.0arXiv

Flexible discrete translational surfaces

  • Georg Nawratil
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Abstract

We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.

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Cite

BibTeXRIS
BibTeX
@misc{nawratil2026flexible,
  title = {{Flexible discrete translational surfaces}},
  author = {Georg Nawratil},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39517},
  eprint = {2609.39517},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39517},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Flexible discrete translational surfaces
AU  - Georg Nawratil
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39517
UR  - https://arxiv.org/abs/2609.39517
AB  - We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.
ER  -