A family of exceptional Stewart-Gough mechanisms of genus 7

TL;DR

This paper introduces a 13-dimensional family of Stewart-Gough mechanisms with unique algebraic motion curves of genus 7, expanding the understanding of their geometric properties.

Contribution

It constructs a new family of exceptional Stewart-Gough mechanisms characterized by algebraic motion curves of genus 7, with a detailed parameter space analysis.

Findings

Family of mechanisms is 13-dimensional.

Motion curves are algebraic of genus 7.

Mechanisms are exceptional, not fitting typical classifications.

Abstract

In this paper we construct a family of exceptional Stewart-Gough mechanisms, whose motion curves are algebraic curves of genus 7. Up to translations, rotations and dilatations this family of mechanisms is 13-dimensional.