Hexapods with a small linear span

TL;DR

This paper classifies the configuration curves of mobile hexapods with one degree of freedom using algebraic geometry, focusing on those with restrictions on their embedding dimension.

Contribution

It provides a classification of configuration curves of hexapods with one degree of freedom based on their embedding dimension, advancing theoretical understanding.

Findings

Configuration curves form projective curves with specific degrees.

Classification results depend on restrictions on embedding dimension.

Enhances theoretical kinematics of hexapods.

Abstract

The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understanding by employing techniques from algebraic geometry. The set of configurations of a mobile hexapod with one degree of freedom has the structure of a projective curve, which hence has a degree and an embedding dimension. Our main result is a classification of configuration curves of hexapods that satisfy some restrictions on their embedding dimension.