Liaison Linkages

TL;DR

This paper investigates the algebraic properties of hexapods with mobility one by establishing bounds on their configuration curves' degrees and constructing examples using liaison techniques.

Contribution

It provides an upper bound for the degree of configuration curves of general hexapods and constructs examples with maximal degree via liaison methods.

Findings

Upper bound for the degree of configuration curves

Construction of hexapods with maximal degree curves

Application of liaison in algebraic geometry

Abstract

The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In this paper we establish an upper bound for the degree of this curve, assuming the hexapod is general enough. Moreover, we provide a construction of hexapods with curves of maximal degree, which is based on liaison, a technique used in the theory of algebraic curves.