# Rationality Of the Locus Of Singularities Of the General Gough-Stewart Platform

## TL;DR

This paper proves that the singular configurations of a general Gough-Stewart platform can be parametrized rationally, using a reciprocal twist mapping that relates the cubic surface of singularities to a blown-up quadric surface.

## Contribution

It introduces a reciprocal twist mapping and demonstrates that the singularity set admits a rational parametrization, linking cubic surfaces and blown-up quadrics.

## Key findings

- The set of singular configurations has a rational parametrization.
- The reciprocal twist mapping relates the cubic surface of singularities to a blown-up quadric surface.
- The approach provides a new geometric understanding of the singularity locus.

## Abstract

We prove that the set of singular configurations of a general Gough Stewart platform has a rational parametrization. We introduce a reciprocal twist mapping which, for a general orientation of the platform, realizes the cubic surface of singularities as the blowing up of a quadric surface in five points.