A FRAME-INDEPENDENT VECTOR EXPRESSION OF THE SINGULARITY LOCUS OF THE GOUGH-STEWART PLATFORM

This paper presents a vector expression of the singularity locus of the Gough-Stewart platform. In order to obtain this expression, several algebraic operations are performed on the manipulator's Jacobian matrix such as relocating the origin of the reference frame and linearly combining columns. The third-degree vector expression thus obtained does not contain a constant term, which allows the factorization of an instance of the position vector An alternative notation that reduces the number of times that the position vector appears in the expression is then presented. It is also demonstrated that a simplified architecture such as that of the MSSM can significantly reduce the length of the expression. Finally, some numerical examples of singularity loci are presented, which were estimated by combining the proposed formulation with interval analysis in the cases of a generic Gough-Stewart platform and of an MSSM. The results obtained illustrate how the precision of interval analyses are influenced by the form of the symbolic expression of the singularity locus.