Property Identification of the Singularity Loci of a Class of Gough-Stewart Manipulators

Abstract

In this paper we address the problem of identifying the property of the singularity loci of a class of 6/6-Gough-Stewart manipulators in which the moving and base platforms are two similar semiregular hexagons. After constructing the Jacobian matrix of this class of 6/6-Gough-Stewart manipulators according to the theory of statical equilibrium, we derive a cubic polynomial expression in the moving platform position parameters, which represents the constant-orientation singularity locus of the manipulator. Graphical representations of the singularity locus of the manipulator for different orientations are quite various and complex. Further, we analyze the singularity locus of this class of 6/6-Gough-Stewart manipulators in the principal section, where the moving platform lies. This shows that singularity loci of this class of 6/6-Gough-Stewart manipulators in parallel principal sections are all quadratic expressions. We have also found that, for this class of 6/6-Gough-Stewart manipulators, there are also some special singularity cases in which six lines associated with the six extensible links of the manipulator can intersect one common line and the unwanted instantaneous motion of the manipulator is a pure rotation.