Position-Singularity Analysis of a Class of the 3/6-Gough-Stewart Manipulators based on Singularity-Equivalent-Mechanism

This paper addresses the problem of identifying the property of the singularity loci of a class of 3/6‐ Gough‐Stewart manipulators for general orientations in which the moving platform is an equilateral triangle and the base is a semiregular hexagon. After constructing the Jacobian matrix of this class of 3/6‐Gough‐Stewart manipulators according to the screw theory, a cubic polynomial expression in the moving platform position parameters that represents the position‐singularity locus of the manipulator in a three‐dimensional space is derived. Graphical representations of the position‐ singularity locus for different orientations are given so as to demonstrate the results. Based on the singularity kinematics principle, a novel method referred to as ‘singularity‐equivalent‐mechanism’ is proposed, by which the complicated singularity analysis of the parallel manipulator is transformed into a simpler direct position analysis of the planar singularity‐equivalent‐mechanism. The property of the position‐singularity locus of this class of parallel manipulators for general orientations in the principal‐section, where the moving platform lies, is identified. It shows that the position‐singularity loci of this class of 3/6‐Gough‐Stewart manipulators for general orientations in parallel principal‐sections are all quadratic expressions, including a parabola, four pairs of intersecting lines and infinite hyperbolas. Finally, the properties of the position‐singularity loci of this class of 3/6‐Gough‐Stewart parallel manipulators in a three‐ dimensional space for all orientations are presented.