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-singularit...

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