Property analysis of the position-singularity loci of the Stewart manipulator using the cross-section of Z-plane

This paper addresses the property analysis of the position-singularity loci of 6/6-SPS Stewart manipulators. After constructing the Jacobian matrix of the 6/6-SPS Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constant-orientation position-singularity locus of the manipulator, is derived. Graphical representations of the position-singularity locus of the manipulator for different orientations are illustrated with examples to demonstrate the theoretical results. Based on this analytical expression, a quadratic expression that represents the position-singularity locus of the manipulator in Z-plane is derived, and further the property of position-singularity loci of the manipulator in parallel Z-planes is identified. It shows that position -singularity loci of 6/6-SPS Stewart manipulators in parallel Z-planes are all quadratic expressions which include infinite hyperbolas, four pairs of intersecting lines and a parabola.