Property Identification of the Singularity Loci of the 6/6-SPS Stewart Manipulator by Using the Method of Z-Plane

摘要

The problem of identifying the property of singularity loci of 6/6-SPS Stewart manipulators is addressed. 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 singularity locus of the manipulator, is derived.Graphical representations of the singularity locus of the manipulator for different orientations are illustrated with examples. Based on this analytical expression, a quadratic expression that represents the singularity locus of the manipulator in Z-plane is derived, and further the property of singularity loci of the manipulator in parallel Z-planes is identified. it shows that singularity loci of 6/6-SPS Stewart manipulators in parallel Z-planes are all quadratic expressions including infinite hyperbolas, four pairs of intersecting lines and a parabola.