Position-singularity Analysis of the Stewart Parallel Mechanism

For a special class of the Stewart parallel mechanism whose moving platform and base platform are two dissimilar semi-regular hexagons,the position-singularity of the mechanism for a constant-orientation is analyzed systematically.Based on constructing the force Jacobian matrix,a cubic symbolic expression that represents the 3-dimensional position-singularity locus for a constant orientation is derived.The concept of the characteristic plane is proposed.Further analysis shows that the 3-dimensional position-singularity locus of the mechanism for a given position is very complicated,and the geometric characteristics of the position-singularity locus lying in a general oblique plane are difficult to be identified.The plane where the moving platform lies is defined as the characteristic plane.Research shows that the position-singularity curves in the characteristic planes are all quadratic curves,including infinity many sets of hyperbolas,four pairs of intersecting lines and a parabola.For some special orientations,the quadratic position-singularity curves in the characteristic planes degenerate into two parallel lines or even one line which are all parallel to the ridge line.Two theorems concerning the geometric characteristics of the position-singularity curves in the characteristic planes are advanced and proved.Moreover,the kinematic property of the position-singularity locus is briefly analyzed based on the Grassmann line geometry and the screw theory.