Yi Cao, Meiping Wu, and Hui Zhou
Parallel mechanism, position-singularity, characteristic plane
For a special class of the Stewart parallel mechanism whose moving platform and the base are two dissimilar semi-symmetrical hexagons, the position-singularity of the mechanism for a constant orientation is analysed systematically. After expanding the determinant of the Jacobian matrix, a cubic symbolic polynomial representing the three-dimensional (3D) position-singularity locus of the mechanism is derived and graphical representations of the 3-D position-singularity locus are illustrated. Based on this cubic polynomial, a quadratic polynomial that represents the position-singularity locus of the mechanism in the characteristic plane is derived. It is shown that the characteristic of the position-singularity loci in parallel characteristic planes includes infinity many sets of hyperbolas, four pairs of intersecting lines, a parabola and even two lines or one line for some special orientations.
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