Orientation-singularity representation and orientation-capability computation of a special class of the Gough-Stewart parallel mechanisms using unit quaternion

Singular configuration seriously affects the performance of the Gough-Stewart parallel mechanism and has attracted many researchers' attentions. However, most of existing topics often focus on the position-singularity of the mechanism for a constant-orientation, but few reports research the orientation-singularity for a given position. In order to investigate the orientation-singularity of the Gough-Stewart parallel mechanisms with two dissimilar semi-regular hexagonal platforms for a given position, after constructing the discrimination matrix of the singular configuration of the mechanism and computing the determinant of this matrix by using unit quaternion as the orientation parameters which can avoid the singularities in parameterization, a general symbolic expression representing the three-dimensional orientation-singularity locus for a given position is obtained and the three-dimensional view of the orientation-singularity locus is further described. The orientation-singularity-free void exists inside the orientation-singularity locus, but the shape of the orientation-singularity-free void is irregular and inconvenient for the design of the mechanism. The minimal inscribed sphere of the three-dimensional orientation-singularity locus namely the orientation-singularity-free ball is described. The radius of the ball orientation-capability is used as the measurement for the orientation-singularity-free void size. A new efficient algorithm is proposed for the computation of the orientation-capability. Finally, the influences of the geometry parameters and the different positions of the mechanism on the orientation-capability are discussed. A new method of the singularity analysis of the Gough-Stewart parallel mechanism is advanced based on the unit quaternion, and the research finds have important referential value for the configuration parameters optimization of this class of the parallel mechanisms with the goal of having the maximal singularity-free zone.