Orientation-singularity and nonsingular orientation-workspace analyses of the Stewart-Gough Platform using unit quaternion representation

This paper mainly addresses the orientation-singularity analysis and the nonsingular orientation-workspace computation of the Stewart-Gough Platform. Employing a unit quaternion to represent the orientation of the moving platform, an analytical symbolic expression that represents the orientation-singularity locus of the manipulator at a fixed position is derived. It is shown that for the Stewart-Gough Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace. Using the orientation representation and applying the inverse kinematics solution of the Stewart-Gough Platform, a discretization method is proposed for the computation of the nonsingular orientation-workspace of the Stewart-Gough Platform. Based on the research on the orientation-singularity and nonsingular orientation-workspace of the manipulator, a new concept of “practical orientation-capability” is introduced as a performance index for the orientation-capability analysis of the Stewart-Gough Platform at a certain position in the position-workspace. Examples of a 6/6-SPS Stewart-Gough Platform are given to demonstrate these theoretical results.