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Singularity analysis is a basic problem of parallel mechanism, and this problem cannot be avoided in both workspace and motion planning. How to express the singularity locus in an analytical form is the research emphasis for many researchers for a long time. This paper presents a new method for the singularity analysis of the 6-SPS parallel mechanism. The rotation matrix is described by quaternion, and both the rotation matrix and the coordinate vectors have been expanded to four-dimensional forms. Through analyzing the coupling relationship between the position variables and the orientation variables, utilizing properties of the quaternion, eight equivalent equations can be obtained. A new kind of Jacobian matrix is derived from those equations, and the analytical expression of the singularity locus is obtained by calculating the determinant of the new Jacobian matrix. The singularity analysis of parallel mechanisms, whose moving platform actuated by 6 links and the vertices of both the base and the moving platforms has been placed on a circle respectively, can be solved by this analytical expression. parallel mechanism, singularity analysis, quaternion, Jacobian matrix Citation:Cheng S L, Wu H T, Wang C Q, et al. A novel method for singularity analysis of the 6-SPS parallel mechanisms.

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Singular configurations must be avoided in the practical manipulation of parallel mechanism. This paper presents an approach of singularities analysis of six degrees of freedom (DOF) parallel mechanism applying geometric algebra. Twists of all passive joints in each limb are described in geometric algebra while all the active joints are locked. And wrenches produced from each limb and acting on the moving platform are derived from the calculations of the outer product and its dual of the corresponding twists. The singular condition of parallel mechanism depends on whether the wrenches acting on the moving platform failed to constrain all the motions, which can be accomplished by the outer product with its duality followed. Two six-DOF parallel mechanisms 6-UPS and 6-PUS are introduced to verify the approach proposed in this paper. The results indicate that geometric algebra can also be used for singularity analysis of six-DOF parallel mechanism.