This paper presents a procedure to obtain a singularity-free task workspace with a new method to deal with singularities. In order to get an enlarged singularity-free task workspace, we first optimize the volume of the workspace, then we identify singularities in the optimal workspace, and finally we refine the singularity-free task workspace from the optimal workspace. The effects of four physical constraints on the workspace are analyzed, subject to which the optimization is realized. The traditional approach of singularity analysis is based on the Jacobian Matrix which is direct but has limitations, especially when the analytical form of the Jacobian is difficult to obtain. To solve this problem, we define a pseudo-singular space which encloses all singularity loci. By searching the pseudo-singular space numerically, we are able to obtain a singularity-free task workspace. We illustrate this method in the designing process of a 6-RSS parallel mechanism as a haptic device which has been integrated in a simulated dentist training system.

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