The singularity-free workspace of parallel mechanisms is important in the trajectory planning and the kinematic design of the mechanisms. The planar parallel mechanism with revolute actuators, which the expression for the singularity locus and the algorithms for determining the singularity-free zones involve both the Cartesian and the joint variables, has been studied in the paper. Algorithms are proposed here to simplify the determination of the singularity-free zones in Cartesian space. The methodology and procedures for determining the singularity-free zones of planar parallel mechanisms with revolute actuators are introduced. The numerical results show that the simplified algorithms and the techniques are correct and efficient in determining singularity-free zones in the workspace of planar parallel mechanisms.