Determination of the maximal singularity-free zone in the whole workspace of 3-RRR planar parallel mechanism

The singularity-free zones of 3-RRR (R denotes actuator joint) planar parallel mechanisms are studied. The methods and procedures of determination of maximal singularity-free zone of planar 3-RRR parallel mechanism, both for centered on given point and for in the whole workspace, are introduced. For 3-RRR parallel mechanism, the expression for the singularity locus and the algorithms for determining the singularity-free zones involve both the Cartesian and the joint variables. To make the algorithms to be simplified and be efficient, the methods to simplify the algorithms for determining the singularity-free zones in Polar space is proposed. The methodology and procedures for determining the singularity-free zones centered on given point of 3-RRR planar parallel mechanisms are introduced. Then a self-modifying technique for searching the center of the whole workspace maximal singularity-free zone was developed, so that the theoretical center of the whole workspace maximal singularity-free zone can be obtained step by step automatically. The calculating results show that the simplified algorithms and the techniques for determining the singularity-free zones of planar parallel mechanism are correct and efficient.