determination of maximal singularity free zones in the workspace of parallel manipulator

due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singularity-free zones in the workspace of parallel manipulators by using pso algorithm. the obtained zone is completely free from singularities and has its maximal value. the largest singularity-free cylinder in the one point of the workspace for any orientation ranging around a reference orientation angle of moving platform is plotted. to this end, for finding the radius of the cylinder, we will find the closest point on the singularity surface to the axis of the cylinder by using particle swarm optimization. comparing the obtained results of pso algorithm on 3-rpr planar parallel manipulator and previous methods can show attention and simplicity of used algorithm. also the singularity free zone is improved with determination of circle center and reference orientation angle.