Based on its simple structure, base-fixed actuators, high payload capacity, high accuracy, and high mechanical rigidity, the 3-RlowbarRR mechanism is a valuable planar parallel manipulator. However, the 3-RlowbarRR mechanism is known to have singular loci within its workspace affecting its use. In this paper, singularity avoidance of the 3-RlowbarRR mechanism using kinematic redundancy is presented. First, singularity analysis of the proposed 3-RlowbarPlowbarRR mechanism is described and a simple and effective redundancy resolution algorithm based on local optimization suitable for real-time control is developed. Here, the cost function in the optimization is designed to avoid the most problematic singularity configurations, where the end-effector can be locally moved even though all actuated joints are locked. Results from simulation show that the resultant 3-RlowbarPlowbarRR mechanism can be used to avoid singularities associated with the 3-RlowbarRR mechanism, and enlarges the usable workspace.