This paper presents the two degree-of-freedom (DOF) planar parallel mechanism, called the $2{underline{R}}RR-RP$ manipulator, whose degree-of-freedom is dependent on an additional passive constraining leg connecting the base and the platform. First, the kinematic analysis of the mechanism is performed: the inverse and forward kinematic problems are analytically solved, the workspace is systematically derived, and all of the singular configurations are examined. Then, in order to determine the geometric parameters the optimization of the mechanism is performed considering its dexterity, stiffness, and space utilization. Finally, the kinematic performances of the optimized mechanism are evaluated through the comparison study to the conventional 5-bar parallel manipulator.