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