A systemic approach to the structure synthesis of fully-isotropic three degree-of-freedom(DoF) planar parallel manipulators was presented. Firstly, the necessary conditions for designing fully-isotropic planar parallel manipulators were discussed by use of the screw theory. Based on the different control functions of each limb for the moving platforms, the actuation screw, actuated screw and mobile unactuated screws of every limb were derived in terms of the reciprocal screw theory. Then, all possible limbs were enumerated according to the different connectivity numbers of the kinematic chain. Finally, the desired manipulators, including 3 167 new types, were obtained by connecting the moving platform to the fixed base by using three limbs according to some assembling conditions. Each kinematic Jacobian of these manipulators is an identical matrix and their conditioning numbers are all equal to 1, so the manipulators can offer very good motion and force transmissions, and show prospective applications in industrial robots, micro-manipulating robots, and medical robots.