The precision of parallel robots is limited by backlash in their joints. This paper investigates algorithms for designing inexpensive planar parallel robots with prescribed backlash-free workspace. The method of closing the backlash of the actuators uses preloaded flexible joints to replace the passive joints. These flexible joints may be made using standard joints with preloaded springs or by using preloaded flexure joints. Given a norm-bounded wrench acting on the robot, an algorithm is presented for determining the required preload for the flexible joints in order to guarantee backlash-free operation along a path or within a prescribed workspace. An investigation of the effects of the preloaded flexible joints on the stiffness is carried out using performance measures comparing the same robot with or without preloaded joints. These performance measures use an extended stiffness definition based on three noncollinear vertices on the moving platform. This paper presents simulations of the statics, stiffness, and backlash prevention algorithm, followed by experimental validations.