This paper presents parallel kinematic XY mechanism designs that are based on a systematic constraint pattern. The constraint pattern, realized by means of double parallelogram flexure modules, is such that it allows large ranges of motion without over-constraining the mechanism or generating significant error motions. Nonlinear force-displacement characteristics of the double parallelogram flexure are used in analytically predicting the performance measures of the proposed XY mechanisms. Comparisons between closed-form linear and nonlinear analyses are presented to highlight the inadequacy of the former. Fundamental design tradeoffs in flexure mechanism performance are discussed qualitatively and quantitatively. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of Finite Element Analysis and experimental measurements.