This paper introduces a position-space-based reconfiguration (PSR) approach to the reconfiguration of compliant mechanisms. The PSR approach can be employed to reconstruct a compliant mechanism into many new compliant mechanisms, without affecting the mobility of the compliant mechanism. Such a compliant mechanism can be decomposed into rigid stages and compliant modules. Each of the compliant modules can be placed at any one permitted position within its position space, which does not change the constraint imposed by the compliant module on the compliant mechanism. Therefore, a compliant mechanism can be reconfigured through selecting different permitted positions of the associated compliant modules from their position spaces. The proposed PSR approach can be used to change the geometrical shape of a compliant mechanism for easy fabrication, or to improve its motion characteristics such as cross-axis coupling, lost motion, and motion range. While this paper focuses on reducing the parasitic motions of a compliant mechanism using this PSR approach, the associated procedure is summarized and demonstrated using a decoupled XYZ compliant parallel mechanism as an example. The parasitic motion of the XYZ compliant parallel mechanism is modeled analytically, with three variables which represent any permitted positions of the associated compliant modules in their position spaces. The optimal positions of the compliant modules in the XYZ compliant parallel mechanism are finally obtained based on the analytical results, where the parasitic motion is reduced by approximately 50%. The reduction of the parasitic motion is verified by finite-element analysis (FEA) results, which differ from the analytically obtained values by less than 7%.