###### Abstract
The input coupling means that the input force on one actuation stage will cause the primary motion of another motion stage and thus bring additional loads on the actuator. Its effects can be neglected in a conventional parallel manipulator because the adopted motors have large stiffness and can bear any type of reacting force. For a CPM, however, the input coupling will cause unwanted deformations and even clearance between an actuator and the actuation point, which will result in difficulties to the motion control. Moreover, CPM adopts a piezoelectric actuator as its actuation element due to the actuator's high precision and resolution, large stiffness, high push force, and fast response. However, the piezoelectric actuator is made of multiple piezoelectric layers glued together and is thereby sensitive to pulling and bending forces that may damage the actuator. Therefore, the input coupling has adverse effects on the CPM and should be carefully considered in its design and development process. [PERSON] [16; 19] first proposed the decoupling performance design requirements of the parallel XY compliant mechanism. In order to realize actuation isolation, the actuator was required to be connected to the actuation point by means of a decoupler, which transmitted the axial force and absorbed any transverse motion without generating transverse loads. [PERSON] [20] employed two types of distributed-compliance compound flexure modules and a mirror symmetric structure to reduce the input and output coupling of a novel 2-DOF compliant stage. [PERSON] [21] utilized statically indeterminate symmetric structures to attenuate the cross-axis coupling of a proposed XY CPM. [PERSON] [22] investigated the design and development of a decoupled compliant stage with displacement amplifiers. The output decoupling was achieved by resorting to compound parallelogram flexures; the double compound parallelogram flexure and the amplifier acted as the decoupler to ensure this stage had excellent input decoupling characteristics. There have already been several efficient and intuitive design approaches related to the compliant mechanisms, including the kinematic substitution method [20; 23], constraint-based design method [24], and freedom and constraint topology [25; 26]. However, these methods focus on the type synthesis and only guarantee the DOFs of the compliant mechanism instead of considering other performances. Additionally, they regard the degree and constrain of the compliant mechanism as those of the rigid mechanism. While the compliant mechanism moves through the deformations of materials, its DOFs are coupled with the stiffness property. Therefore, the type synthesis and structural design of the compliant mechanism are supposed to be integrated with the consideration of multiple performance indicators. The systematic design method for compliant mechanisms with excellent performances is still a great challenge. The practical CPMs are mostly directly provided in the present studies and there lacks a systematic process for guiding the design of a CPM with excellent decoupling performance. Considering the 2-DOF CPM [16; 17; 18; 19; 20; 21; 22; 23; 27; 28; 29; 30] is the most practical compliant mechanism, this work's motivation is to present a systematic design of a decoupled 2-DOF CPM. The requirement on the kinematic structure for realizing totally output decoupling performance has been discussed. A flexure-based decoupler was chosen and its detail structure design was studied to minimize the input coupling of the CPM. Unlike the previous works, which only provided qualitative analyses, the specific definition and analytical model of the input coupling degree (ICD) of the CPM have been provided. According to the established model, the geometric parameters of the 2-DOF were optimized to directly minimize its ICD and the other key performance indicators were also guaranteed through constraint conditions. Finally, a prototype of the 2-DOF CPM was fabricated based on the optimized result, and several experimental tests were performed.