###### Abstract
A typical compliant mechanism mainly consists of a mechanical structure with flexure members for motion transmission, piezoelectric elements for actuation, ultra-precision sensors for displacement output measurement, and controllers for motion control. Among them, the mechanical structure determines the performance of the compliant mechanism to a great extent. Two kinds of kinematic structures are commonly adopted, i.e., serial and parallel types [6]. Serial compliant mechanisms generally adopt a stack structure with one 1-DOF positioning stage mounted on another 1-DOF stage. This is a simple structure that is easy to manufacture and control, which has already been successfully applied in commercial products. However, it has the disadvantage of different dynamic characteristics of each axis, a reduced natural frequency as a result of the stacked stage increasing the moving mass, and cumulative motion errors [7]. The serial compliant stage will be suitable for applications where the motion along one axis is considerably faster than the others. [PERSON] [8] utilized a serial-kinematic nanopositioning stage for raster-type scanning, in which one axis is chosen for high-speed scanning while the other is designed for low-speed motion. Compared with the serial type, the parallel structure has inherent advantages in terms of high stiffness, large load capacity, low inertia, high natural frequency, and an absence of accumulation errors [9]. However, there have been many problems during the development of the parallel manipulator, particularly regarding conventional joints and rigid links. First, there are passive joints in the parallel manipulator, which are difficult to manufacture with high precision, such as sphere and universal joints. Meanwhile, the kinematic chains of the parallel manipulator are generally composed of elongated rods, which are prone to deformation and vibrate under external loads [10; 11]. Because the displacement output of the terminal platform cannot be measured in real time to realize a closed-loop control, the above adverse factors will significantly decrease the motion accuracy of the parallel manipulator. Moreover, the kinematic model of parallel manipulator is complicated, which creates difficulties in kinematic calibration and motion control. The performance indicators, such as stiffness, dexterity, acceleration ability, will all change when the pose of the manipulator varies. Therefore, conventional parallel manipulators have not achieved their expected success in industry applications. Fortunately, the above issues will cease to be problems when the parallel structure is utilized in the development of a compliant mechanism. Apparently, there are no joints in the compliant parallel mechanism (CPM) and its displacement output can be measured directly as it relates to its micro motion stroke. Moreover, the pose of the CPM can be considered as a constant because its motion stroke is very small when compared to the geometric dimensions. This guarantees that the CPM can have a linear force-displacement relationship, identical mechanical bandwidth for each axis, and even decoupled kinematic model. Therefore, parallel structure has a great potential to be utilized in the development of a compliant mechanism, and numerous researchers have already begun working on it [12; 13; 14; 15]. Though the CPM has advantages over its rigid counterpart, there are specific challenges in its design and development, which include the realization of cross-axis decoupling and actuation isolation [16; 17; 18], also known as output and input decoupling. Output coupling refers to any motion along one axis is affected by the actuation/input force along another axis. It results in a complicated kinematic model and additional calibration should be performed in the absence of terminal feedback. This is a typical character of a parallel manipulator due to its parallel kinematic type.