## 1 Introduction  
Recently, high-precision parallel alignment between two surfaces has become an important mechanical problem for pattern fidelity in nanoimprint lithography [1; 2; 3] and some electrochemical micro/nanofabrication techniques [4; 5]. The parallel misalignment between the template and the substrate can lead to non-uniform microstructures fabricated over a large area [1]. The parallel alignment can be achieved by rotations about the axes that lie in the template surface. If the rotation axes do not lie in the template surface, a coupled lateral shift of the imprint position can be generated during the parallel alignment process [2]. Therefore, the parallel alignment can be considered as tip/tilt motions around two perpendicular axes located in the template surface. To achieve the alignment motions of the template, the parallel alignment stage with a remote center compliance (RCC) characteristic is increasingly being adopted for its advantages, such as no friction, no wear, no need for lubrication, and compact structure. The RCC mechanism was originally designed as a passive wrist accommodator for automatic assembly to compensate for positioning errors between a machine and a part. At Draper Laboratory, [PERSON] et al. developed a series of representative RCC systems for automatic assembly devices [6; 7]. Later, several other new types of RCC devices were also developed and used in various applications [8; 9; 10]. Some RCC mechanisms are still commercially available from a number of companies. According to the principle of the RCC mechanism, several orientation stages that borrow features from the traditional RCC mechanisms have been developed for nanoimprint machines. [PERSON] et al. [2] first developed a flexure template stage for nanoimprinting by serially assembling two sets of four-bar-linkage compliant mechanisms. [PERSON] et al. [11] developed an active orientation head with the function of distributed force feedback control. [PERSON] et al. [12; 13] developed two types of parallelogram-based compliant remote-center-of-motion stages for active parallel alignment. In terms of the analytical model of RCC mechanism, [PERSON] et al. [14] presented an accurate model for the RCC mechanism using screw theory to characterize the interesting properties of remote compliance. [PERSON] et al. [15; 16] gave a detailed analysis of rotational precision for leaf-type isosceles-trapezoidal flexural (LITF) pivot used in the one-dimensional RCC mechanism. [PERSON] et al. [17] derived a symbolic formulation of the compliance and stiffness matrices for several RCC mechanisms. In the design of RCC mechanisms, the compliance properties and rotational precision are two important specifications determining the range of motion and precision of the RCC mechanisms, respectively. The rotational precision criterion is especially important for some precision-required applications of the flexural mechanisms [15]. Therefore, this paper focuses on the analysis of compliance properties and rotational precision for a class of RCC mechanisms. This kind of RCC mechanism is combined in parallel with two round beams-based LITF pivots, and can achieve two rotations around two perpendicular axes in the remote plane. An analytical model of the RCC mechanism based on the stiffness matrix method is first established to obtain the close-form equations for compliance factors in all directions. The rotation center locations are then derived using the screw theory to analyze the rotational precision of the RCC mechanism. The results of the analytical model, finite elements analysis (FEA), and experimental tests are all compared to validate the high accuracy of the analytical model, which can be utilized in the design and optimization of the RCC mechanisms. The main contribution of this manuscript is to establish an analytical model for the calculation of the structural compliances and position of rotation center for a class of RCC mechanisms.