## 1 Introduction  
The model support mechanism works under a complex load environment in the wind tunnel, and stiffness is a vital index to guarantee the stability of the model during experiments [1, 2]. Among the existing model support technologies, cable and magnetic suspension can solve the airflow interference problem. However, fundamentally difficult problems, such as precise control and high cost of technology, are encountered [3, 4, 5, 6]. Mechanical support technology has been the research hotspot in recent years; nonetheless, the lack of flexibility and avoiding singularity are essential risks for the parallel support mechanism [7, 8, 9]. Airflow interference and large moment of inertia are factors that restrict the extensive development of the serial support mechanism [10, 11]. Thus, the hybrid mechanism can avoid the shortcomings of both factors effectively. Geng proposed a five-degrees-of-freedom (DoF) hybrid model support mechanism [12]. However, it was only used in a low-speed wind tunnel, and the precision and stability of the test could not be ensured when it worked in the supersonic wind tunnel. A cost-effective and reliable technique is demanded to propose a hybrid support mechanism that is composed of a parallel part and serial part, as shown in Figure 1.  
The parallel part of the support mechanism can realize three independent motions (two translations in axes X,Y and one rotation about axis Z-yaw) in the X-Y plane. We set a 3-DoF planar mechanism with actuation redundancy to improve the stiffness and enlarge the workspace. The serial part of the support mechanism has the ability of two additional rotational movements (pitch and roll), which ensures the flexibility of the model. The aircraft model can produce six directions of deformation during the experiment because of the complexity of the aerodynamic load. The stiffness of the planar parallel part determines the stability and accuracy of the whole support mechanism. The research in this article was primarily motivated by the need to make the parallel part have appreciable spatial stiffness characteristics. Therefore, further investigation is necessary to explore the approach of calculation and evaluation for stiffness of the planar parallel mechanism. The stiffness of the 3-DoF planar mechanism has been investigated meticulously in the past decades. Generally, most researchers obtained a \(3\times 3\) stiffness matrix from the kinematic Jacobian, and they used stiffness as an optimal design index [13; 14; 15; 16]. However, the end-effector needs to resist the deformation in six directions (X, Y, Z, pitch, yaw, and roll). Most researchers focused on the active stiffness in the plane movement without considering the constraint stiffness. [PERSON] analyzed the spatial stiffness of a 3-PPR (P stands for a prismatic joint and R denotes a rotation joint) planar mechanism by using the eigen-screw decomposition to explore the effect of actuators of nonlinear stiffness on the mobile platform (MP) [17].The stiffness model was established by virtual spring, which was not suitable for analyzing the influence of the parameters of planar mechanism on the active and constraint stiffness. Among the existing methods of stiffness analysis of parallel mechanisms, finite element analysis is the most accurate and adaptable method for analyzing stiffness parallel mechanisms [18; 19]. However, it has limitations in building the relationship between the stiffness model and the geometric dimension of the end-effector. In addition, it needs to re-mesh when the geometry of the end-effector changes. The structural matrix approach is mostly based on the kineto-elasto dynamic method, which uses substructure assembly to condense the stiffness matrix of the components (beam, shell, and entity) into the assembly stiffness matrix.