## 1 Introduction  
The robot can perform many tasks in order to help human beings in industrial fields. For example, machining and welding are classical. It is necessary to study the factors that are the obstacles for the improvement of the robot tasks. The classical applications in a factory usually generate forces and torques at the end-effector (EE) of the industrial robot, and the stiffness is the factor that should be considered in order to obtain good performance. The industrial robot requires suitable compliance while performing industrial tasks. Especially when the industrial robot performs the tasks with a high precision requirement, the accuracy of the EE is often influenced by the stiffness characteristic. Lots of attention has been directed at studying the factors that influence the accuracy of the EE and how to deal with these issues [1; 2]. One solution to this problem is to identify the stiffness parameters of the industrial robot and then use the deformation compensation algorithm to improve the performance of the robot's tasks. The joint stiffness identification is one aspect of robot calibration. Some researchers have studied robot calibration and defined three levels of calibration methods. [PERSON] presented the analysis of calibration methods for the robot, and stiffness identification belongs to the level of non-geometric calibration [3]. Many researchers have studied how to improve the accuracy of the EE and the performance of the robot force control while considering stiffness. These efforts led to joint stiffness modeling and stiffness identification of the robot, and there are some groups of stiffness identification algorithms. For example, the finite elements analysis (FEA) method constructs the physical model based on many of finite elements and the corresponding relative stiffness matrices [4; 5; 6]. [PERSON] presented a method of evaluating the relationship between a numerical tool and a general stiffness map of the robot based on FEA [7]. The matrix structure analysis (MSA) method uses beams and nodes to construct the stiffness model under the assumption that the links are not subject to bending [8]. [PERSON] [8] proposed a method to calculate the parallel kinematic machines based on matrix structural analysis in a closed form, and the method can obtain high accuracy specifications. The virtual joint method (VJM) uses the idea of rigid links and compliant joints, and then the calculation of the Jacobian matrix is needed to formulate the stiffness model [9]. [PERSON] presented an approach to identify the elastostatic parameters of both links and joints in a real industrial environment based on VJM, and this approach comprises of physical algebraic and statistical model reduction methods [10]. The compliance is important for the analysis of mechanism stiffness characteristics in Cartesian space [11; 12; 13; 14; 15]. The stiffness characteristics of industrial robots influence the requirement of the accuracy and the force commands [16]. Numerous papers concern the stiffness analysis and optimization in order to improve the accuracy of the location of the EE as well as the force control [17; 18]. Therefore, in order to obtain a broad, successful application, the industrial robot must have reasonable elastostatic performance. [PERSON] et al. studied the stiffness model of redundant parallel kinematic mechanisms (PKM) and presented a decoupling method for explicit stiffness analysis of redundant PKM. After that, they discussed the optimization and control of the PKM when external forces were applied to the mechanisms [19]. [PERSON] et al. studied the stiffness model and the structural parameters of a multibackbone continuum robot based on screw theory, and then obtained the relationship between the force and the deformation of the continuum robot. Then, a theoretical real-time control algorithm was provided based on the stiffness analysis [20].