## 1 Introduction  
Shield machines are widely used in fields such as rail transportation and water facilities. Shield machine hobs are a class of wearing parts that need to be replaced frequently, but replacing hobs usually requires operation under pressure, so there is a great danger. The application of a tool-changing robot for tool replacement is a feasible method. The tool-changing robot is a multi-degree of freedom system. The robot will leave necessary clearances at the joints to complete the machining assembly and meet certain relative motion requirements. Unnecessary clearances will also be generated at the joints due to limitations of machining accuracy during the manufacturing process. The extent of clearance can seriously affect the mechanism's motion accuracy and motion characteristics [1, 2, 3]. Therefore, the influence of joint clearance on the motion characteristics of the tool-changing robot needs to be analyzed. In the process of analyzing the dynamic characteristics of the mechanism with clearance, it is necessary to establish a motion model that can accurately and logically describe the dynamic characteristics of the contact collision at the clearance joints and the corresponding mathematical model of the contact force [4, 5, 6, 7]. The collision models for mechanisms with clearance can be summarized into the following three categories: continuous contact model, two-state model, and three-state model [8; 9; 10; 11; 12; 13]. [PERSON] et al. [14] first proposed a continuous contact-based model arguing that the two components are always in continuous contact, so that it is possible to define the mechanism with clearance as a multi-link mechanism and establish the differential equations of motion for the whole system. Based on the L-N model and the improved Coulomb friction model, [PERSON] et al. [15] investigated the effect of the number of rotating pairs with clearance and clearance size on the dynamic characteristics of the crank slider. [PERSON] et al. [16] studied a crank-slider mechanism based on the L-N model, neglecting the tangential friction at the gap hinge, and analyzed the influence of the input speed and the position where the clearance occurs on the kinematic parameters of the mechanism during operation. [PERSON] et al. [17] optimized the design of the rod mass based on a particle swarm optimization algorithm and found that the optimized dynamic performance of the mechanism improved significantly. [PERSON] et al. [18] established a contact force collision model with clearance by vector analysis method and used it for the dynamic characteristics analysis of a turbine valve mechanism. [PERSON] et al. [19] investigated the dynamics and dynamic wear characteristics of a two-axis-position mechanism of satellite antennas with joint clearance based on a non-linear spring damping model. [PERSON] et al. [20] studied the effect of cycloid reducer rolling body clearance on motion accuracy. Based on the L-N model, [PERSON] et al. [21] investigated the influence of material characteristics of the two different components on the kinematic characteristics of a crank-slider mechanism with clearance, considering the effect of frictional forces at the clearance. [PERSON] et al. [22] investigated the dynamic characteristics of the crank-slider mechanism containing deep groove ball bearing with clearance based on Hertz contact theory and continuous contact force model, and verified the correctness of the theoretical modelling with ADAMS. [PERSON] et al. [23] present a novel robust decentralized control of electrically driven robot manipulators. The proposed control employs a voltage control strategy, which is simpler and more efficient than the conventional torque control strategy, due to being free from manipulator dynamics. [PERSON] et al. [24] developed an error model of translational manipulator based on motion/force transferability. The effect of motion/force transferability on the theoretical accuracy is revealed.