# Nonlinear Analysis and Reliability Analysis of Multilink Mechanism Considering Mixed Clearance
## 5 Response Analysis of Rigid Body Dynamics of Clearance Containing Mechanism
### Effect of Combined Clearances on Rigid Body Dynamic Response of Mechanism  
This section analyzes the impact of mixed clearances on the rigid body dynamic response of the mechanism. The L-N model and modified Coulomb friction models are used for normal impact and tangential friction, respectively, in the study of influence of various clearance values and travelling speeds on dynamic response of rigid body of an eight-bar mechanism.  
5.3.1 Effect of Clearance Values in the Response of Rigid Body Dynamics of Mixed Clearance Mechanism  
In this section, influence of clearance values on dynamic response of mechanism in presence of a mixed clearances will be investigated, with particular reference to the effect of 0.1 mm, 0.2 mm, and 0.3 mm clearance values. Assuming that clearance values of composite external joint clearance A and prismatic joint clearance F are the same. Figures 11 and 12 illustrate at drive speed of crank 1 set to 60 revolutions per minute, the dynamic response of mechanism with a clearance friction coefficient of 0.2.  
Figure 11: Motion characteristics of slider with various clearance values: (a) slider displacement; (b) slider velocity; (c) slider acceleration.  
Figure 10: Kinematic characteristics of the slider under different types of clearance: (a) slider displacement; (b) slider velocity; (c) slider acceleration.  
Figure 11 shows displacement, velocity, and acceleration graphs of the slider under mixed clearances (combined external rotary clearance A and prismatic clearance F) with clearance values of 0.1 mm, 0.2 mm, and 0.3 mm, respectively. The kinematic characteristics show that characteristics of displacement and velocity of a slider mixed clearances mechanism with different values of the clearances show a relatively stable trend, with the displacement curves close to the ideal state, while the velocity curves have a slight fluctuation. As the clearance value gradually increases, peak acceleration is delayed, and its value shows an obvious upward trend. Specifically, the peak acceleration of the slider occurs at 1.67 s with a value of 305.1 m/s\({}^{2}\) at 0.1 mm, at 1.78 s with a value of 531.2 m/s\({}^{2}\) at 0.2 mm, and at 1.85 s with a value of 766.5 m/s\({}^{2}\) at 0.3 mm. Wear-induced clearances will lead to an increase in motion pair clearances, thereby increasing relative motion space between components of mechanism. Larger clearances allow for greater ranges of motion, directly resulting in an increase in the maximum values of slider displacement, velocity, and acceleration.  
As shown in Figure 12, the center trajectories at the clearances of revolute joint A\({}_{1}\), revolute joint A\({}_{2}\), and prismatic joint F reveal that, with clearance values of 0.1 mm, 0.2 mm, and 0.3 mm, respectively, as the clearance value of the kinematic pair increases, the center trajectories at clearances exhibit increasingly complex dynamic characteristics. These are manifested as increased frequencies of free motion states and collision events of the shaft within the bearing and slider on the guideway. This variation leads to deviations in dynamic behavior between the actual mechanism with clearances and theoretically ideal mechanism. As clearance size increases from 0.1 mm to 0.3 mm, eccentricity between shaft and bearing and between slide and the guideway increases accordingly due to a significant increase in clearance width. This change in geometry leads to a significant increase in instantaneous collision forces in the clearance region, which deepens the depth of penetration of the shaft into the bearing and the slide into the guideway. Together, these effects influence dynamic response of mechanism in terms of faster vibration frequency and higher vibration amplitude, which further affects the kinematic and dynamic behavior of the mechanism at a deeper level.