# 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
#### 5.3.2 Effect of Driving Speed on Dynamic Response of the Rigid Body of a Mixed Clearance Mechanism  
In order to investigate the effect of driving speed on the rigid-body dynamic response of a mechanism containing a mixed clearance (a combination of external rotary joint clearance A and prismatic joint clearance F), three sets of speeds were chosen for the study, i.e., 30 rpm, 60 rpm, and 150 rpm for crank 1. The clearance values were set to 0.2 mm. The  
Figure 12: Center trajectories at clearances with different values: (**a**) revolute joint clearance A\({}_{1}\); (**b**) revolute joint clearance A\({}_{2}\); (**c**) prismatic joint clearance F.  
displacement, velocity, and acceleration plots of the slider as well as the center trajectories for different clearances are shown in Figures 13-16. As illustrated in Figures 13-15, as the driving speed of crank 1 increases from 30 rpm to 60 rpm, and then to 150 rpm, the peak values and vibration frequencies of the dynamic responses also increase accordingly. The driving speed has a direct impact on the relative motion states between components in clearance kinematic pairs, accelerating the transition rates of motion states between the shaft and the bearing, and subsequently, intensifying the wear process of the kinematic pairs. The displacement, velocity, and acceleration graphs of the slider show that, in mechanisms with mixed clearances, peak displacement of slider exhibits high stability and is almost unaffected by the presence of clearances. Furthermore, as driving speed gradually increases, velocity fluctuations  
Figure 14: Velocity of the slider: (**a**) \(\omega_{1}\) = 30 rpm; (**b**) \(\omega_{1}\) = 60 rpm; (**c**) \(\omega_{1}\) = 150 rpm. of slider significantly intensify, with peak velocity also increasing. An intensification of acceleration fluctuations of the slider similarly results from an increase in driving speed, and the peak acceleration values also increase notably. Specifically, when driving velocity is 30 rpm, the maximum acceleration value is 8.2 m/s\({}^{2}\). When driving velocity is 60 rpm, the maximum acceleration value reaches 531.2 m/s\({}^{2}\). When driving velocity is 150 rpm, the maximum acceleration value soars to 2183.5 m/s\({}^{2}\). In some data plots, there are instantaneous changes in values at several positions. For instance, in the acceleration data plot Figure 15b, during the time interval from 1.3 s to 2 s, there are two significant fluctuations, mainly concentrated in two regions. These fluctuations are primarily caused by the collisions between the slider and the guide rail. This indicates that during this stage, the four collision states transition relatively frequently, resulting in high-incidence collision zones. Especially when the clearance is small, the mechanism is more prone to being in a state of continuous contact and collision, thereby leading to an increase in the oscillation frequency and abrupt changes in the values of velocity and acceleration. This is illustrated in Figure 16, where center trajectories for the second cycle are analyzed. When the drive speed is increased from 30 rpm to 150 rpm, collision frequency between the shaft and the bearing is accelerated, leading to a more confused and disorganized state of movement of the shaft and slider in the bearing on the guideway. This leads to an increase in collision forces between components, exacerbating the degree of confusion in the center trajectory at the clearance and making recoil and prismatic joints more prone to failure. As the drive velocity rises, the center trajectory becomes more chaotic and freer and collision states occur more frequently. As the mechanism operates at higher speeds, the relative speed of motion between the shaft and bearings increases. Due to the presence of clearance or friction, the motion of the shaft inside the bearing may become unstable, leading to sudden changes in acceleration.