# Nonlinear Analysis and Reliability Analysis of Multilink Mechanism Considering Mixed Clearance
## 1 Introduction
[18] conducted an in-depth investigation of the nonlinear dynamics of a rigid-flexible coupling slider-crank mechanism with rotary joint clearances, utilizing phase plane diagrams, Poincare section maps, and bifurcation diagrams. [PERSON] et al. [19] conducted a comparative analysis focusing on the differences in dynamic responses between rigid sliding crank mechanisms and rigid-flexible coupling slider-crank mechanisms with revolute joint clearances. They used ADAMS software for simulation to verify the accuracy of their theoretical analysis. The prismatic joint is an indispensable component in mechanism construction and a crucial factor for realizing and transmitting the intended functions of a mechanism. More complex mechanisms require more prismatic joints to achieve their functional requirements. The stability and accuracy of prismatic joints significantly impact the performance of the mechanism. Thus, examining mechanisms with prismatic joint clearance is of significant importance. [PERSON] et al. [20] developed and elaborated a new dynamic modeling method for crank-slider mechanisms with prismatic joint clearance based on the theoretical framework of nonsmooth dynamics. They conducted an in-depth analysis of how prismatic joint clearance impacts kinematic and dynamic properties of these systems. [PERSON] et al. [21] adopted the Lankarani-Nikravesh (L-N) model framework to establish dynamic equations for a slider-crank mechanism with clearance. They comprehensively analyzed the specific influence of velocity factors on the dynamic behavior of this mechanism. [PERSON] et al. [22] constructed a 3D geometric representation of a prismatic joint with clearance and thoroughly investigated nonlinear dynamic properties of the system using numerical analysis, simulations, and experimental validation. [PERSON] et al. [23] conducted modeling analysis for pin-groove joints with clearance and thoroughly investigated the influence of various kinematic constraints and contact force models on the dynamic characteristics of the mechanism. [PERSON] et al. [24] developed dynamic models for mechanisms with multiple joint clearances and deeply explored the influences of clearance size and restoring force coefficient on the dynamic behavior of these mechanisms with clearance. [PERSON] et al. [25] selected the slider-crank mechanism as their research object. They used Poincare maps to analyze nonlinear dynamic characteristics exhibited by the slider, connecting rod, and clearance area, and further explored the bifurcation behavior of the mechanism as the clearance value changes at different operating speeds. [PERSON] et al. [26] proposed a kinematic modeling and identification approach for a 6-PSU parallel robot incorporating joint clearances, utilizing actuation acceleration information. [PERSON] et al. [27] investigated how joint clearance influences the dynamic performance of a planar system with two actuating links and gaps in its sliding joints, considering variations in the system's input velocities. [PERSON] et al. [28] introduced a straightforward and efficient kinematic model and approach, leveraging [PERSON]'s N-bar rotatability principles, to evaluate magnitude of positional uncertainty induced by joint clearances in any linkage or manipulator employing revolute or prismatic pairs. [PERSON] et al. [29] systematically studied the nonlinear dynamic characteristics of a mechanism considering piston rod flexibility and double prismatic joint clearance using phase diagram analysis, maximum Lyapunov exponent calculation, and Poincare section mapping. In keeping with the development of the times and to achieve a richer variety of functions, the composition of machinery has become increasingly complex. Mechanisms with stronger functionality contain more revolute joints and prismatic joints. Mixed clearances formed by the clearances between revolute joint and prismatic joint will affect performance of the mechanism. This effect is not a simple addition of the impacts of revolute joint clearance and prismatic joint clearance.