# Nonlinear Analysis and Reliability Analysis of Multilink Mechanism Considering Mixed Clearance
## 1 Introduction
Therefore, exploration of mechanisms with mixed clearances has practical significance. [PERSON] et al. [30] conducted comparative studies on the dynamic responses and nonlinear traits of rigid systems with mixed clearances and rigid-flexible hybrid systems with similar clearance combinations. [PERSON] et al. [31] selected the sliding crank mechanism as a research paradigm to explore the influence of dual clearance on rigid body dynamic of mechanisms. Their research revealed significant dynamic interaction effects between clearance joints in multibody mechanical systems. [PERSON] et al. [32] introduced a precise dynamic modeling technique for rigid-flexible coupled multilink mechanisms (MLMs) considering rotational and translational clearances, establishing clearance models for revolute and prismatic joints. [PERSON] et al. [33], based on a six-bar mechanism, used the Lagrange multiplier method to establish dynamic equations for rigid body systems considering dry friction, studying the impact of rotational and translational clearance on accuracy and stability of planar mechanism. [PERSON] et al. [34] utilized Lagrange multiplier method to establish dynamic equations for rigid body systems of six-bar mechanisms considering the coupling effects of dry friction, rotational clearances, and translational clearances. [PERSON] et al. [35] introduced the first kinematic model to evaluate the impact of joint clearance superposition on nominal output link position in linkage mechanisms that include both rotational and prismatic joints. [PERSON] et al. [36] introduced a comprehensive kinematic reliability assessment technique for typical planar parallel manipulators (PPMs), incorporating the tolerance variables of both revolute and linear joints. Additionally, manufacturing uncertainties and input variations are taken into consideration. [PERSON] et al. [37] established for a planar slider-crank mechanism. Each revolute and prismatic joint clearance is represented by a short clearance link. [PERSON] et al. [38] proposed a comprehensive dynamic modeling approach for spatial parallel mechanisms featuring multiple spherical joint clearance, utilizing the Lagrange multiplier method. [PERSON] et al. [39] proposed an innovative methodology to address the operational complexities arising from nonideal conditions in spatial revolute joints through the application of three-dimensional finite element-based modeling. [PERSON] et al. [40] developed a closed-form analytical framework for solving the Reynolds equation in radial bearing lubrication scenarios, addressing both infinitely extended and finite-length bearing configurations under side leakage constraints. [PERSON] et al. [41] investigated the dynamic response characteristics of automotive scissor door mechanisms incorporating clearance-type kinematic pairs through an innovative hybrid nonlinear continuous contact force formulation. [PERSON] et al. [42] studied rigid-flexible coupling mechanisms under the influence of clearance, and built a testing platform for experimental verification. [PERSON] et al. [43] considered coupling of lubricated clearance and component flexibility and established related model for a rigid-flexible coupling 2-DOF mechanism with lubricated clearances to study. Unlike conventional Newton-Euler, Lagrange, and finite element methods, hybrid clearance modeling transcends the limitation of investigating single kinematic pair clearance effects on specific mechanisms. Instead, it adopts a holistic perspective of multilink mechanical systems to comprehensively analyze complex dynamic responses arising from simultaneous existence of revolute and prismatic joint clearances, including impacts on system dynamic accuracy, stability, and reliability.