# Nonlinear Analysis and Reliability Analysis of Multilink Mechanism Considering Mixed Clearance
## 1 Introduction  
With the swift economic advancement, the machinery manufacturing sector is steadily evolving towards greater speed, enhanced precision, and increased productivity. The mechanical system's functionality and efficiency are critically dependent on the mechanism, which is essential for its overall operation. Therefore, the study of mechanism dynamics is of considerable practical significance and has a significant impact on the development of the manufacturing industry. Among these mechanisms, multilink mechanisms, serving as critical components, have found extensive applications across a variety of fields, including medical devices, mobile robotics, aerospace, agricultural machinery, and compression equipment, garnering considerable attention and in-depth investigation from scholars. In multilink mechanisms, various components are interconnected through revolute and prismatic joints. Yet, due to factors like manufacturing tolerances, installation inaccuracies, and friction losses, clearances often arise in the kinematic pairs. Clearances can result in adverse interactions among the kinematic pairs, substantially impacting precisionand stability of the mechanism's movement [1; 2; 3; 4; 5; 6; 7; 8; 9]. So, it is crucial to conduct comprehensive study on the dynamic behaviors of multilink mechanisms, particularly those with mixed clearances. Many mechanisms in the real world consist of one or more revolute joints, which are essential for their proper functioning. However, the existence of clearances in these joints causes discrepancies between ideal and actual motion of the mechanisms. Therefore, investigating the effects of clearances in revolute joints is of significant importance for understanding and improving the performance of such systems. [PERSON] et al. [10] employed the Newton-Euler equation system to establish a dynamics model for a slider-crank mechanism with multiple rotary joint clearances, aiming to explore impact of these clearances of the mechanism's performance. [PERSON] et al. [11] constructed a corresponding rigid body dynamics model for a sliding crank mechanism with a single rotary joint clearance and further proposed a stabilization control strategy based on the Pyragas principle. [PERSON] et al. [12] utilized finite element analysis to discretize slider components in a multi-body system and conducted an in-depth study on deformation characteristics of slider in a slider-crank system with clearances. [PERSON] et al. [13] integrated the Absolute Nodal Coordinate Formulation (ANCF) with finite element analysis to build a dynamics model that comprehensively considers bearing stiffness, joint clearance, and flexible links, and used this model to predict the dynamic accuracy of high-speed stamping mechanisms. [PERSON] et al. [14] constructed a six-DOF vehicle shimmy dynamics model incorporating multiple clearances and deeply explored the specific impact of clearance factors on vehicle shimmy response. By analyzing phase diagrams and Poincare section maps, they revealed the presence of chaotic dynamic behavior in this vehicle shimmy system. [PERSON] et al. [15] comprehensively investigated the dynamic characteristics of an over-constrained planar parallelogram mechanism with revolute joint clearances, focusing on influences of these clearances on mechanism's dynamic performance. [PERSON] et al. [16] selected a planar 4-bar mechanism with a single revolute joint clearance as a case study and constructed a dynamics model based on the second kind of Lagrange's equations. They thoroughly investigated the influence of revolute joint clearances on nonlinear dynamic properties of mechanism by examining phase plane diagrams, Poincare maps, and bifurcation diagrams. [PERSON] et al. [17] selected the RU-RPR mechanism, taking into account the clearances in revolute joints, and analyzed its chaotic behavior through phase portraits, Poincare maps, and the highest Lyapunov exponent. [PERSON] et al.