Dynamic Precision and Reliability of Multi-Link Linkages with Translational Pair Clearance

This study investigates the dynamic behavior and reliability of planar multi-link linkages with clearance in translational pairs. Using the Lagrange multiplier method, a dynamic model that accounts for clearance effects is developed. Furthermore, a reliability model is established by combining the first-order second-moment method with the stress-strength interference theory. Numerical simulations were performed to evaluate the impact of varying clearance sizes and driving speeds on motion errors and system reliability. This study also explores the nonlinear dynamics of the end-effector. The results indicate that increased clearance and higher driving speeds lead to certain changes in motion errors and operational reliability. Phase diagrams and Poincaré maps reveal directional differences in dynamic stability: chaotic motion along the X-direction and periodic oscillations along the Y-direction. These findings provide valuable insights for optimizing mechanism design and enhancing operational reliability.