Study on Rigid-Flexible Coupling Nonlinear Dynamics of Hybrid Mechanisms with 3D Revolute Joint Clearances

Previous research on mechanisms with clearances has primarily focused on planar mechanisms and simple 3D mechanisms. Limited related studies have been conducted in field of hybrid mechanisms that consider the combined effects of three-dimensional joint clearances and flexible components. Based on the 3-PRPaR-RUPUR hybrid mechanism, this paper investigates the coupled effects of clearances and flexible components on various aspects of the mechanism, including acceleration, velocity, displacement of the mechanism, the driving force of original components, impact force within clearances, central trajectory at clearances, dynamic accuracy reliability, and nonlinear characteristics. Firstly, an Absolute Nodal Coordinate Formulation based theoretical model for a 3D two-node flexible beam element is established. Additionally, a kinematic theoretical model for revolute joint clearance is constructed. Secondly, the impact force at clearances is simulated by combining the Flores normal contact force theoretical model and the modified Coulomb tangential theoretical model. A rigid-flexible coupling dynamic model for 3-PRPaR-RUPUR hybrid mechanism is developed based on the Lagrange multiplier theoretical theory. Then, using Stress-Strength Interference model and First-Order Second-Moment theoretical method to built the mechanism's reliability theory model to analyze the influence of 3D revolute joint clearances and component flexibility on mechanism reliability. The nonlinear characteristics of the mechanism are explored by using phase diagram, Poincaré maps and Largest Lyapunov exponent. The results indicate that coupled effects of 3D revolute joint clearances and flexible components affect the stability of the mechanism, causing fluctuations in its dynamic response, generating chaotic phenomena, and reducing its reliability. And with the addition of more clearances, the chaotic phenomena of the mechanism at certain specific moments may weaken, and its reliability may also improve.