Dynamic responses and non-probabilistic reliability analysis of flexible manipulator considering clearance joint and multiple uncertainties

Joint clearances and uncertain parameters in the space manipulator are inevitable, which adversely affect the motion accuracy and reliability of the manipulator system. In this paper, dynamic model and a novel reliability calculation method are presented to analyze the performance of the flexible manipulator considering clearance joint and multiple uncertainties. Firstly, the nonlinear contact-impact model in the clearance joint is established. Based on the Euler-Bernoulli beam theory, the deformation of the flexible arm is modeled using assumed-mode method. Furthermore, dynamics equations of two-link manipulator are established by utilizing the Lagrange method. The uncertainties are defined as interval parameters, and a Chebyshev-based interval method is proposed to calculate the dynamic response bound of flexible manipulator system with high-dimensional uncertainties. To predict the motion reliability, a limit state function and an innovative non-probabilistic reliability index are proposed. Finally, numerical simulations are implemented to verify the effectiveness of the proposed approaches. Results show that the proposed methods can effectively obtain accurate dynamic responses and reliability prediction, which provide basis for performance evaluation and motion control of manipulator systems.