Time-dependent system kinematic reliability analysis for planar parallel manipulators

Time-dependent system kinematic reliability of the planar parallel manipulator refers to the probability of the pose error falling into the allowable safe region over the whole specified trajectory, which is essential for its work performance. However, works regarding this issue are quite limited. Consequently, this study conducts time-dependent kinematic reliability analysis for planar parallel manipulators considering joint clearance, input uncertainty, and manufacturing imperfection based on the first-passage method. First, the limit-state pose error function is established by means of the Baker–Campbell–Hausdorff formula and the theory of the Lie group and Lie algebra. Then, the analytical solution to the outcrossing rate of the non-stationary vector stochastic kinematic process is derived by employing the expectation propagation and closed-form properties of conditional and marginal statistical moments (mean and covariance) of the multivariate Gaussian. On this basis, the time-dependent system kinematic reliability is calculated upon the assumption that the outcrossing events are independent. Finally, the planar 3-RRR parallel manipulator is used to demonstrate the proposed method, and its effectiveness is validated by comparison with the Monte Carlo simulation method.