Abstract 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- R RR parallel manipulator is used to demonstrate the proposed method, and its effectiveness is validated by comparison with the Monte Carlo simulation method.

中文翻译：

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平面并联机械手的瞬态系统运动学可靠性分析

摘要 平面并联机械手的瞬态系统运动学可靠性是指在整个指定轨迹上位姿误差落入允许安全区域的概率，对其工作性能至关重要。然而，关于这个问题的工作非常有限。因此，本研究基于首过法对考虑关节间隙、输入不确定性和制造缺陷的平面并联机械手进行了瞬态运动可靠性分析。首先，利用Baker-Campbell-Hausdorff公式和李群理论和李代数理论建立极限状态位姿误差函数。然后，利用多元高斯的条件和边际统计矩（均值和协方差）的期望传播和封闭形式特性，推导出非平稳向量随机运动过程的异交率的解析解。在此基础上，基于异交事件独立的假设计算了瞬态系统运动学可靠性。最后，利用平面3-R RR并联机械手对所提出的方法进行了验证，并通过与蒙特卡罗模拟方法的对比验证了其有效性。时间相关系统运动学可靠性是根据异交事件独立的假设计算的。最后，利用平面3-R RR并联机械手对所提出的方法进行了验证，并通过与蒙特卡罗模拟方法的对比验证了其有效性。时间相关系统运动学可靠性是根据异交事件独立的假设计算的。最后，利用平面3-R RR并联机械手对所提出的方法进行了验证，并通过与蒙特卡罗模拟方法的对比验证了其有效性。