关节齿隙对空间机械臂末端定位精度的影响

研究齿隙存在情况下机械臂末端定位误差达到要求精度的概率。分析了现有齿隙模型的优点和缺点,对其中的死区模型进行改进,提出齿隙的随机变量模型。将此模型作为3关节机械臂的关节误差,导出机械臂末端定位误差的随机模型,并利用Taylor公式对模型作了近似处理,得到以关节误差的二次函数表示的简化模型，并在关节空间中讨论了末端定位误差的最大值和最小值问题。分4种情形给出定位误差达到要求精度的概率，为多阶段任务系统的路径规划和任务优化提供了依据。

Effect of Gear Backlash on Positioning Precision of Manipulator End-effectors

The probability of that the positioning error of the end-effectors in a manipulator with gear backlash meets the desired accuracy is studied. The advantages and disadvantages of existing gear backlash models are analyzed, and a random variable model of gear backlash is presented based on the improvement of one of the models. A random model of positioning errors of the manipulator end-effectors is derived by taking the random variable model as angular displacement errors of 3-joint manipulator. A simplified model expressed by a quadratic function of angular displacement errors is obtained by approximating the random model with Taylor's formula. The maximum and minimum of the positioning error in joint space are discussed as well. The probability of that the positioning error of the manipulator end-effectors meets the desired accuracy is presented according to four cases, which provides basis for route planning and task optimization in multi-phase mission system.