具有解析式正解的Stewart衍生型并联机构的位移输入协调关系

Displacement input coordination of Stewart derivative parallel mechanism with analytical positive solution

针对6自由度冗余驱动并联机构实时控制较难的问题,以具有解析式正解的Stewart衍生拓扑构型为研究对象,研究了位移输入的协调关系。通过设计二重复合球铰链和可转换主动、从动模式的移动副,实现了6种不同冗余度的低耦合驱动模式。根据动平台上4个位置点之间的尺度约束关系,构建了一种正向运动学全解析算法,验证了位姿正解模型的正确性。推导化简了位移输入的6个协调方程,分别运用Newton-Raphson法和Broyden法得到了协调方程的数值解,对比结果发现,Broyden法的计算时间约为Newton-Raphson法的78%,Newton-Raphson法的精度优于Broyden法至少3倍。从许可初值偏差和结构参数两个方面研究了各种驱动模式对冗余协调算法的影响,结果表明,随着动平台边长的增大以及移动副初始长度的减小,冗余协调算法允许有更大的许可初值偏差。进一步地,基于区间分析理论引入并定义扰动适应性能评价指标,计算出本机构的最佳冗余度为5,并且得出Broyden法的综合扰动适应性能优于Newton-Raphson法的1.27倍。最后,结合数值性态给出了Stewart衍生型并联机构移动副驱动模式优选的3点选取原则。研究方案可为6自由度冗余驱动并联机构的结构模型优化及实时控制提供参考依据。

Aiming at the difficulty of real-time control of 6-DOF redundantly actuated parallel mechanism,the coordinated relation of displacement input was studied for Stewart derivative topological configuration with analytical positive solution.Six low-coupling driving modes with different redundancy were realized by designing double composite spherical pair and convertible master-slave output prismatic pair.According to the scale constraints between the four positions on the moving platform,a forward kinematics algorithm with whole analytical solutions was constructed,and the correctness of the forward displacement solution model was verified.Six compatibility equations of displacement input were derived and simplified.The numerical solutions of the compatibility equations were obtained by using Newton-Raphson method and Broyden method respectively.The comparison results show that the computing time of Broyden method is about 78%of that of Newton-Raphson method and the accuracy of Newton-Raphson method is at least three times higher than that of Broyden method.The influence of various driving modes on the redundant coordination algorithm was studied from two aspects of admissible initial deviations and structural parameters.The results show that the redundant coordination algorithm has larger admissible initial deviations with the increase of the side length of the moving platform and the decrease of the initial length of the prismatic pair.Furthermore,introducing and defining the perturbation adaptive performance evaluation index based on interval analysis theory,the optimal redundancy of the mechanism is calculated to be 5 and the comprehensive perturbation adaptive performace of Broyden method is 1.27 times better than Newton-Raphson method.Finally,combined with the numerical performance,the three selection principles for the driving mode optimization of the Stewart derivative parallel mechanism is given.The research scheme can provide reference for structure model optimization and real-time control of 6-DOF redundantly actuated parallel mechanism.