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提出了一种在笛卡儿空间实现机器人操作手最优位姿轨迹规划新方法。基于欧拉刚体有限转动定理，根据旋量理论和计算几何中三维直纹面路程参数生成原理，求以等效角位移矢量在空间的运动轨迹形成的直纹曲面面积及其变化率并考虑运动时的灵活性为泛函的泛函极值来实现以路径最短、运动灵活性最好、或动力学性能最优为目标的机器人位置和姿态轨迹优化生成，建立了相应的优化数学模型及求解方法。最后，用该法对三自由度平面机器人操作手进行了仿真计算。
A new method of trajectory planning of robot manipulator position in Cartesian space is proposed. Based on the Euler rigid body finite rotation theorem, according to the theory of spin and theory of geometric parameters of three-dimensional ruled surface, the area and the rate of ruled surface formed by the trajectory of equivalent angular displacement vector are calculated and considered The flexibility of the functional end-function to achieve the optimal position and attitude trajectory of the robot with the shortest path, the best movement flexibility, or the optimal dynamic performance, and the corresponding optimal mathematical model and solution are established method. Finally, this method is used to simulate the manipulator of three degrees of freedom planar robot.