Tool path smoothness is important to guarantee good dynamic and tracking performance of robot manipulators. An analytical C³ continuous tool path corner smoothing algorithm is proposed for robot manipulators with 6 rotational (6R) joints. The tool tip position is smoothed directly in the workpiece coordinate system (WCS). The tool orientation is smoothed after transferring the tool orientation matrix as three rotary angles. Micro-splines of the tool tip position and tool orientation are constructed under the constraints of the maximum deviation error tolerances in the WCS. Then the tool orientation and tool tip position are synchronized to the tool tip displacement with C³ continuity by replacing the remaining linear segments using specially constructed B-splines. Control points of the locally inserted micro-splines are all evaluated analytically without any iterative calculations. Simulation and experimental results show that the proposed algorithm satisfies constraints of the preset tool tip position and the tool orientation tolerances. The proposed corner smoothing algorithm achieves smoother and lower jerks than C² continuous corner smoothing algorithm. Experimental results show that the tracking errors associated to the execution of the C³ continuous tool path are up to 10% smaller than C² continuous path errors.

刀具路径的平滑度对于确保机械手的良好动态和跟踪性能非常重要。分析Ç ³连续刀具路径角平滑算法，提出了具有6个旋转（6R）关节机器人操纵器。刀尖位置直接在工件坐标系（WCS）中平滑。在将刀具定向矩阵作为三个旋转角传输后，将平滑刀具定向。刀尖位置和刀具方向的微样条线是在WCS中最大偏差误差公差的约束下构造的。然后将刀具方向和刀尖位置与C ³同步到刀尖位移通过使用特殊构造的B样条曲线替换其余线性段来实现连续性。局部插入的微样条曲线的控制点都经过分析评估，而无需进行任何迭代计算。仿真和实验结果表明，该算法满足了预设刀尖位置和刀具方向公差的约束。与C ²连续角平滑算法相比，所提出的角平滑算法可实现更平滑和更低的抖动。实验结果表明，与C ³连续刀具路径的执行相关的跟踪误差比C ²连续路径误差小10％。