Novel high-order procedures follow finite displacements avoiding the adverse effects of the wrist singularity of a serial robot manipulating a curved tool. In robotic welding, this type of end effector is commonly applied to right-angle seams. This tool is symmetric about a line emanating from its tip, which adds an effective revolute-joint axis line to the robot. The curve in the tool places this axis line oblique to the third joint in the robot wrist. When the second wrist axis is out of the plane containing the third joint and tool axes, the tool axis supplies useful kinematic redundancy for mitigating the loss of mobility in a 3-axis wrist on approach to its singularity. A new method plans a path encountering the wrist singularity while satisfying limits on joint rate and acceleration under a constant rate of tool traversal. This method maintains precise position of the tool tip with the seam while allowing rotation of the tool about its symmetry axis. This is accomplished with either zero or nearly zero deviation in pointing direction.

新颖的高阶过程遵循有限的位移，避免了串行机器人操纵弯曲工具时手腕奇异性的不利影响。在自动焊接中，这种类型的末端执行器通常应用于直角接缝。该工具关于从其尖端发出的线是对称的，这为机器人增加了有效的旋转关节轴线。工具中的曲线使该轴线倾斜于机器人手腕中的第三关节。当第二腕部轴超出包含第三关节和工具轴的平面时，工具轴可提供有用的运动学冗余，以减轻3轴腕部接近其奇点时的活动性损失。一种新方法可以规划一条遇到手腕奇异点的路径，同时在恒定的工具遍历速率下满足关节速率和加速度的限制。这种方法可保持刀尖与接缝的精确位置，同时允许刀具绕其对称轴旋转。这可以通过指向方向上的零偏差或几乎零偏差来实现。