Seven degree-of-freedom (DOF) robot arms have one redundant DOF which does not change the translational or rotational motion of the end effector. The redundant DOF offers greater manipulability of the arm configuration to avoid obstacles and steer away from singularities, but it must be parameterized to fully specify the joint angles for a given end effector pose. For 7-DOF revolute (7R) manipulators, we introduce a new concept of generalized shoulder-elbow-wrist (SEW) angle, a generalization of the conventional SEW angle but with an arbitrary choice of the reference direction function. The SEW angle is easy for human operators to visualize as a rotation of the elbow about the line from the shoulder to the wrist and has been used in the teleoperation of space robot arms. Since the conventional SEW angle formulation is prone to singularities, we introduce a special choice of the reference direction function called the stereographic SEW angle which has a singularity in only one direction in the workspace. We prove that such a singularity is unavoidable for any parameterization. We also include expressions for the SEW angle Jacobian along with singularity analysis. Finally, we provide inverse kinematics solutions for most known 7R manipulators using the general SEW angle and the subproblem decomposition method. These solutions are often closed-form but may sometimes involve a 1D or 2D search. Inverse kinematics solutions, examples, and evaluations are available in a publicly accessible repository.

翻译：七自由度机器人手臂具有一个冗余自由度，该自由度不会改变末端执行器的平移或旋转运动。这个冗余自由度增强了手臂构型的可操作性，使其能够避开障碍物并远离奇异点，但必须对其进行参数化处理，以完全确定给定末端执行器位姿下的关节角度。针对7-DOF转动关节（7R）机械臂，我们引入了一个广义肩-肘-腕（SEW）角的新概念，该概念是对传统SEW角的推广，但允许任意选择参考方向函数。SEW角易于操作人员直观理解，表现为肘部围绕肩部到腕部连线的旋转，并已应用于空间机器人手臂的遥操作。由于传统SEW角公式容易产生奇异点，我们引入了一种特殊的参考方向函数选择，称为球极投影SEW角，该函数在工作空间中仅在一个方向上存在奇异点。我们证明了任何参数化都无法避免此类奇异点。本文还给出了SEW角雅可比矩阵的表达式以及奇异点分析。最后，我们利用广义SEW角和子问题分解方法，为大多数已知的7R机械臂提供了逆运动学求解方案。这些求解通常为封闭形式，但有时可能涉及一维或二维搜索。逆运动学求解方法、实例及评估结果均可在公开的存储库中获取。