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该文结合一个实际的具有闭链结构的工业机器人，介绍了它的运动方程及其逆解，文中重点讨论了它的全局退化及局部退化问题。作者通过机器人运动方程的雅可比矩阵秩的分析，找出它的全局退化点，而求解运动方程的机器人坐标，确定出它的局部退化点。找出这些退化点，就可以对机器人结构的设计及路径的规划给予理论上的指导。
In this paper, an actual industrial robot with closed-chain structure is introduced. Its motion equation and its inverse solution are introduced. The global degeneracy and local degeneration problems are discussed in this paper. By analyzing the Jacobian matrix of the robot’s motion equation, the author finds out its global degradation point, and solves the robot’s coordinate of the motion equation to determine its local degradation point. Find out these degradation points, we can give theoretical guidance on the design of robot structure and the path planning.