A General Method to Solve Inverse Kinematics of Spherical Wrist Manipulators

The paper will propose a new method to solve inverse kinematics of spherical wrist manipulators. The idea is separating the manipulator into two parts, and then solve the inverse kinematic of them to get the solution of the whole arm. And there are two steps: the first step of the method is decoupling, to make sure that the first threejoint variables q₁, q₂, q₃ only appear in the unlinear equations of position and the last three joint variables \theta-{n-2}, \theta-{n-1},\theta-{n} only emerge in the attitude matrix; the second step is solving the position equation with the adjusted Newton's method and solving the attitude matrix with the analytic method. Because the new method is a mixture of numerical method and closed method, so the efficiency of the new method is higher than traditional numerical method and it is suitable for all kinds of spherical wrist robot while the close method is unique for a particular manipulator. Moreover the method can control error to any small amount you give. At the end of the paper, the inverse kinematics of three classical manipulators will be solved by the new method and then visulalize the inverse kinematic by trajectory planning.