A novel method for inverse kinematics analysis of non-spherical wrist robotic manipulators based on conformal geometric algebra

Abstract Non-spherical wrist manipulators are widely used in industrial settings, yet they lack effective inverse kinematics solutions. Current methods primarily rely on numerical iteration, which suffers from limitations such as sensitivity to initial values and convergence issues. Meanwhile, algebraic elimination methods require complex elimination techniques to obtain analytical solutions, restricting their practical engineering application. To address the limitations of these existing approaches, this paper innovatively proposes a novel analytical method based on conformal geometric algebra theory. The core of this method lies in utilizing the geometric characteristics of the manipulator to establish a polynomial equation for one of the joint variables, after which the remaining joint angles are solved according to the joint angle solution methodology. The correctness of the proposed method was verified using three sets of joint angles. Additionally, a comparative analysis with the Dixon elimination method was conducted using 100 sets of arbitrary initial joint angles. Example validation demonstrates that the proposed method exhibits significant advantages in computation time, solution completeness, and numerical accuracy, thereby providing a new theoretical tool and practical framework for the inverse kinematics analysis of robotic manipulators.