A quadruped magnetic absorbing wall-climbing robot with omni-directional motion was designed to achieve reliable adsorption and free movement on the iron-based wall with different curvatures. Firstly, the modified Grübler-Kutzbach (G-K) formula was used to analyze the degree of freedom (DOF) of the robot. Then the Denavit-Hartenbery (D-H) method was used to establish the linkage coordinate system of the robot walking legs, and the forward and inverse kinematics of the walking legs were analyzed. Then the robot was regarded as a parallel mechanism, the forward and inverse kinematics of the carrier platform were analyzed, the analytic solution of the inverse kinematics was given, and a numerical algorithm based on Newton's method was used to solve the redundant equations to obtain the numerical solution of the forward kinematics, the complete kinematics mathematical model of the robot was established. To verify the correctness of the model, the calculation program was compiled in MATLAB according to the model, and the same kinematics simulation was performed in MATLAB and Adams respectively to make comparisons. Finally, the Jacobian matrix of the robot was obtained by the screw theory, and the singularity of the robot was analyzed by combining the Grassmann line geometry theory. A forward kinematics singularity in non-redundant driving was verified. The results of DOF analysis showed that the carrier platform has six-DOF, so it can complete the omnidirectional motion in the space, and the structure design of the robot is reasonable. The simulation results of MATLAB and Adams are consistent and the forward and inverse kinematics can mutually verify each other, which illustrates the correctness of the mathematical model, and provides an a theoretical basis for the motion control, trajectory planning of the robot. The singularity of the robot is obtained, which provides an approach to avoid it. No power consumption still is achieved by utilizing the inverse kinematics singularity.
