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In order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, conformal geometric algebra (CGA) is introduced to the construction of kinematics model of industrial robots. In the forward kinematics solving process, the motion expressions of each joint are obtained by using the translation and rotation operators in CGA, and then the pose of the end-effector of the robot is obtained. In the process of solving the inverse kinematics, cross product of the constructed basic geometry is carried out to obtain the position of each joint node, the lines and planes through the joint node are constructed, the inner product is made in the CGA frame to obtain the cosine expression of all joint angles, and then all the solutions of the robot's inverse kinematics are solved. Finally, the MOTOMAN-HP20D 6-DOF industrial robot is used for example calculation, and the accuracy and effectiveness of the algorithm is verified by Matlab/Simulink software, which lays the foundation for the subsequent motion control of the robot.

In order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, Conformal geometric algebra （CGA） was introduced to the construction of kinematics model of industrial robots. In the forward kinematics solving process, the motion expressions of each joint were obtained by using the translation and rotation operators in CGA, and then the pose of the end-effector of the robot was obtained. In the process of solving the inverse kinematics, cross product of the constructed basic geometry is carried out to obtain the position of each joint node, and then the lines and planes through the joint node are constructed, and the inner product is made in the CGA frame to obtain the cosine expression of all joint angles, and then all the solutions of the robot's inverse kinematics are solved. Finally, the MOTOMAN-HP20D 6-DOF industrial robot was used for example calculation, and the accuracy and effectiveness of the algorithm was verified by Matlab/Simulink, which laid the foundation for the subsequent motion control of the robot.