In order to solve the problem that the UR5 robot coordinate system established by the user is inconsistent with the manufacturer's, and the data related to the force, angular velocity, angular acceleration are difficult to be directly used, based on the analysis of the structural characteristics of the UR5 robot, the coordinate system matching the manufacturer's data is established. The kinematics equation of the UR5 robot is established by D-H method to describe the relationship of each joint. According to the structural characteristics satisfying the Pieper criterion of the UR5 robot, the kinematic inverse solution of the UR5 robot is obtained by the separation variable method. The singularity analysis of UR5 robot is completed by differential transformation method, and the singularity analysis and simulation results show the relationship between the joint variables of UR5 robot when the position is singular. The kinematics program is written by using MATLAB software, and the robot system is used to carry out laboratory test and engineering practice verification. The experimental results of MATLAB kinematics program are consistent with the internal data of UR5 system, which verifies the correctness of kinematics analysis. The research result has some reference for further research of UR5 robot continuous trajectory planning.