Taking the copper anode plate picking robot as the research object, the three-dimensional model of the robot was established by solidworks software, and combined with the actual working characteristics of the robot, the workbench software was used to analyze the static mechanics of the robot arm in the most dangerous working condition and the first six orders of modal analysis in three typical working conditions: picking position, putting position and starting position. The simulation results show that the strength and stiffness of the robot arm and the small arm are within the allowable range and meet the design requirements; it is necessary to avoid the low-order frequencies or to strengthen the rigidity of the overall structure of the robot.