For the purpose of engraving, KUKA KR60 mechanical arm was used in the laboratory for research and analysis.Firstly, the improved D-H parameter method was used to establish the D-H coordinate system of the manipulator, and the kinematic equation of the manipulator was obtained by calculating the homogeneous transformation matrix.Secondly, mathematical modeling was carried out with MATLAB Robbtics Toolbox, and the forward and inverse kinematics problems were analyzed and demonstrated to verify the correctness of the kinematic model of the mechanical arm. Thirdly, Monte Carlo method was used to calculate the movement Angle of the mechanical arm joint to reach the working area. Finally, trajectory planning was adopted.The variation curves of Angle, angular velocity and angular acceleration were obtained, and the rationality of its trajectory planning was verified by simulation analysis, which provided a research basis for the next step of carving trajectory path optimization.