In this paper, first, how to establish the kinematics equation of the manipulator and determine the parameters is introduced. Second, how to calculate and analyze the working space of the manipulator, and get the working space range map of the manipulator are discussed based on the MATLAB software. Then, based on the Robotics Toolbox in the MATALAB software working environment, how to simulate the positive kinematics, the inverse kinematics and the trajectory planning of the movement model of the manipulator are investigated. Where, we built and obtain the curve graphs of the angular displacement, angular velocity, angular acceleration of each joint with changing of time. This research results can make the design of the motion space of the manipulator more intuitive and accurate. Moreover, the research results provide the theoretical basis and reference for the design of the manipulator control system, dynamic analysis and trajectory planning.