The mechanical and impedance control problems related to the inserting and pulling holes operation for space manipulator orbit placing the parts of station is discussed. Therefore, combining the conservation of momentum, the relationship between the driving force of inserting and pulling holes at the end of the replacement parts of space manipulator and the friction resistance in the holes, and the second Lagrange equation, the dynamic equation of the system is derived when the position and attitude of the carrier are not controlled. At the same time, according to the design requirements of the related operation and control system, the Jacobian relation between the end of the replacement parts of space manipulator and the basic coordinate system is established by using the geometric relation analysis of the system position. Then, a second-order linear impedance control model is established based on the dynamic relationship between the pose and the driving force of the end of the replacement parts of space manipulator and the impedance control principle. On the basis of the above work, aiming at the uncertainty of kinematics and dynamics in the process of inserting and pulling holes operation for space manipulator orbit placing the parts of station, an exponential impedance control strategy for the end force/pose tracking of the replacement parts of the space manipulator is designed, and the stability of the control system is proved through Lyapunov theory. The control strategy has the advantages of simple structure, fast convergence speed and good stability. The numerical simulation of the system verifies the effectiveness of the above control strategy.