Abstract: In order to paint huge workpieces such as aircrafts, 6DOF (degree of freedom) painting robots are always transported by a mobile platform to different base positions for working. This research aims at finding a base position for the current painting paths at which the painting robot gets best kinematic performance. Firstly, a concept of outer wrist center is proposed and used to make a spherical approximation of the hollow wrist, thereby overcoming the coupling problem. And closed-form inverse kinematics solutions of the robot and the concrete forms of position, orientation and singularity avoidance constraints are also obtained. Afterwards, based on the constraints and joint availability index, cost functions about base positions for single point task and continuous point task are established to evaluate the influence of the base position on the kinematics performance of painting robots quantitatively. At last, the internal penalty function method is used to minimize the cost function and then the corresponding base position is regarded as the desired one. Results of simulations on flat, cylindrical and conical surfaces demonstrate the accuracy of the approximation model and effectiveness of the proposed method. And the efficiency increases by a hundredfold comparing with the existed methods.