An automatic system for a generic approach to detecting the normal vector of an unknown three-dimensional surface using a sensor mounted on the wrist of a collaborative robot is described. As this method proceeds, the end-effector uses three position sensors to measure the normal direction and implementation of the proposed method in a robotic application such as polishing, sanding, scanning, painting, etc., to meet industrial requirements. Here, the auto-normalization algorithm is presented based on the detection system. Firstly, the deviation between the normal vector of the robot and the surface is measured by the sensors installed at the head of any end-effector. Then, the robot target pose is solved inversely by the auto-normalization algorithm. It adjusts the robot to the target pose via pitch and roll rotations about the tool center point. The orientation is corrected in line with the normal vector simultaneously by a Proportional-Integral-Derivative (PID) controller. To test and verify the auto-normalization algorithm, an experimental platform is established using the ABB RobotStudio software under an ideal condition for accurate measurements. The simulation results demonstrate that the detection method and the auto-normalization algorithm are feasible and reliable.