To guarantee the strength and precision of the final welding assemblies, it is necessary to cut welding grooves before welding thick workpieces. General methods to cut welding grooves on plane workpieces need much manual assistance, and some even need manual operation purely. Therefore, this paper proposed a robot system for cutting Y-shaped welding grooves with full automation. Flame cutting technology has been adopted, requiring no jig to fix workpieces, which also causes no direct vibration to robot structure. Vision-based sub-system firstly captures the edges to be cut, which are composed of continuous points, and a laser range finder (LRF) starts to obtain the thickness of the edges precisely. To convert these edges into the trajectory of flamer, Least Square Method and Hermite Interpolation are respectively utilized to fit lines and curves. Robot system subsequently computes the motion-related parameters according to the position of the edges and geometric parameters of the desired welding grooves. The inverse kinematics of this robot is solved by geometry methods, which decreases computation burden and saves much time compared with traditional algebra method. Another core novelty is that a velocity planning method combining optimization algorithm has been put forward, which, we think, is not only useful in this gantry robot but also benefits other motion axes with heavy load. This further reduces vibration. Finally, the simulation and experimental results both prove the feasibility of this system. To date, no available robots or machines tool can finish this process with full automation (to the best of our knowledge).