Abstract: Based on the model of the Motoman SK6 robot and the rotating/ tilting welding positioner, the forward kinematics formula of robot and positioner are extablished with the Denavit-Hartenberg method. Then, the close-type inverse kinematics solution of robot and the downhand welding algorithm for positioner are obtained using a simple analytic geometry method. Through the algorithms, robot can weld the workpiece on downhand welding position, which is easer to ensure the good welding quality. The algorithms are straightforward, fast-running and, therefore, lay a foundation for path-planning and off-line programming for robot welding system. Through the graphic emulation and the running on the robot controller, it is shown that the calculated result can meet the requirement of welding in downhand position.