The purpose of this paper is to develop a method of Collision-Free Path Planning (CFPP) for an articulated robot. First, the configuration of the robot is built by a set of robot joint angles derived from robot inverse kinematics. The joint space, that is made of the joint angle set, forms a Configuration space (Cspcce). Obstacles in the robot workcell are also transformed into the Cobstacles using slice projection method. Actually the Cobstacles means the configurations of the robot causing collision with obstacles. Secondly, a connected graph, a kind of roadmap, is constructed by the free configurations in the Cspace, where the free configurations are randomly sampled from a free Cspace immune from the collision. Thirdly, robot paths are optimally determinant in the connected graph. A path searching algorithm based on $A^*$ is employed in determining the paths. Finally, the whole procedures for the CFPP method are shown for a proper articulated robot as an illustrative example.