This paper presents an effective approach to collision-free motion planning of a robot in the work-space including time-varying obstacles. The free arc is defined as a set composed of the configuration points of the robot satisfying collision-free motion constraint at each sampling time. We represent this free arc with respect to the new coordinate frame centered at the goal configuration and there for the collision-free path satisfying motion constraint is obtained by connecting the configuration points of the free arc at each sampling mined from the sequence of free arcs the optimality is determined by the performance index. Therefore the complicated collision-free motion planning problem of a robot is transformed to a simplified SUB_Optimal Collision Avoidance Problem(SOCAP). We analyze the completeness of the proposed approach and show that it is partly guaranteed using the backward motion. Computational complexity of our approach is analyzed theoretically and practical computation time is compared with that of the other method. Simulation results for two cally and practical computation time is compared with that of the other method. Simulation results for two SCARA robot manipulators are presented to verify the efficacy of the proposed method.