In order to deal with the collision between the components of the reconfigurable cable-driven parallel robot(RCDPR) and the obstacles in operating environment, a novel collaborative obstacle avoidance method is presented based on critical support lines and multi-finger grasp. Firstly, the general model of RCDPR in complex environment is derived by simplifying the robot structures and obstacles. Based on the model, the collision-free area of the RCDPR is estimated using the topological constraint of robot structure and the critical support lines between obstacles. The collision-free force closure workspace of different types of RCDPRs and obstacle distribution is obtained with convexhull method and convexhull mapping method, respectively. The impact of obstacle distribution and robotic type is analyzed. Then, in terms of a specific trajectory for the end-effector of the RCDPR, the optimal distribution of cables is derived with optimization algorithm. Finally, the verification is conduction the RCDPR prototype. The experimental results indicate that the presented method can effectively prevent the collision during the RCDPR movement.