In this paper, we propose a method of planning collision free trajectories for two manipulators along specified joint paths. The joint path of each manipulator is represented by a path parameter and two path parameters generate a two-dimensional space which contains the collision region of two manipulators. In order to connect the path parameter with the time, a time scale factor is introduced. In a three-dimensional space constituted by the two-dimensional space of the path parameters and the time-scale factor, minimum time trajectories for two manipulators are searched under joint torques/forces constraints and collision-free condition by dynamic programming. Numerical example with two two-link manipulators shows the effectiveness of the proposed method.