In this report, we attempt to solve the minimum input trajectory solution under the input conditions that the ankle or knee joint is passive. Because we expect to realize the optimal biped locomotion by using fewest actuators to reduce the weight of biped mechanism and to simplify the control algorithm. As a result, we obtained nearly optimal trajectory solution when the ankle joint is passive. When the knee joint is passive, however we cannot get an optimum solution that satisfies, the dynamic constraint condition of the passive joint. Then, we obtained the optimum trajectory solution without knee collision and found that the gait without knee collision consumes more energy than that with the knee collision. Moreover, we calculated the optimal trajectories for various values of stride length and clarified that the optimal stride length is 0.3 m in terms of energy consumption and average speed.