With the development of robotic sciences, lots of research has been conducted in the area of biped robots and many industries have been attracted to the application of these robots. Therefore, a great number of humanoid robots have been developed all over the world. As the humanoid robots have the same structure as human beings, they have the ability to handle many tasks which are normally done by human beings. Also because of the uncontinuous nature of walking, biped do not face problems that wheeled or snake-like robots do in moving on stairs and ditches. Among the subjects which have been studied on biped motion, investigation of the stability, path generation, optimization, and control can be considered as more important issues. It is of great importance for the biped robots to walk with an optimized stable path. Consumed energy, actuator torques, and the velocity of walking are among the most important indices which have been considered for optimization by the researchers. Among these, the velocity of the biped robot always shows the superiority of the robot in comparison to the other prototypes. Due to complexity of system and different requirements not direct method which can be used to determine the maximum speed for the robot. In this research, we try to find a method to determine the maximum possible speed of a seven link biped robots during stable walking in sagittal plane without slippage. The method should consider actuator torque limits in addition to kinematic constraints of normal walking. To achieve this, firstly, a parameter study is done to investigate the effect of the length and time of each step. To this end a Genetic Algorithm based path planning was developed and used. However, this method is time consuming and has computational complexity. Regarding these defects, the research has been continued to find the minimum time trajectory of a biped robot in one step using phase plane analysis. To do so, minimum time trajectory algorithms used for fixed robots is employed. Considering the fact that the biped robot has the structure of a serial manipulator in single support phase, and behaves like a parallel manipulator in double support phase, the minimum time algorithms for serial and parallel manipulators have been used for single support and double support phases, respectively. Then an appropriate algorithm to find the solution curve in phase plane has been proposed, which satisfies the continuity condition of the velocity at the start and end of a step. Finally, the effects of some physical parameters such as coefficient of friction, the length of the step, etc have been investigated on the minimum time solution and the speed of walking has been considered. Keywords: biped robot, fast walking, phase plane analysis, actuator torque limitation, stability and non-slippage