In this paper an Energy Dissipation Rate Control (EDRC) method is introduced, which could provide stable walking or running gaits for legged robots. This method is realized by developing a semi-analytical pattern generation approach for a robot during each Single Support Phase (SSP). As yet, several control methods based on passive dynamic walking have been proposed by researchers to provide an efficient human-like biped walking robot. For most of these passive based controllers the main idea is to shape the robot’s energy level during each SSP to restore the mechanical energy which has been lost in the previous Impact Phases (IP); however, the EDRC method provides stable gaits for legged robots just by controlling the robot’s energy level during each IP. In this paper EDRC is applied to a Six-Link Three-Point Foot (6L3PF) model, to realize an active dynamic galloping gait on level ground. As the point-foot contact assumption for the 6L3PF imposes one degree of under-actuation in the ankle joint, it is not clear how to specify the forward kinematic defining the swing leg position and velocity as a function of actuated joint angles. So, a new strategy for solving the dynamic and kinematic equations of the robot is introduced for deriving suitable joint trajectories during each SSP. Simulation results show that the proposed methods in this paper are effective and the robot exhibits a stable dynamic galloping gait on level ground.