Abstract: In order to explore the mechanism of leg movements enhanced by spinal movements, a cheetah-mimicking quadruped running robot with 2-DOF (degree of freedom) articulated trunk is designed. The mechanical processes of the running motion in bound gait with flying phase are described. The dynamics model of the quadruped robot is established using a damped spring loaded inverted pendulum (D-SLIP) model. Referring to the running mode of cheetahs, the trajectories of the coupled motions of the spine joints and leg joints of the quadruped robot are planned. An improved PSO (particle swarm optimization) algorithm is proposed to solve the nested optimization problem with target mutual exclusion between the dimensional parameters of actuation mechanism of robot spine joint and the control parameters of motion trajectory. The dynamic simulations of the running motion of the quadruped robot in bound gait are carried out. The results show that the coordinated movements between the spine and the legs can increase the stride length of the quadruped robot and allow the robot generating flying phases, so as to improve the running speed of the robot.