Abstract: To improve obstacle climbing performance of the quadruped robot, stability margin is selected as the criterion of quadruped static balance, and quadrant boundary formed by touchdown points is taken as the stride possibility criterion in various initial conditions. All gaits are classified into 24 types by stride sequences. Based on the evaluation guidelines including minimal locomotion space demand, maximal stability margin, and best body adjustment coordination, contrast analyses on all 24 basic gaits are performed. Furthermore, a projection method combined with planar statically balanced gait theory is proposed to solve stair climbing gait problem, and systematic simulation of stair climbing gait is implemented to meet the 3 evaluation guidelines mentioned above. The simulation results provide theoretical foundation for selecting quadruped walking and stair climbing gaits. Experiments testify the validity of this method.