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Some of the fundamental problems of the gait control of a quadruped walking vehicle are addressed. It is shown that the product of the duty factor and the stride length is equal to the length of the boundary of the reachable area of the leg. Furthermore, the mathematical expression representing the relationship between the stability margin, the stride length and duty factor are also formulated. These equations are expressed in terms of quantities that specify the configuration of the quadruped walking vehicle. Based on the derived results, a graphical approach to determine the required stride length and the duty factor that corresponding to a regular gait with a prescribed static stability margin is presented. This graphical approach is then adopted to determine the regular gait of a quadruped walking vehicle, and the results agree with the analytic approach.