In this paper, a quadrupedal quasi-passive dynamic walking robot using a rocking motion has been investigated. Experimental results show that this robot can walk on the level ground and that walking speed is related to a phase difference of rocking motion. Through investigation of a shape of soles, we revealed Duke has a nonholonomic constraint that is comparable to that of "two-wheeled robot" on its sole. As a result of analyses based on the nonlinear control theory, we conclude that the sole shape contributes to the transition of walking speed accompanying with change of a phase difference.