—In this work, we link the various parameters that characterize a quadruped robot to the gait that it eventually opts for the steady state part of its locomotion. We then introduce an appropriate class of motion patterns, and provide some evidence that certain parameter values tend to favor specific pattern subclasses. This offers a new robot walking behavior qualitative view and some novel guidelines for legged systems design, in regard to the gait-effects of each design parameter. To accomplish the above, we adopt the use of an underactuated quadruped robot, and the Hildebrand diagrams paradigm for the succinct portraiture of its gaits, as well as the use of two distinct definitions regarding the motion stride.