Gait study plays an important role in the walking robot, because it is the foundation of walking robots. The robot must first determine the walking pattern and rules, thus we can evolve further design, control, analysis or study. This research focus on hexapod and quadruped walking robots, and establishes a mathematical model which can fully describe natural and artificial gaits, and systematically plan and express them. Another point of this research is planning walk trajectory of robot. Here we purpose a new concept of foot trajectory planning, and establish S-V-A-J models for feet motion. We try to make robots move forward with constant velocity, as a goal, by using piecewise function of cam design theory. Therefore robot can walk with constant velocity and maintain the continuity of acceleration.