In this paper, the dynamics of quadruped trot, gallop, and bound will be examined using a simple model for the quadruped. The body of the quadruped is modeled as a uniform bar and the legs are modeled by massless springs. It will be shown that symmetry can be used to study the locomotion of this system. Using symmetry, a technique will be developed to obtain periodic solutions for each of the gaits of the quadruped model. These periodic solutions will be computed at various speeds. The energy levels will be compared for each of the gaits. The exchange of energy between its different forms will be shown for different gaits. It will be shown that even without body flexibility, there are significant savings in energy due to gait transition from trot to gallop. The energy levels will be used to predict the trot-gallop transition speed. These results will be compared with the experimental results for horses and dogs.

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