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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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This paper utilizes a kinematic-geometric approach to study the first-order motion characteristics of wheeled vehicles on even and uneven terrain. The results obtained from first-order studies are compared to those obtained from second order kinematic analyses, and special situations where the first-order analysis is inadequate are discussed. This approach is particularly suited for studying actively actuated vehicles since their designs typically do not include intentional passive compliances. It is shown that if a vehicle-terrain combination satisfies certain geometric conditions, for instance when a wheeled vehicle operates on even terrain or on a spherical surface, the system possesses a singularity—it possesses finite range mobility that is higher than the one obtained using Kutzbach criterion. On general uneven terrain, the same vehicles require undesirable ‘kinematic slipping’ at the wheel-terrain contacts to attain the mobility that it possesses on these special surfaces. The kinematic effects of varying the vehicle and/or terrain geometric parameters from their nominal values are discussed. The design enhancements that are required in existing off-road vehicles to avoid kinematic slipping are presented for a class of vehicles that include two-wheel axles in their designs.