This two-part paper presents a dynamic model of a legged vehicle for travel on a variable-topographic terrain. In Part 1 of the paper, we develop expressions for the kinematics of the vehicular system. These expressions, in turn, form the foundation for the dynamic analysis of the robotic vehicle presented in Part 2 of the paper. The model applies to a system composed of a cargocarrying body supported by four multi-degree-of-freedom linkage assemblies whose configurations are adjustable to accommodate terrain irregularities. The mobility of the locomotion system is provided by four rigid wheels which serve as a base to the kinematic chains that extend from the platform of the vehicle. To assure dynamic equilibrium of all members in the system, torque actuators are employed at the joints between inter-connecting bodies to facilitate the adjustment of each articulated chain configuration without reducing the adaptability of the vehicle to ground profile variations. The dynamic model used for determining the system response to environmental contact forces is based on a Newton-Euler recursive formulation.