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This paper presents a kind of modeling method for a two-body mobile robot, provides with its kinematic structure parameters and analyzes the forward kinematics and inverse kinematics. Considering the case of surpassing obstacles actively for this two-body mobile robot, the solutions of inverse kinematics are given out based on the geometric approach. Surpassing obstacles and turning analysis are made and the simulation is undertaken via the dynamics software. Three different turning modes are considered in this paper and a lot of trials are compared based on different speeds of two-side wheels. The effect of included angle between front body and rear body on the turning ability is also verified through computer simulations, at last the simulation results demonstrate the effectiveness of this two-body mobile robot in climbing over obstacles.