This paper introduces an originally designed wheelchair robot. This robot is equipped with a novel type of Variable Geometry Single Tracked Mechanism (VGSTM) that can actively control the robot shape and the track tension. So it becomes possible to improve the obstacle clearing capability of the robot by adapting the robot shape for the obstacle. The track tension is closely related to the performance of this original wheelchair robot, so with the aim of stair-climbing, which is the most fundamental obstacle clearing performance of the wheelchair robot, the optimization model of the track tension is established based on the geometric model and the static model of the robot. Then the simulation is performed, and the optimal track tension values of the robot for different phases of stair-climbing are obtained. Finally, these track tension values are verified through the experiment.