Wire-moving robots are mechanical systems that can maintain their balance and move on tightropes. Their name comes from the manner in which tightrope walkers maintain their balance by rolling or moving a pole from left to right. In order to investigate the internal laws of these systems and to apply a mechanism of self-balance control to them, a new mechanical structure for wire-moving robots is presented here. This structure consists of a rotational pole and a translational pole coupled with each other in a parallelogram. The robot is an underactuated system. A dynamic model of the robot is established here based on the Lagrange method, and the controller of the system was designed using a partial feedback linearization control algorithm. Finally, the efficiency of the algorithm and the stabilization were verified by computer simulation and experimentation using a prototype.