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The broken strand in the overhead ground wire (OGW), which is caused by thunder lighting, variation, etc., is a serious fault in power grid. The maintenance work, with high working intensity and risk is generally carried out in the high voltage live line by specially trained workers. This paper presents the development of a novel mobile robot designed for the OGW broken strand repair in power grid. The mobile robot with passive joints can run along the OGW and cross counterweights and splicing sleeves. After approaching the fault location, with the specialized tools, the robot first returns the broken strand back to the original position and then fastens the broken strand tightly through specialized clamp. With the consideration of practical application, safety and performance on obstacle-crossing and maintenance, the robot prototype has been developed. A calculation method has been proposed for the resolution of inverse kinematics with force constraints. Robot experiments in laboratory have been carried out and the results are shown in this paper.