The parallel mechanism of 3-UPU is sensitive to the pair clearance. It is easy to form a bizarrerie. The current method is used to eliminate the singularity. There is anabnormal rotation problem. This is a concomitant motion, which often forms the interference. In this paper, a concomitant motion elimination method was proposed.The actuation redundancy branched chain method was used to obviate the disturbances in 3-UPU parallel mechanism mining. The strength of the problem of undesired rotation existed in 3-UPU parallel mechanism was assessed. According to the evaluation results, the reciprocal product between the helix and the associated rotationwas limited tononzero, and the helix was limited to do work to the associated rotation. The bound norm description of the concomitantrotational freedom motion was obtained.According to the bound norm, the interference amplitude of the error limitation to the unexpected rotation was detected. The actuation redundancy branched chain method was used to obviate the concomitant motion in parallel mechanism mining. The experimental results show that the working space of parallel mechanism under the eliminatingmethod of the concomitant motion can meet the requirements of the mining heavingamplitude and displacement.