A screw drive in-pipe robot is promising inspection equipment for small pipes. However, most of the existing screw drive in-pipe robots have problems of motion interference and slipping inside curved or irregular pipes. These problems result from the coupled relations among the steering motion, the motion speed and the load ability of the robot. In order to deal with the problems, the axiomatic design (AD) theory is applied to evaluate and analyze the existing designs. Then an uncoupled concept design based on the AD theory is proposed and the complete AD decomposition process is presented. After that, the proposed robot based on a tri-axial differential angle modulation mechanism is designed to realize the uncoupled concept. Finally, the uncoupled property is verified in a dynamics simulation system. The simulation results indicate that the motion speed, load ability and steering motion of the proposed robot can be adjusted individually compared with the robots that have inclining-angle-fixed rollers. Owing to the uncoupled design, the proposed robot can mechanically adapt to straight pipes and curved pipes with less roller slipping.