Climbing robots, with their expansive workspace and flexible deployment modes, have the potential to revolutionize the manufacturing processes of large and complex components. Given that the surfaces to be machined typically exhibit variable curvature, good surface adaptability, load capacity, and motion accuracy are essential prerequisites for climbing robots in manufacturing tasks. This paper addresses the manufacturing requirements of climbing robots by proposing an asymmetric independently steerable wheel (AISW) for climbing robots, along with the motion control method. Firstly, for the adaptability issue of the locomotion mechanism on curved surfaces under heavy load, an asymmetric independently steerable wheel motion module is proposed, which improves the steering difficulty of the traditional independently steerable wheel (ISW) based on the principle of steering assisted by wheels. Secondly, a kinematic model of the AISW chassis is established and, on this basis, a trajectory tracking method based on feedforward and proportional–integral feedback is proposed. Comparative experimental results on large, curved surface components show that the asymmetric independently steerable wheel has lower steering resistance and higher motion accuracy, significantly enhancing the reachability of climbing robots and facilitating their application in the manufacturing of large and complex components.