Wheel is a great invention of human beings. The wheeled mobile system has brought great convenience to humans in production and daily life. Therefore, the wheeled robot is a very important development direction. To overcome the problem of insufficient adaptability of ordinary wheels to complex terrain, many research works have been investigated including the adhesion mode between wheels and supporting surface, the wheels’ geometry, the steering mode and so on. In this paper, based on the mechanism of wheels changing sliding friction into rolling friction, this paper proposes three new wheel structures, including tri-mode transformable wheel, magnetic adhesion wheel and variable parameter omni-directional wheel, and their corresponding wheel mobility structure, which aims at the requirements of uneven terrain crossing, vertical wall climbing and ground omni-directional movement. Through the linkage mechanism, the tri-mode transformable wheel switches its geometry among round mode, claw mode and hook mode, and the bi-directional obstacle crossing of the robot is realized; Through the magnetic adhesion wheel and passive suspension with three degrees of freedom, the robot can move on the wall with all wheels attached to the surface; Through applying the spatial mechanism to adjust the roller installation angles, the direction of wheel friction can be controlled and the omni-directional driving of the robot can be realized; through prototype construction and experimental study, the feasibility of the proposed innovative designs are verified.