This paper describes the dynamics and intermittent impact model of a novel rimless wheel with radially expanding spokes confined to move in a vertical plane. The wheel has two degrees of freedom, namely rotation in the plane and change of radius. The system has intermittent impacts with the ground and its mathematical model is discontinuous. The motions of the wheel on a horizontal and an inclined plane are investigated. The contact point of the wheel with the ground is assumed to have no slip. We derive the equations of motion in between the collisions and velocity change before and after the wheel impact. We construct the return map of its cyclic motion and plan the motion in between impacts to obtain a stable gait. Dynamic simulations are performed using MATLAB and are presented in the paper.