This paper describes the analysis and simulation of a novel 3-wheel vehicle with expanding wheels. The motivation for this design is to attain added navigation capability by expanding the wheels according to the requirements of the terrain. For this vehicle, we present the analysis of motions in the plane and in 3D space. In these models, it is assumed that the contact point of the wheel with the ground is directly underneath the center of the wheel and has no slip. The kinematic models are studied for the property of differential flatness and this property is used to plan the trajectory and design feedback controllers. The paper presents simulations performed using MATLAB. Currently, a vehicle with these features has been fabricated at University of Delaware.