In this paper, the concept of the Intelligent Mobility Platform with Active Spoke System (IMPASS) is introduced in the first place as an alternative locomotive method that allows for multiple modes of motion. Based on this concept, a walking machine with two actuated spoke wheels and one tail is developed. Observations on the motion of this mobile robot indicate that it is able to change its topology by changing the contact scheme of its spokes with the ground. In order to investigate its transformable configuration, the robot is treated as a mechanism with variable topologies (MVTs) and the Modified Grübler–Kutzbach criterion is adopted to identify the degrees of freedom (DOF) for each case of its topological structures. The mobility analysis demonstrates that, with the assistance of Grassmann Line Geometry, the DOF in all possible configurations can be determined straightforward. The nature of the IMPASS’ locomotion is revealed through the mobility analysis and the theoretical results are validated with an experimental prototype.