A parallel locomotion mechanism can be defined as "a mechanism with parallel configuration that has discrete contact with respect to the ground which renders a platform the ability to move". The actuated spoke wheel robot IMPASS (Intelligent Mobility Platform with Active Spoke System) presented in this paper serves as an example of such locomotion mechanisms. The current prototype of IMPASS has two actuated spoke wheels and one passive tail with its lower portion designed as convex surface. The robot is considered as a mechanism with variable topologies (MVTs) because of its metamorphic configuration. Closed-form solutions to the kinematics of the variable topologies are developed and verified with numerical simulations. The analytical expressions to these solutions allow themselves to be used directly in the real-time motion planning and monitoring of the robot.
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