Discrete approximations to toroidal continua for mobility of robotic vehicles on unstructured terrains are considered in this paper. Tensegrity paradigm, which derives pre-stressable structures composed of axially loaded members, is used to furnish various topologies for the discretization process. Discrete topologies that function as wheels are analyzed for their structural properties under static and dynamic loading configurations. Tensegrity dynamics is utilized to derive structural properties to aid in comparison of candidate topologies. It is shown that the discrete approximations developed using mechanics principles aid broader exploration and evaluation of design topologies owing to the simplicity of the physics. Numerical simulations using representative discrete approximations of continuum wheel designs provide optimism towards the use of tensegrity paradigm in modeling and realizing innovative wheels for planetary exploration.
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