The iBOT, a revolutionary personal mobility device developed by DEKA Research and Development Corporation, contains several belts that transfer mechanical power through the system. The dynamic characteristics of the belts are obviously important to the operation of the iBOT. Our task is to create a mathematical model of some aspects of the belt dynamics. Partial differential equations and Lagrangian dynamics are employed to understand the elements of this electro-mechanical system. Ultimately, finite difference numerical methods are applied to solve the rather complicated system of partial differential equations developed.