This paper presents a proposed design of a leg rehabilitation system. The system will be implemented on a reconfigurable wheelchair prototype in order to provide additional two rotational degrees of freedom (DOF) for serving more rehabilitation purposes. Lagrangian dynamic formulation is used to derive the system dynamics. Joints frictions based on Coulomb friction model are considered in the leg rehabilitation system. The system equations of motion are linearized since the model is dealt with in state space representation. LQR control approach is considered and derived for stabilization of the system. Simulation Results validating the model and the control approach are presented and discussed.