A method is provided for optimally engineering a toroidal transmission having a desired input/output ratio to implement the desired ratio of the transmission while meeting the torque and efficiency requirements of the design. Nanoparticle technology is used to manufacture the stator walls to replace the cutting and milling procedures now in use. A novel Mitchell bearing sleeve and its particular hydrodynamic lubrication and cooling method are proposed herein, as well as the introduction of a novel, ultra smooth, amorphous non-oxidizing contact sleeve material used to form the contact sleeve of the drive rollers. A novel self-lubricating system is further provided that includes an oil reservoir disposed within an output shaft of the transmission.