While introducing harmonic gearbox drives, kinematics relations and design parameters are derived and studied. The flexible ring which is driven via a wave generator and loaded by a force of magnitude of P, is modeled and both horizontal and vertical displacements are determined. Results indicate that the ratio of the two displacements (vertical to horizontal) is constant for all values of P, provided the geometry of the flexible ring remains intact. The finite element results also support the relations derived for the two type of load generators adapted to the problem. The results also indicate that for a proper engagement of the ring gear and that of the flexible ring, the maximum tooth difference between the two gears can only be four, among which, only the values of 2 and 3 are acceptable.