This article investigates the kinematic relationships in a harmonic drive gearbox with a fixed circular spline. According to derived equations, as well as finite element results on flexspline, the ratio of vertical to horizontal deflection is constant for all values of the applied load. This ratio barely depends on geometric dimensions of the flexspline. According to kinematic relations, the difference in gear teeth of the flexspline and that of circular spline can only take values of 2 or 3. Finite element results, enforces value of 2 to be used. According to the results, flexspline deflection reveals similar behavior to that of a cylindrical shell. This similarity manifests itself in terms of a correlation factor Cf, through which one can find the flexspline deflections ratio using cylindrical shell results. A complete knowledge on this factor can eliminate any cumbersome work on finite element modeling of the flexspline. Moreover, using the proposed design curves (based on finite element results), one can calculate the required force for a full engagement of gear teeth without exceeding the bearing stress values of a flexspline, in a typical harmonic drive gearbox.

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