The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. On the other hand, in this type of transmissions there exist two major drawbacks, namely, backlash and torque ripple Backlash, the angle through which the output shaft can rotate when the input shaft is held fixed, has a degrading effect on the output accuracy. Torque ripple, the variation in mechanical advantage as the input shaft rotates, causes vibrations and could lead to dynamic instability of the machinery. If the cycloid drive were manufactured to the ideal dimensions, there would be no backlash nor torque ripple. However, in reality, there will always be some machining tolerances. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. This model is used in Part II of this investigation to determine the effect of machining tolerances on backlash and torque ripple. As a result, simple and practical equations for design synthesis of this type of drives are formulated.

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