نبذة مختصرة : A harmonic drive (HD) is a precision reduction device widely utilized in the core joints of high-end equipment such as spacecraft and robots. The design of an excellent tooth profile is the core challenge related to the performance of HD. This investigation aims to propose a design method of a fully conjugated cycloid tooth profile (CTP) for HD. Firstly, the rationality of CTP use for HD is analyzed, and the cycloidal characteristics of the tooth trajectory are studied by use of canonical warping distance. Then, initial CTP equations are constructed, adopting the trajectory mapping results. Presetting the addendum CTP of circular spline, the conjugate CTP of flexspline is then designed using the envelope method. Subsequently, the envelope of the designed flexspline addendum is used to reverse-design the circular spline dedendum. The backlash is calculated to evaluate the CTPs designed with different radial displacement coefficients. Research shows that the tooth trajectory has cycloidal characteristics; therefore, the HDs that use CTP can realize a fully conjugate engagement. Moreover, the variable control parameters enable the proposed CTP expression to have excellent fitting characteristics, resulting in small and uniform mesh backlash distribution. The CTP is expected to become one of the ideal tooth profiles of HD.
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