In order to analyze the influence of the engagement algorithm and structure parameter on the transmission performance of harmonic drive（ HD）,the involute tooth profile is used for the HD,an exact engagement algorithm and its approximation are obtained based on the envelope theory and the exact calculations for the rotation angles of flexspline（ FS）,moreover,the conjugate existent domain（ CED） and the conjugate tooth profile（ CTP） that based on the aforementioned algorithm are studied,furthermore,the influence of the wave generator（ WG） and the coefficient of radial displacement are researched here. The results demonstrate that two CEDs and double conjugated phenomenon are found,and the approximate algorithm,the coefficient of radial displacement,the WG have little effect on the CED,CTP,engagement deviation for the CED one,but obviously influence on the CED,CTP,engagement deviation for the CED two.