| Abstract On the base of reading literatures, according to study and development of the small tooth difference planetary transmission and the active tooth planetary transmission, the cycloid steel ball planetary transmission to belong to new type mechanical transmission is firstly studied in our country. The construction composing principle of the steel ball cycloid groove side surface engagement pairs made up the planetary disc, the center disc and steel ball as well as the steel ball ring groove side surface engagement pairs, the equi-speed output mechanism and the clearance adjustment mechanism is researched and analyzed. The drive principle of realizing speed transformation between input shaft and output shaft by the cycloid groove engagement pairs and the ring groove engagement pairs is analyzed and introduced. The type analysis of the cycloid steel ball planetary transmission is made. According to the construction constituted and the drive principles, the formation methods of the theoretical tooth shape and the practical tooth profile for hypocycloid and epicycloid are studied, and the right-angle coordinate equations and the complex number vector equations are deduced respectively. The relation planetary motion in the planetary disc, central disc and steel ball is researched, and the right-angle coordinate equations and the complex number vector equations of the steel ball motion posiiion are deduced. The equations of the curvature, curvature radius, main curvature and main curvature radius on hypocycloid抯 and epicycloid抯 theoretical tooth shape and practical tooth profile are deduced respectively. The theoretical tooth shape and the practical tooth profile curves as well as the curvature radius variety curves of the theoretical tooth shapes are drawn respectively by using differential geometry. The fixed drive ratio property, right engaging conditions, practical tooth profile continues engaging conditions and their affect factors of the steel balls engaging with hypocycloid and epicycloid tooth profiles are studied and analyzed. The drive ratio formulas of all kinds of the cycloid steel ball planetary transmission are deduced respectively. The importance properties for no reverse error transmission, large overlap degree and high meshing efficiency are analyzed and demonstrated. The spatial mechanics model for multi-steel ball (multi-point contact of each steel ball) engagement pairs of the cycloid groove and the circular groove are creatively established. The maximum acting force formulas of the cycloid groove engage pair and the ring groove engage pair are deduced by using ultra static distort harmony condition. The acting force between the turning arm bearing and the planetary disc is analyzed. The pressure angle formulas of inside and outside profiles of the cycloid grooves are respectively deduced, and the pressure angle variety curves are drawn. The strength weakness links and main failure forms of the cycloid steel ball ?III ? di __ planetary transmission are analyzed and defined. On the base of force analysis, using tooth profile synthesis theory, meshing theory and Hertz stress theory, the contact fatigue strength of the cycloid grooves practical tooth profiles and the ring groove engagement pair are analyzed and calculated. The maximum stress variety curves of the practical tooth profiles are drawn. The d...
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