Abstract: A group of formulae for the geometric parameters, such as the gear mounting distance, crossed axes angle, center distance, and the helix angle of tooth trace in reference plane of reference rack, of a crossed-axes gear drive of different arrangements are derived based on the analysis of the spatial mesh relationship between conjugate gears and their reference rack, and a set of mounting parameter guarantee design method for conical involute gear pairs with crossed axes is presented. The formulae can be applied not only to all of the possible independent forms of the crossed-axes gear drive, but also to the case of gearing with parallel axes and intersecting axes. As a result, any conical involute gears, which transmit rotational motion between two shafts in any relative positions, can be readily designed by means of this group of formulae. The design theory and methods are tested by the design and processing of several sets of crossed axes gears, and is also expected to be the theoretical foundation for further researching the design of conical involute gears.

Key words: Crossed-axes, Conical involve gears, Gearing principle