As an efficient manufacturing method for gears, shaping technology developed for non-circular helical gears will greatly break through the dilemma of their applications; especially for those gears with part of pitch curves being concave, being not able to be hobbed. Two fundamental linkage-models for external non-circular helical gears were built based on the meshing theory of non-circular gears in this article. According to four linkage methods in plane and two kinds of additional rotation in vertical direction, eight shaping strategies and their practical linkage-models (1)–(8) were developed. Taking a three-order elliptic helical gear as an example, the kinematic characteristics of the eight practical linkage-models were analyzed, which reveals that equal arc-length of gear billet (models (3) and (4)) have the highest accuracy under a given efficiency. The dynamic characteristics of models (3) and (4) were analyzed, which shows that model (4) (equal arc-length of gear billet and additional rotation on shaper cutter) is better in performance, and is an optimal one. The optimal linkage-model was demonstrated to be valid by a virtual shaping, and be able to shape those non-circular helical gears with part of pitch curves being concave. Moreover, the accuracy among every gear tooth is uniform. The theory developed and the results of the virtual shaping were illustrated with a shaping experiment. The train of thought and the results will be useful for any external non-circular helical gears with free pitch curves.
