Kinematic and power-flow analysis of bevel gears planetary gear trains with gyroscopic complexity

•We extended the Willis formula to bevel gear trains.•We deduced the power ratios between gears in a planetary bevel gear train.•We performed power flow analysis of gear wrists with gyroscopic complexity.

In this paper the authors propose a method for the kinematic and power-flow analysis of bevel epicyclic gear trains with gyroscopic complexity. By gyroscopic complexity, we mean the possibility of the gear carrier to be a floating link as, for instance, in robotic gear wrists.Thanks to the new formulas herein deduced, the methods based on the graph representation of planetary spur gear trains have been extended to bevel gear trains. In particular, the well known Willis equation has been modified to maintain its validity for bevel gears. The modified Willis equation was then embodied in new power ratio expressions. Under our simplifying hypotheses of absence of friction and constant angular speeds, it is shown that gyroscopic torques do not enter into power flow analysis. Two numerical examples are discussed.