Kinematic Design and Analysis of Coupled Planetary Bevel-Gear Trains

One of the most common methods in analyzing speed ratios of planetary gear trains has been the tabulation method. For complex mechanisms where many gear trains are coupled together, this method becomes inconvenient. With bevel gears in the gear train, it fails to apply. Some textbooks also use formulas which apply only to gears with parallel axes of rotation. This fact is often not stated in machine design texts. These methods can become incorrectly used in the design and analysis of planetary bevel gear trains with nonparallel axes of rotation. With the use of computers and graphics, a convenient and reliable method can be derived. Freudenstein and Yang have derived the early graphical method for analyzing gear trains. This paper describes an algorithm to extend the graphical method for analyzing coupled planetary bevel gear trains. A matrix formulation is used to include speeds of all gears rotating about their respective axes. Such formulation will aid designers and analysts in determining correct speed ratios of all gears in a planetary gear train system.