AN APPLICATION OF GRAPH THEORY TO THE ANALYSIS OF PLANETARY GEAR TRAINS

Graph theory offers a means for representing the structure of mechanisms. In this work, it is applied for the representation of a new type of continuously variable transmission. The analysis of this transmission may be reduced to the analysis of its equivalent planetary gear train. The computation of the efficiency of the transmission is the final objective of this work. The definition of the concept of equivalent planatery gear train makes it possible to evaluate the efficiency. This gear train has the same graph as the continuously variable transmission and its gear ratios have been obtained by averaging the original power balance equations. The efficiency of the equivalent planetary gear train has been symbolically obtained by means of a symbolic mathematical computation program. This program computes the efficiency of a planetary gear train, among other important design variables. The input for this program is given from the graph of the equivalent planetary gear train. Thus, this work shows how two different tools as Graph Theory and Symbolic Computation, may be used for the analysis of planetary gear trains.