A universal kinematic analysis of geared mechanisms

A methodology for the kinematic analysis of planetary gear trains is presented. First, a definition for the gear train entity (GTE) is introduced, using the planet gears as the dividing element. Second, it is shown that the speed ratio of a GTE can simply be expressed symbolically in terms of its planet gear ratios. Then, for any planetary configuration, however complex, a single governing kinematic equation is developed, which then is manipulated to determine all possible overall speed ratios. Algebraic expressions for the speed ratios, of any GTE and/or planetary gear mechanism, can be obtained in terms of the teeth numbers, easily. Finally, three examples are presented; one includes a complicated fifteen-link PGT, to illustrate the simplicity of the method, the other compares the results of a bevel gear train with those of previous study.