Similarity and Equivalence of Nutating Mechanisms to Bevel Epicyclic Gear Trains for Modeling and Analysis

Abstract

This paper addresses similarities between various nutating or wobbling mechanisms, in particular kinematic similarities. A case is made for the generalization of these mechanisms into a mechanism “class” having common kinematic characteristics, which is typified by bevel epicyclic gear trains. A similarity index is proposed to describe the quality of kinematic similarity, with the best degree of similarity termed “equivalence.” It is proposed that kinematic analysis of mechanisms belonging to this “class” can be simplified by modeling them as bevel-gear trains, and that static-force, power-flow, and efficiency analyses can also be greatly simplified in the case of “equivalent” mechanisms. Simplified kinematic, force, and efficiency analyses are demonstrated for a unique wobbling speed reducer using this new concept of equivalent geared mechanisms.