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.

Dynamic modal analysis of double-sided meshing nutation drive with double circular arc spiral bevel gears

“…Gupta and White (1975) studied the kinematics of the nutating mechanical drive and deduced the nutating unbalanced motion equation. Uzuka et al (2009) (Oda et al, 2010), etc., and also analyzing the magnetic field of the nutation magnetic motor (Kadota et al, 2013). Itzhak (2008) performed kinematics and kinetics of rotors and wobbling bodies in nutation drive.…”

“…Itzhak (2008) performed kinematics and kinetics of rotors and wobbling bodies in nutation drive. Nelson and Cipra (2005) studied the basic principles of nutating mechanisms and analyzed the respective characteristics of nutating gear mechanism and planetary gear mechanism. Huang et al (2016) designed a novel non-contact nutation drive mechanism, and the experimen-tal analysis was carried out.…”

Modeling and Simulation for Nutation Drive with Rolling Teeth

“…Nutation drive with rolling teeth is a new type gear transmission developed in recent years [1,2] . The drive has unique features when compared to conventional gear arrangements which include very high profile contact ratio, high reduction ratio in one stage, and the potential for low vibration or noise levels, high efficiency and design flexibility.…”

Transmission Ratio Analysis and Controllable Tooth Profile Modeling for the Nutation Drive with Double Circular-Arc External and Internal Spiral Bevel Gears

“…The dynamic analysis of mechanical seals, rotors, and wobbling bodies in nutation drive had been completed by Itzhak Green [5]. Carl and Raymond [6] proposed the advantages of modeling wobbling mechanisms as similar or equivalent bevel-gear trains through the analysis of a unique speed reducer using its equivalent bevel-gear train. Zhao and Zhang [7] presented the fundamental principle analysis of a nutating gear train mechanism.…”