The structural synthesis of planetary gear trains using matrix characteristic equations of parent
Authors:
Open Access
- 1 January 2023
- conference paper
- Published by AIP Publishing in AIP Conference Proceedings
- Vol. 2787 (1)
Abstract
Planetary gear trains (PGTs) structural synthesis can aid in the evolution of novel transmission systems in machinery. The synthesis of 1-DOF PGTs has received a lot of attention over the last half-century. However, the majority of works on PGT synthesizing are limited to single-planet gear trains. Based on parent graphs and permutation group theory, this article describes a systematic technique for synthesizing PGTs. To begin, we define the PGT adjacency matrix. Then, using the permutation groups, we propose an algorithm for assigning values to adjacency matrix elements to generate the characteristic equations. The characteristic equation for each family is determined in order to synthesize 1-DOF graphs. These equations result in no isomorphic configurations being generated. The link assortments for seven-link 1-DOF PGTs are generated automatically. Finally, for each link assortment family, parent graphs are synthesized. To the best of our knowledge, the synthesis method of the 7-link 1-DOF PGT is a novel method that has not yet been published in the literature.Keywords
This publication has 17 references indexed in Scilit:
- The Complete Set of One-Degree-of-Freedom Planetary Gear Trains With Up to Nine LinksJournal of Mechanical Design, 2019
- Damage of functionalized self-assembly monomolecular layers applied to silicon microgear MEMSTribology International, 2019
- An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear MechanismsJournal of Mechanical Design, 2002
- An efficient methodology for the structural synthesis of geared kinematic chainsMechanism and Machine Theory, 1997
- Automatic Detection of Embedded Structure in Planetary Gear TrainsJournal of Mechanical Design, 1997
- Automatic synthesis of displacement graphs for planetary gear trainsMathematical and Computer Modelling, 1994
- Displacement isomorphism of planetary gear trainsMechanism and Machine Theory, 1994
- Automatic Analysis of Kinematic Structure of Planetary Gear TrainsJournal of Mechanical Design, 1993
- Standard code technique in the enumeration of epicyclic gear trainsMechanism and Machine Theory, 1993
- A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear TrainsJournal of Mechanical Design, 1992