Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

Kamesh, Vinjamuri Venkata; Rao, Kuchibhotla Mallikarjuna; Rao, Annambhotla Balaji Srinivasa

doi:10.1115/1.4036306

Cited by 29 publications

(10 citation statements)

References 18 publications

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“…Planetary gear trains (PGTs) are widely used in transmissions of vehicles, pulley blocks, wristwatches, machine tools, and robots. The synthesis 1–13 and analysis 14–18 of planetary gear trains (PGTs) based on graph theory have become a hot topic in mechanism research over the past half-century. Up to date, many works exhibiting different synthesis methods have been implemented.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis method for planetary gear trains without using rotation graphs

Cui

Sun

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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The displacement graphs (d-graphs) are the final form of planetary gear trains (PGTs) synthesis. The existing configuration synthesis methods for the d-graphs of PGTs need rotation graphs (r-graphs) as the intermediate step and produce a large amount of isomorphic KCs. This paper proposes a method to obtain d-graphs directly from the geared graph. Meanwhile, a uniform isomorphism identification method suitable for parent graphs, geared graphs, and d-graphs is presented. Finally, a fully automatic method based on parent graphs is tested on synthesizing 1-DOF PGTs with up to nine links. Our synthesis results and those in the literature are comparatively analyzed, and the reasons for contradictory synthesis results are analyzed.

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Section: Introductionmentioning

confidence: 99%

“…Up to date, many works exhibiting different synthesis methods have been implemented. They can be classified into three main types: the parent-graph-based method, 1–6 the recursive method, 8–12 and the acyclic-graph-based method. 13 The PGTs with 1 DOF are most widely studied.…”

Section: Introductionmentioning

confidence: 99%

Synthesis method for planetary gear trains without using rotation graphs

Cui

Sun

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Rajasri [16] proposed an approach in accordance with the hamming number and generated EGTs with up to 7 links. Kamesh [17] applied the vertex incidence polynomial and proposed a synthesis method. Then he reported all 1-DOF non-isomorphic EGTs with up to 6 links.…”

Section: Introductionmentioning

confidence: 99%

Configuration Synthesis and Performance Analysis of 9-Speed Automatic Transmissions

Ding

Cai

Chen

et al. 2020

Chin. J. Mech. Eng.

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Current research of automatic transmission (AT) mainly focuses on the improvement of driving performance, and configuration innovation is one of the main research directions. However, finding new configurations of ATs is one of the main limitations of configuration innovation. In the present study, epicyclic gear trains (EGTs) are applied to investigate mechanisms of 9-speed ATs. Then four kinematic configurations are proposed for automatic transitions. In order to evaluate the performance of proposed mechanisms, the lever analogy method is applied to conduct kinematic and mechanical analyses. The power flow analysis is conducted, and then transmission efficiencies are calculated based on the torque method. The comparative analysis between the proposed and existing mechanisms is carried out where obtained results show that proposed mechanisms have reasonable performance and can be used in ATs. The prototype of an AT is manufactured and the speed test is conducted, which proves the accuracy of analysis and the feasibility of proposed mechanisms.

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“…In graph-based synthesis, the graph theory is used to represent a product and define the relationships between its components, and the graph concepts and theorems are employed to generate design candidates [23]. For now, graph-based synthesis approaches have been widely used in the synthesis, analysis and optimization process of linkage systems [24][25][26] and epicyclic gear trains [27,28]. Moreover, Bin proposed a computational conceptual design synthesis model based on space matrix [29], and he also integrated the functional synthesis of mechanisms with mechanical efficiency and cost to find out the optimal solution [30,31].…”

Section: Introductionmentioning

confidence: 99%

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

Han

Yang

et al. 2020

Chin. J. Mech. Eng.

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The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements. This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation. The graph framework of the synthesis approach is built firstly, and it involves: (1) the kinematic function units extracted from mechanisms; (2) the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain; (3) two graph representations, i.e., walk representation and path representation, of design candidates; (4) a weighted matrix theorem that transforms the synthesis process into polynomial operation. Then, the formulas and algorithm to the polynomial operation are presented. Based on them, the computational flowchart to the synthesis approach is summarized. A design example is used to validate and illustrate the synthesis approach in detail. The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically, but also helpful to make that enumeration process computable.

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Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

Cited by 29 publications

References 18 publications

Synthesis method for planetary gear trains without using rotation graphs

Synthesis method for planetary gear trains without using rotation graphs

Configuration Synthesis and Performance Analysis of 9-Speed Automatic Transmissions

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

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