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Research Papers: Design of Mechanisms and Robotic Systems

New Graph Representation for Planetary Gear Trains

[+] Author and Article Information
Wenjian Yang

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: ywj19900125@163.com

Huafeng Ding

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: dhf@ysu.edu.cn

Bin Zi

School of Mechanical Engineering,
Hefei University of Technology,
No. 193 TunXi Road,
Hefei 230009, China
e-mail: binzi.cumt@163.com

Dan Zhang

Lassonde School of Engineering,
York University,
4700 Keele Street,
Toronto, ON M3J1P3, Canada
e-mail: dzhang99@yorku.ca

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 18, 2017; final manuscript received October 17, 2017; published online November 9, 2017. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 140(1), 012303 (Nov 09, 2017) (10 pages) Paper No: MD-17-1567; doi: 10.1115/1.4038303 History: Received August 18, 2017; Revised October 17, 2017

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

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Figures

Grahic Jump Location
Fig. 1

(a) The Watt kinematic chain, (b) the graph representation, and (c) the adjacency matrix

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Fig. 2

(a) An eight-link 1DOF multiple joint kinematic chain, (b) the graph representation, and (c) the adjacency matrix

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Fig. 3

(a) The schematic diagram of the Simpson gear train and (b) the conventional graph representation

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Fig. 4

The graphs that are pseudo-isomorphic with Fig. 3(b)

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Fig. 5

The process of acquiring the rotation graph of Fig. 3(a)

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Fig. 6

(a) The canonical rotation graph of Fig. 5 and (b) the adjacency matrix

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Fig. 7

The process of acquiring the displacement graph of Fig. 3(a)

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Fig. 8

(a) The canonical displacement graph of Fig. 7 and (b) the adjacency matrix

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Fig. 9

The parent graphs of five-link 1DOF PGTs

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Fig. 10

Geared graphs derived from the first parent graph in Fig. 9

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Fig. 11

(a) The rotation graph of the first graph in Fig. 10(b) and (b) the adjacency matrix

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Fig. 12

(a) The canonical rotation graph of Fig. 11, (b) the relabeled rotation graph, and (c) the canonical adjacency matrix

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Fig. 13

Nonisomorphic rotation graphs of five-link 1DOF PGTs

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Fig. 14

Canonical displacement graphs derived from the first rotation graph in Fig. 13

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Fig. 15

Nonisomorphic displacement graphs of five-link 1DOF PGTs

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Fig. 16

Two nonisomorphic displacement graphs acquired in Ref. [2]

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Fig. 17

Two pseudo-isomorphic graphs using the graph representation in Ref. [25]

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Fig. 18

Different rotation graphs using the operation in Ref. [3]

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