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Research Papers: Design of Mechanisms and Robotic Systems

Studying the Optimal Layout of Topological Graphs to Facilitate the Automatic Sketching of Kinematic Chains

[+] 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

Yong He

School of Automation,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: heyong08@cug.edu.cn

Min Wu

School of Automation,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: wumin@cug.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 21, 2016; final manuscript received May 1, 2017; published online June 1, 2017. Assoc. Editor: Massimo Callegari.

J. Mech. Des 139(8), 082301 (Jun 01, 2017) (10 pages) Paper No: MD-16-1851; doi: 10.1115/1.4036781 History: Received December 21, 2016; Revised May 01, 2017

The sketching of kinematic chains is important in the conceptual design of mechanisms. In general, the process of sketching kinematic chains can be divided into two steps, namely sketching topological graphs and converting them into the corresponding kinematic chains. This paper proposes a new method to automatically sketch topological graphs including both planar and nonplanar graphs. First, two parameters called moving sign (MS) and moving sign string (MSS) are defined, based on which a new algorithm is proposed to acquire all feasible layouts of the contracted graph by moving inner edges. All topological graphs synthesized from the same contracted graph are identified to have the shared feasible layouts, and another algorithm is proposed to determine the optimal layout for each topological graph. Then, topological graphs are sketched automatically by determining the location of vertices. The method has low complexity and is easy to be programmed using computer language.

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References

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Figures

Grahic Jump Location
Fig. 2

(a) Planar contracted graphs, (b) nonplanar contracted graphs, and (c) 14-link 3DOF topological graphs

Grahic Jump Location
Fig. 1

(a) K3,3 graph and (b) K5 graph

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Fig. 3

The moving modes of inner edge e13 corresponding to MS = 1, 0 and 1, respectively

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Fig. 4

The layouts corresponding to (a) MSS = (−1, 1, 0, 0), (b) MSS = (0, 0, 1, 1), (c) MSS = (0, 0, 1, 1), (d) MSS = (0, 0, 1, 1), (e) MSS = (1, 1, 0, 0), (f) MSS = (1, 1, 0, 0), (g) MSS = (−1, 1, 0, 0), and (h) MSS = (0, 0, 1, 1)

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Fig. 7

The feasible layouts for Graph Two corresponding to Figs. 4(a)4(f)

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Fig. 5

The flow chart of the layout algorithms

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Fig. 6

The layout acquired by moving e13 and e25 simultaneously

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Fig. 8

The process of locating vertices on the topological graph

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Fig. 9

The automatic sketching of an excerpt of planar topological graphs with (a) 14-link 3DOF, (b) 12-link 1DOF, (c) 13-link 2DOF, (d) 18-link 7DOF, and (e) 19-link 8DOF

Grahic Jump Location
Fig. 10

(a) Layout for MSS = (0, 0, 0, 1, 0), (b) layout for MSS = (0, 0, 0, 1, 0), (c) 14-link 1DOF topological graphs, (d) 15-link 2DOF topological graphs, and (e) 19-link 6DOF topological graphs

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Fig. 11

The kinematic chains corresponding to the topological graphs in Fig. 9(b)

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