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Research Papers

Assur-Group Inferred Structural Synthesis for Planar Mechanisms

[+] Author and Article Information
Shujun Li

College of Mechanical Engineering
and Automation,
Northeastern University,
Shenyang 110004, China
State Key Laboratory of Robotics,
Shenyang Institute of Automation,
Chinese Academy of Sciences,
Shenyang 110016, China
e-mail: shjunli@mail.neu.edu.cn

Hongguang Wang

State Key Laboratory of Robotics,
Shenyang Institute of Automation,
Chinese Academy of Sciences,
Shenyang 110016, China
e-mail: hgwang@sia.cn

Jian S. Dai

Center for Advanced Mechanisms
and Robotics,
MOE Key Laboratory for Mechanism Theory
and Equipment Design,
Tianjin University,
Tianjin 300072, China
Center for Robotics Research,
King's College,
University of London,
Strand, London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Manuscript received April 5, 2013; final manuscript received November 5, 2014; published online March 11, 2015. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 7(4), 041001 (Nov 01, 2015) (9 pages) Paper No: JMR-13-1061; doi: 10.1115/1.4029116 History: Received April 05, 2013; Revised November 05, 2014; Online March 11, 2015

In order to obtain a comprehensive list of possible mechanisms with various choices of both R and P pairs and mechanism inversion of planar mechanisms, a new structural synthesis method is developed by integrating Assur groups (AGs) as elements in the newly developed group-based adjacency matrix. This extended adjacency matrix is proposed with the diagonal elements representing three fundamental elements as the frame link, driving link, AG and augmented AG (AAG) if metamorphic mechanisms are to be synthesized. The off-diagonal elements provide information on group combination and connection forms of the above three fundamental elements and that on the associated kinematic pairs. Based on the extended adjacency matrix, all assembly modes for the given AGs can be established and isomorphism mechanisms can be identified at the same time. Considering all types of the AGs in the extended adjacency matrix, group permutation and combination are used and connection forms are generated including variation of the driving link and mechanism inversion. The structural synthesis is then extending to generating a comprehensive list of types of mechanisms and illustrated by the synthesis for class II 6-bar planar mechanisms with both R and P pairs, generating a list of 588 types of mechanisms that are derived for the first time. The paper further applies the approach to metamorphic mechanisms, and obtained five connection forms of the 7-bar 2DOF metamorphic mechanisms.

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Topics: Linkages
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References

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Figures

Grahic Jump Location
Fig. 6

Notation for the driving link and frame link

Grahic Jump Location
Fig. 5

Classes III and IV AAG in which all the joints are R pairs

Grahic Jump Location
Fig. 4

notation of the linkages for class II AAG

Grahic Jump Location
Fig. 3

Classes III and IV AG in which all the joints are R pairs

Grahic Jump Location
Fig. 2

Notation of linkages for class II AG

Grahic Jump Location
Fig. 1

Notations of nodes for pairs and links in the AG

Grahic Jump Location
Fig. 7

One 1DOF 6-bar mechanism

Grahic Jump Location
Fig. 8

Notation for the links and the joints of the mechanism shown in Fig. 7

Grahic Jump Location
Fig. 9

A 2DOF metamorphic mechanism

Grahic Jump Location
Fig. 10

Notation for the linkages and the joints for the disassembled mechanism

Grahic Jump Location
Fig. 12

Six types of connection forms of the planar 2DOF 5-bar or 7-bar metamorphic mechanisms

Grahic Jump Location
Fig. 11

Eight connection forms of 1DOF 6-bar planar mechanisms

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