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Research Papers

Autoderivation of Topological Graphs for Type Synthesis of Planar 3DOF Parallel Mechanisms

[+] Author and Article Information
Yi Lu

College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinaluyi@ysu.edu.cn

Ling Ding

College of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinadl197139@yahoo.com.cn

Jianping Yu

College of Foreign Studies, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinayjp@ysu.edu.cn

J. Mechanisms Robotics 2(1), 011002 (Nov 12, 2009) (8 pages) doi:10.1115/1.4000521 History: Received December 10, 2008; Revised July 23, 2009; Published November 12, 2009

The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.

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References

Figures

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Figure 1

Some TEGs and valid TGs versus valid linkages 1–4 in Table 1

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Figure 2

Two different TEGs I and II with 4T versus valid linkage 5 in Table 1

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Figure 3

20 different TGs with 4T and 6B versus 20 different arrays in Table 2

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Figure 4

24 valid TGs versus the 24 valid arrays in Table 3

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Figure 5

(a) A TEG with 2T and 1Q versus valid linkage 6; (b) a TEG with 2T and 2Q versus valid linkage 7

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Figure 6

25 valid TGs versus the 25 valid arrays in Table 4

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Figure 7

54 valid TGs versus 54 valid arrays in Table 5

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Figure 8

A TEG with 3T and 1Pe

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Figure 9

Some valid TGs with 3T, 1Pe, and 8B

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Figure 12

A flow diagram of the subprogram for judging whether two arrays are the same

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Figure 11

A flow diagram of the program for identifying isomorphism

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Figure 10

Flow diagram of program for finding all arrays

Tables

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