Research Papers

Derivation of Topological Graphs of Some Planar 4DOF Redundant Closed Mechanisms by Contracted Graphs and Arrays

[+] 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, Hebei 066004, P.R. Chinadl197139@yahoo.com.cn

Shuyan Li

 CERI Yingkou Equipment Development and Manufacturing Co., Ltd., Yingkou, Liaoning 115004, P.R. Chinalishuyan@ceri.com.cn

Jianping Yu

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

J. Mechanisms Robotics 2(3), 031011 (Jul 23, 2010) (9 pages) doi:10.1115/1.4001735 History: Received April 19, 2009; Revised February 03, 2010; Published July 23, 2010; Online July 23, 2010

Some planar redundantly closed mechanisms (RCMs) have better dexterity, less singular configuration, and higher stiffness. In this paper, the derivation of valid topology graphs (TGs) of some planar four degrees of freedom (4DOF) RCMs is studied based on the contracted graph (CG), arrays, and topology graph with digits (DTG). First, some CGs without any binary links are constructed for the planar 4DOF RCMs, some curves with only binary links are distributed over CGs, and some valid TGs of the planar 4DOF RCMs are derived. Second, a complicated derivation of TG is transformed into an easy derivation of array and DTG, and some programs are compiled in VISUAL BASIC ; all valid arrays corresponding to nonisomorphic TGs are derived, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined and removed by the compiled programs. Third, many valid TGs of the planar 4DOF RCMs with various basic links are derived from valid arrays and DTGs. Finally, some application examples are illustrated.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

(a) A CG with 2Ts, (b) a DTG with 2T+7B represented by digits, and (c) a TG with 2T+7B and 10Js

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Figure 2

Some CGs and valid DTGs versus ALs 1–4 in Table 1

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Figure 3

CGs I and II with 4Ts versus AL 5 in Table 1

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Figure 4

The 28 valid DTGs versus the 28 valid arrays and two isomorphic TG 2 versus DTG 2 and TG 29 versus DTG 29

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Figure 5

The 39 valid DTGs versus the 39 valid arrays

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Figure 6

(a) A CG with Q+2T versus AL 6; (b) a CGs with Pe+3T versus AL 8 in Table 1

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Figure 7

The 46 valid DTGs versus the 46 valid arrays in Table 5

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Figure 8

Four different CGs with 2Q+2T versus AL 7 in Table 1

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Figure 9

(a) The 115 valid DTGs versus the 115 valid arrays in Table 6; (b) the 237 valid DTGs versus the 237 valid arrays in Table 7

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Figure 10

All valid TGs versus all valid DTGs in Figs.  4579

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Figure 11

Two planar 4DOF RCMs and their two DTGs and TGs

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Figure 12

Two planar 4DOF redundant parallel machine tools and their DTGs and TGs




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