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Research Papers

On the Correctness and Strictness of the Position and Orientation Characteristic Equation for Topological Structure Design of Robot Mechanisms

[+] Author and Article Information
Ting-Li Yang

Changzhou University,
Changzhou 213016, PRC;
SINOPIC Jinling Petrochemical Corp.,
Nanjing 210042, PRC
e-mail: yangtl@126.com

An-Xin Liu

PLA University of Science and Technology,
Nanjing 210007, PRC
e-mail: liuanxinn@163.com

Hui-Ping Shen

Changzhou University,
Changzhou 213016, PRC
e-mail: shp65@126.com

Yu-Feng Luo

Nanchang University,
Nanchang 330029, PRC
e-mail: yfluo@ncu.edu.cn

Lu-Bin Hang

Shanghai University of Engineering Science,
Shanghai 201620, PRC
e-mail: hanglb@126.com

Zhi-Xin Shi

Nanchang University,
Nanchang 330029, PRC
e-mail: shizhixin@ncu.edu.cn

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received June 19, 2010; final manuscript received February 14, 2013; published online April 23, 2013. Assoc. Editor: Delun Wang.

J. Mechanisms Robotics 5(2), 021009 (Apr 23, 2013) (18 pages) Paper No: JMR-10-1080; doi: 10.1115/1.4023871 History: Received June 19, 2010; Revised February 14, 2013

Position and orientation characteristic (POC) equations for topological structure synthesis of serial and parallel mechanisms were proposed in a published paper by the authors. This paper will further prove the correctness and strictness of the theoretical foundation for POC equations and also be a reply to the reviewers of our follow-up papers. The main contents of this paper include: symbolic representation of mechanism topological structure and its invariance, velocity characteristic (VC) set and POC set of link and its invariance, one-to-one correspondence between elements of the VC set and POC set, POC equations for the serial mechanism and 10 corresponding “union” operation rules, and POC equations for the parallel mechanism and 14 corresponding “intersection” operation rules. In addition, the interrelations and differences among three methods (POC set based method, screw theory based method, and displacement subgroup based method) for mechanism topological structure design are concluded.

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Figures

Grahic Jump Location
Fig. 1

Six basic dimension constraint types

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Fig. 3

A planar parallel mechanism

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Fig. 4

Output velocity of P pair

Grahic Jump Location
Fig. 5

Output velocity of R pair

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Fig. 7

A planar serial mechanism

Grahic Jump Location
Fig. 6

Output velocity of H pair

Grahic Jump Location
Fig. 8

Velocity analysis of serial mechanism

Grahic Jump Location
Fig. 9

SOC{-R∥R∥R-} and its equivalent types: (a) SOC{-R∥R∥R-}, (b) SOC{-R∥R⊥P-}, and (c) SOC{-P⊥R⊥P-}

Grahic Jump Location
Fig. 11

SOC{-R1(⊥P2)∥R3-R4R5︷-}

Grahic Jump Location
Fig. 12

Four SOCi{-Ri1(⊥Pi2)∥Ri3-Ri4Ri5︷-} PM

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Fig. 13

A parallel mechanism with two branches

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